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VIII Milan European Economic Workshop, June 11th - 12th 2009 Università degli Studi di Milano

EIBURS project, European Investment Bank

PPP FINANCING IN THE ROAD SECTOR: A DISEQUILIBRIUM ANALYSIS

BASED ON THE MONETARY CIRCUIT

MASSIMO CINGOLANI

Working Paper n. 2010-09

APRILE 2010

JEAN MONNET CHAIR

Economics of European Integration

PPP Financing in The Road Sector: A Disequilibrium Analysis Based on The Monetary Circuit M. Cingolani European Investment Bank – 100 Bd Konrad Adenauer - Luxembourg 21 February 2010 JEL codes: D60 - Welfare Economics: General E600 - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook: General L920 - Railroads and Other Surface Transportation Keywords: Public Private Partnerships; Monetary circuit; Roads

Abstract

This contribution discusses public and private financing of infrastructure acknowledging the fact that a larger set of monetary equilibria than the neoclassical barter equilibrium can prevail in the economy. In this context money is not neutral and financing has an impact on allocation. Welfare comparison should be done between two positions that remain suboptimal before and after the realization of a project rather than between a suboptimal reality and an ideal optimum, as it is usually implied in many policy discussions. A systematic welfare comparison between private and public financing of infrastructure under these assumptions reveals that, contrary to a widely held view, there are very few rational arguments that may lead to prefer private financing to public financing of road infrastructure, particularly where local incomes are low. The argument is developed in terms of “disequilibrium”, a term used to cover all situations where any of the optimality conditions that define neoclassical equilibrium is not fulfilled. These situations are of interest for economic policy, because a real economy is likely to be always in such positions. Post Keynesian analysis in general (Eichner and Kregel, 1975), and its monetary variant of the circuit, as developed notably by Parguez and Graziani (Halevi and Taouil, 2002), are seen as useful tools for the analysis of public investment policies in such a disequilibrium context (Cingolani, 2009). In particular, some features of the monetary circuit approach are well suited to address the economic problems raised by the analysis of Public Private Partnerships (PPP), notably: a) the full integration of the banking sector and the recognition of its role in monetary creation by the private sector; b) the monetary creation by the State within a macroeconomic framework fully integrating public finance; and, c) the necessary link between uncertainty and disequilibrium, which, in such a monetary context, clarifies the Keynesian causality from investment to savings. Against this macroeconomic background, a partial equilibrium analysis based on realistic microeconomic configurations of costs and transport demand parameters, shows that, contrary to the widespread idea that PPP help removing existing constraints on public expenditures, they do not add anything to the level of effective demand, being in fact the other flip of the coin of restrictive budgetary policies. PPP thus play essentially a role in mobilising part of the passively accumulated savings that the State is forbidden to attract directly because of debt ceilings. They have a softening effect on the Government debt constraints similar to that that could be reached if the Government was allowed to accrue investment like the private sector, but are a less transparent solution, because the relevant debt is not necessarily recognized in the balance sheet that services it.

PPP Financing in The Road Sector: A Disequilibrium Analysis Based on The Monetary Circuit(*) M. Cingolani European Investment Bank 100 Bd Konrad Adenauer - Luxembourg 21 February 2010 1. Introduction This contribution discusses the implications of Public Private Partnerships (PPP) for the distribution of revenues and for employment based on a “disequilibrium” approach, where monetary equilibria allow for these variables to diverge from the level they would reach in a neoclassical barter equilibrium. Against this background, it is natural to look at the comparison between private and public financing in the provision of road infrastructure in terms of the likely size of this divergence. The post Keynesian approach in general (Eichner and Kregel, 1975), and its monetary variant of the circuit, as developed notably by Parguez (1975, 1996, 2001) and Graziani (2003), can be used for the analysis of public investment policies in such disequilibrium context (Cingolani, 2009, pp. 6-15). In particular, the analysis of the monetary circuit is well suited to examine Public Private Partnerships (PPP), because it integrates the banking sector, the State sector, and the private sector, disaggregated into consumers (or users) and producers. Moreover, the circuit definition of money allows to discuss PPP in situations that under neo-classical modeling would be qualified as disequilibria, for instance where marginal distribution relations do not hold (factor prices are different from marginal productivities in real terms), and hence profits are different from zero, or when the productive capacity and/or the labour force are not fully employed1. To discuss the effects of public and private provision of infrastructure it is indeed necessary to have a model with at least the two sectors distinguished. Furthermore, the case of real tolls cannot be analysed separately from that of the shadow tolls and availability payments if the private sector is not further subdivided between enterprises and households and is distinguished from the State sector. Finally, to examine issues relating to financing, it is necessary also to break down enterprises between non-financial (corporates) and financial (banks) and introduce money, distinguishing between money creation by the State and money creation by the commercial banking sector. The model of the monetary circuit is built around the above mentioned distinctions. Money is defined as a liability issued by a third party (banking sector and/or State) that is used by the other parties (producers and consumers) as a mean of payment. Hence the model requires from the very start to have at least three sectors distinguished: producers, consumers and banks2. The working of the circuit can be illustrated fully with these three sectors without introducing the State, demonstrating that a monetary economy can exist based only on privately issued money (inside money).3 Although this three sectors framework was introduced by Wicksell in his model of the pure credit economy, usually neo-classical and neo-Keynesian authors neglect money creation by the private banking sector and assume instead that all money is a liability issued by the State (outside money). The

* Revised version of a paper presented at the VIII Milan European Economic Workshop, June 11-12, University of Milano in the framework of the EIBURS project, sponsored by the European Investment Bank. Views expressed are personal. The author is grateful for comments received from Michel Deleau, Massimo Florio, Alain Parguez, Malcolm Sawyer, Mateu Turró and Christian Zellner, as well as participants to the workshops “Vth Conference on Applied Infrastructure Research”. Berlin 6-7 October 2006 and “Highways: cost and regulation in Europe”, Bergamo November 26-27, 2004. The usual disclaimer applies. 1 If the economy to be represented behaves as a fully dynamic model in historical time, it would always be in “disequilibrium” in such sense. 2 Banks are usually neglected in the neoclassical model, and do not play any significant role in the realisation of its equilibrium. 3 An introductory illustration of the pure credit economy is provided in Cingolani (2009, section 5.1). This is complemented below in 3.2 that integrates the State.

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analysis of the circuit can integrate outside money once the State is added as a separate sector in the circuit. In this broader version, the circuit admits both outside money, created by the State, and inside money, created by the private commercial banking sector, a distinction that is relevant for instance in the choice between loan and grant financing. This is also true for the analysis of PPP financing in EU12 (“New Member States”) as well as candidate and pre-accession countries, where significant investment is to be realized to upgrade the transport and other networks, but where stringent budgetary constraint do not allow to finance this investment by current surpluses before interest or by new debt, despite the availability of EU grants. Section 2 presents the general conceptual framework, focusing on Kalecki’s identity, which is useful to discuss the distribution of the surplus produced by the economy, and with the help of a small macroeconomic model of the monetary circuit that integrates public finance, which illustrates the emergence of equilibrium unemployment in a monetary economy. Section 3 further develops the analysis of PPP through an accounting model of the circuit that illustrates the effects of various combinations of private, public and mixed financing under different forms of PPP. This discussion underlines the causal role played by the exogenous expectations of producers in determining the level of effective demand and the corresponding equilibria of the circuit. Section 4 discusses the microeconomic factors likely to shape the formation of these expectations and discusses their welfare implications in terms of a breakdown of the monetary demand projection in its price and volume components. Section 5 draws the conclusions of the analysis. 2. The conceptual framework In a fully dynamic model4, different decisions are taken in historical time5 and determine the net monetary claims and liabilities that are accumulated by each sector6 or economic agent present in the economy. These observed balances reflect the “ex post” equality between investment and savings and their analysis is relevant for the welfare judgments to be given on PPP. The Kalecki identity presented in section 2.1 offers a synthetic view of these net claims and liabilities. A distinctive feature of post Keynesian analysis is that this identity, which holds in any particular moment of time, has a causal interpretation, with investment determining savings. This causality can be rationalized in a sequential model of the monetary circuit, where the decision taken by producers at the beginning of the period, which concerns both the volume and the price of output, creates the revenues whose distribution determines effective demand. In this model it is clear that there is no guarantee that the level of effective demand generated will be the full employment one. A macroeconomic model illustrating this aspect is presented in section 2.2. 2.1 The Kalecki identity: In disequilibrium, as defined above, a wide variety of situations can arise that can be seen as “generalisations” of the neo-classical equilibrium. Different analytical frameworks can be used to study these cases, but the Kalecki identity is a particularly useful one as it always holds, including in the case where a neoclassical equilibrium prevails7. If technology is given, as one can assume it is the case in the context of PPP financing of road infrastructure, the neo-classical equilibrium can be kept as a normative reference for the welfare analysis of the effect of a public

4 Davidson (2007-2009, pp. 31-35 and 184-185) argues that one of the main differences between post Keynesian and neoclassical analysis is the rejection of the ergodicity axiom by the former, which explains why, even if prices are fully flexible, unemployment equilibria can be persistent over time. A model where the axiom of ergodicity does not hold, i.e. where uncertainty applies as opposed to risk, can be considered as fully dynamic. It is the stochastic counterpart of a deterministic historical model, which could also be considered truly dynamic. 5 Davidson (2009, p. 3) observed ironically that “Time is a device for preventing everything from happening at once”. 6 The word sector is used in the National Income Accounts meaning of “Institutional Sector”. 7 The essential terms of this identity are spelled out in Kalecki (1991a [1929] pp. 15-16), as well as in Kalecki (1991b, [1944], p. 152) and Kalecki (1991b [1954] p. 239). Steindl (1982, p. 71) refers also to its descent from Kahn (1972 [1931]).

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investment (Cingolani, 2009). Therefore, it makes sense to look at the Kalecki identity in terms of deviations of profits from their neo-classical equilibrium value, deviations that can be due to monopolistic pricing and/or other departures from the full employment conditions, as discussed below and further in section 4. One can start from the version of the Kalecki identity used by Steindl (1982). It states that business net profits, equal to the difference between entreprises gross savings and investment SE − I( ), the Government surplus T − G( ), the balance of payments current account deficit M − X( ) and the net savings of households, equal to gross savings less residential investment SH − H( ), must balance each other out. This relation, can be studied empirically, as it represent the link between real national economic accounts and financial or flow of funds accounts. It shows immediately that, from the macroeconomic point of view, business profits increase with Government deficits, balance of payments current account surpluses and households’ indebtedness. 8

SE − I( ) + T −G( ) + M − X( ) + SH −H( ) = 0 (1)

Seen from a disequilibrium viewpoint, the causality in this identity goes from the autonomous decisions on expenditure of the four sectors concerning business investment I, Government expenditures G, foreign demand for domestic exports X and households’ residential investment H, which are the “causal factors”, to gross business savings SB, taxes T, imports M and households’ savings SH, which are caused by the formers. In order words, the causality goes from investment to savings9. The monetary circuit illustrates this post Keynesian causality of investment on savings defining money as part of the production process that takes place in sequential time. Money pre-finances production before any output is completed (initial finance). The decisions on the level of output is taken by producers and validated by the credits granted by the banking sector. It create the revenues (salaries and profits) that are used to pay for the output, once it is produced. Revenues that are not saved by households are immediately recovered by enterprises through sales, whereas the part that is not saved in liquid form can be recovered by issuing bonds sold to savers (final finance). All liquidity recovered through sales and bond issues is used by enterprises to repay the initial loans granted by the banking sector, generating a destruction of money and closing provisionally the circuit. To the extent that enterprises do not recover all money initially put in circulation because savers keep liquid holdings, which is the normal case, they remain necessarily indebted towards the other sectors and in particular towards banks. Since there is no equilibrium level of this debt, which depends inter alia on the liquidity preference of households as influenced by their perception of uncertainty, and on banks willingness to endorse firms’ decisions, there is no specific solution of the model that emerges as a prominent equilibrium concept in the circuit10. In an uncertain environment, the initial decisions of enterprises on the level of output based on their expectations are thus to be seen as bets that require to be validated by the banking sector to

8 To simplify, in relation (1) the banking sector profits have been incorporated into the business sector. Breaking down the business sector profits, the identity can be written as: SNFE − I( ) + PFI + T − G( ) + M − X( ) + SH − H( ) = 0 , where SNFE − I( ) represents the net profits of the non financial enterprises sector (firms) and PFI represents the net profits of the financial intermediaries (banks). This shows that, for a given level of output, the higher are the banking profits the lower will the corporate profits be. In recent years, the share of profits of banks in total private sector business profits has increased disproportionably, with the portion of banking profits coming from the non-interest margin component (“capital gains”) being by far the fastest growing component. For the US: “The share of corporate profits generated in the financial sector rose from 10% in the early 1980s to 40% in 2006, while its share of the stock market’s value grew from 6% to 23%. (Crotty, 2009, pp. 575-576). 9 Within each parenthesis, from the right to the left. 10 Particularly not the neo-classical one, characterised by the usual intertemporal budget constraint, which becomes irrelevant out of perfect foresight (or out of the analytically equivalent risk situations with rational expectations and no uncertainty).

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become effective11. These bets are exogenous causal factors that drive the dynamic of the model12. When they are successful, they represent a real wealth creation, otherwise they feed inflation and other imbalances (Schmitt, 1984)13. 2.2 A simple macroeconomic model integrating the public sector: It follows from relation (1), that when the State is present, the model of the circuit allows in principle for two ways of financing an investment:

i) through the mobilization of savings accumulated from past investments, a case further discussed in paragraph 2.2.1;

ii) through the creation of new real savings by the investment itself as a consequence of a winning bet of the public or of the private sector14, as discussed in paragraph 2.2.2.

The advantages and disadvantages of financing a road investment programme through PPP should be looked at in the light of these two above alternatives. As argued further in sections 3 and 4, when public infrastructure provision is linked to the amount of savings that the private sector is ready to create or mobilize for such purpose, as it is done for toll PPP, or to the amount of previously accumulated savings, as it is obtained de facto by the combination of PPP in general (whether real or shadow toll or availability payments)15 with budgetary constraints on investment, the State creates much less investment demand than what it could possibly do by creating directly the money that is necessary for financing all “feasible” investment. 2.2.1 Mobilization of savings from past investments: With some small adaptations, the above alternatives can be illustrated in more detail with the help of a two sector model developed by Graziani (1985 and 2003, ch. 5, pp. 100-110) for the analysis of public expenditure in the circuit, as done in this paragraph for case i) above. 2.2.1.1 The case of a transfer (PPP with shadow tolls): The case where a public expenditure finances a transfer to producers linked to the use of the infrastructure can be assimilated to the case of a PPP with shadow tolls. As discussed below in sections 3.4 to 3.6, with a shadow toll the State transfers a grant to the private sector based on a certain level of traffic, in order to compensate for a shortfall between users willingness to pay and what is the cost estimated ex ante for the provision of infrastructure of a certain capacity that has to be provided by the private sector. Since they are linked to traffic, shadow tolls are ultimately a function of the revenue of the users and can thus be analysed as a State transfer proportional to households’ revenues. Graziani (1985) examined this case retaining the simplifying assumption that the transfer is financed by a government deficit covered by new public debt sold to the Central Bank, and thus by creation of new State money16. In the following, the subscripts c and I refer to the consumption and the investment sector respectively and, for the rest, the following symbols apply:

11 For the question of government financing, the version of the circuit developed by Parguez (1975 and 1996) and Graziani (2003) in the tradition of Kalecki (see Halevi and Taouil, 2002), appears as more relevant and is referred to and used here. The version of the circuit due to Schmitt (1966 and 1984) has several original features that make it interesting in abstract, but it is more difficult to practical economic policy issues, except for the exchange rate questions related to the opening of the circuit to external trade, cf. Cingolani (2010). 12 Davidson (1982-3) explained why, in the face of “fundamental uncertainty” as opposed to the case of “risk”, expectations must necessarily be exogenous to the model, contrary to the requirement of endogenous expectations expressed by Lucas(1980). The subprime crisis, started in August 2007, confirmed that we leave in a non-ergotic world, since all official forecasts done in the spring were projecting “vigorous growth” for the following semesters. For a diagnosis and therapy of the crisis from a non-ergotic perspective, see Davidson (2007-2009, pp. 190-202). 13 Schmitt discussed the potentially inflationary consequences of depreciation, but the argument can be extended to any “wrong bet”. 14 Liquidity created as a consequence of a wrong or loosing bet creates inflation and/or financial imbalances (see 3.1.4). 15 In a pure toll PPP all investment is paid by the private sector based on revenue expected to be recovered from tolls paid by the users during the life of the infrastructure. In PPP with pure shadow tolls or availability payments the investment is paid by the State. In a shadow toll, the “average” toll is defined at the beginning of the concession contract at a level depending upon future traffic. Availability payments cover the case where the state pays contributions for the availability of the infrastructure to the concessionaire independently from traffic. With a toll or a shadow PPP, the concessionaire takes traffic risk, whereas this is not the case with availability payments. 16 To simplify, all State debt thus created is hold by the Central Bank and households only hold private debt, an assumption that can be removed without changing the conclusions of the argument.

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Nc , NI , N Number of employees in the consumption, c, s Propensity to consume and to saveand investment sectors, total w Wage rate

πc , πI Labour productivity in both sectors b Percentage of workers workingpc , pI Monetary prices in both sectors in the capital goods sectorPc , PI ,P ,PN ,PR Profits in both sectors,total profits, net and real Bc ,BI ,B Stock of private debt placed in C Total consumption in real terms each sector and totalIc , II Real investment in both sectors BG Stock of public debtKc , KI Capital stock in both sectors i interest rate paid on debt hold by householdsa Proportionality coefficient between iBK interest rate paid on debt hold by banks

capital (debt) and labour G public expenditure in money termsg Proportionality coefficient between YW Revenue of workers

public expenditure and the wage bill Y Total revenuet Tax rate L(i) Fraction of current income kept liquidLF Labour Force E EmploymentU Unemployment TR Public transfer

Graziani also assumed that the budget deficit does not influence the decisions of producers on the level of output and employment to be provided, which implies either that the transfer is limited in size17 or that the corresponding State deficit is already known and integrated in the output decisions of producers,18. Productivity is assumed to be constant and thus technology is given. Monetary revenues are defined by the following identities:

YW = wN + iB (2) G =TR + iBG = g wN + iB( ) (3)

Y = 1+ g( ) wN + iB( )= 1+ g( ) w + ia( )N (4) Y = π cNc + π INI (5)NINc

=IIIc

=b

1− b(6)

BIBc

=IIIc

=b

1− b(7)

B = aN; BI = aNI ; Bc = aNc (8) L = L i( ) wN + iB( ) (9)

LF = h + ib, i > 0 (10) E = j + kb, 0 < i < k . (11)

Relation (2) defines the monetary revenue of households before public transfers YW, which is given by the sum of the wage bill wN and the interest revenue perceived on private debt hold by households iB. The first part of relation (3) reflects the fact that public expenditure is entirely used to finance a transfer TR to households and to pay interest iBG to the central bank on the public debt it holds. Since the transfer is proportional to revenues, public expenditure can also be expressed as a fraction g of private disposable income before transfer YW, as expressed by the second equality in this relation. Hence total income Y will be given by relation (4), where use is also made of the first of relations (8).19 Relation (5) defines output with a linear production function in a labour economy. Relations (6) and (7) derive from the assumption of a constant productivity, which implies that all investment is in capacity expansion and will be distributed proportionally between the two sectors. The model can thus be seen as depicting a steady state where the proportion of workers employed in the two sectors remains constant at b/(1-b). This proportion applies also to the ratio between investment in the two sectors and, if private debt is issued proportionally to the increase in the capital stock as in the first of relations (8), it also applies to the ratio between the stock of debts in the two sectors. Hence, as indicated by (8), in this model private debt is proportional to employment in each 17 If the shadow toll covers only a fraction of the total cost, then the rest is financed by a real toll paid by users, which, as discussed below, is also financed by pre-existing savings. 18 As it is the case when budgetary ceilings are put on public expenditure and/or deficit. This case would correspond to an “unwanted” (or one could also say passive) deficit in the terminology of Parguez (2009, p. 13): “Decreasing growth imposed unwanted government deficits which had not the least positive impact on expectations; herein lies the perfect example of what must be deemed ‘bad deficits’.” These passive deficits contrast with Parguez’s proposal of “planned” deficits (p. 3): “The Agenda is rooted into a long-run planned deficits commitment of which the counterpart is the planned growth of public investments creating tangible and non tangible real wealth”. 19 Implicitly the model assumes that the transfer is paid to households, but relation (3) and, in real terms, relation (4), as well as the conclusions of the model, hold also if the transfer is paid to producers.

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sector. Retaining the assumption of a deficit financed by money creation, in a closed economy the bank debt of firms equals the liquid balances of savers. Relation (9) assumes that these liquid balances are a fraction L(i) of current income, fraction that can be assumed to depend on the rate of interest. Finally relations (10-11) define a small reduced form of the labour market, expressed as a linear function of the investment rate b20. In this reduced form, the labour force is supposed to respond positively to the level of activity as it is the case for employment, but with a lower coefficient. Under the assumptions retained, from the conditions for balancing supply and demand in the two sectors, it is possible to derive the following pricing relations:

pc = 1+ g( ) 1− s1− b

w + iaπ c

(12) pI = 1+ g( ) 1− s1− b

w + iaπ I

(13)

Since enterprises do not have other costs than wages and interest paid to savers, the term (w+ia)/π in (12) and (13) represents unit costs, whereas the term (1+g)(1-s)/(1-b) represents the mark-up. These relations show that the level of prices depends directly from the propensity to save s and from the propensity to invest b. The fact that in this model these propensities can be different reflects the Kaleckian hypothesis that, under pure competitive conditions, real investment is financed by real profits Kalecki (1991[1942]). The latter are generated by the mark-up on wage costs that is defined in the pricing decision of firms that takes place at the beginning of the circuit. The mark-up reflects the peculiar “disequilibrium” nature of the model of the circuit. In a neo-classical model the equality between b and s would always hold because the financial market would be cleared by the interest rate at any moment in time, implying a null-mark-up in the absence of Government expenditure. In the circuit since money is endogenous, interest rates are exogenous (Parguez, 2001). Therefore, whereas in neo-keynesian models that do not retain the distribution assumptions of Kalecki, changes in the propensity to consume (c=1-s) or in the propensity to invest b influence prices only indirectly through changes in employment beyond full employment, in the circuit both propensities can affect the level of prices whether there is unemployment or not. It is clear in (12) and (13) that the level of prices does not depend directly from the quantity of money BG created, nor from the level of employment N, but that it depends directly from the level of public expenditures g. Hence, once a certain level of public expenditure is decided, if the deficit is financed by issuing bonds sold to the public, the latter will hold a greater stock of debt, whereas in the contrary case the public will hold higher liquid balances, but in both cases the price level will be the same. In this model it is thus irrelevant for inflation if the deficit is financed through money creation or by placement of bonds to the public. Price mark-up equations such as (12) and (13) are a key feature of the version of the monetary circuit developed by Graziani and Parguez. As indicated, this version derives from Kalecki and is thus consistent with the large stream of post-Keynesian analysis that refers to this author (Halevi and Taouil, 2002). It is noteworthy that these “production prices” are in fact expected prices, being defined at the beginning of the production process before exchange takes place. They thus include notably a component of expected profits. As discussed in section 4, this component can or cannot include a monopolistic element, which is however not included in the model of Graziani discussed here, where the mark-up only finances real investment. 21 From the price equations it is possible to derive the level of nominal and net profits after payment of interest, as done respectively in relations (14-15) and (16-18), as well as real net profits (19):

20 In line with Kalecki distribution theory, in the model the level of activity is driven by investment expenditure. 21 However the monetary circuit can integrate also an element of speculative investment, which is of help when trying to understand the recent financial crisis. Whether or not this element is included, the possibility of a monetary realization of profits at the stage of initial finance provides an interpration of Kalecki’s theory of profits that solves many historical debates in the history of economic doctrines, including Say’s law and its Sismondian and Malthusian critiques (Renaud, 2000). See also discussion in par. 3.1.2.

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Relations (14) and (15) show that the level of profits increases with the increases in prices provoked by public expenditures through g, however real profits are unchanged (gross or net), as profits increase by the same amount as prices (1+g), and therefore public expenditure generates a redistribution inside the group of wage earners in favour of those who get the subsidies and against those who don’t.

Pc = 1+ g( )b − s1− b

w + ia( )Nc (14) PI = 1+ g( )b − s1− b

w + ia( )NI (15)

P = 1+ g( )b − s1− b

w + ia( )N (16) Pn = 1+ g( )b − s1− b

− iBKL i( )⎡ ⎣ ⎢

⎤ ⎦ ⎥ w + ia( )N (18)

PR =PNpI

=b − s1− b

−iBKL i( )

1+ g( ) 1− s( ) 1− b( )⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥ π IN (19)

Relations (18) and (19) show that on the contrary the interest paid by enterprises to banks iBK subtracts to monetary profits and real profits22. An increase in public expenditure which increases prices thus provokes a redistribution from banks to enterprises because it decreases the real cost of bank debt. 2.2.1.2 The case of purchases of public goods and services (PPP with availability payments): The case where public expenditure finances purchases of goods and services can be assimilated to the case of a PPP with availability payments. As discussed below in sections 3.4 to 3.6, with availability payments the State pays the private sector based on certain technical specifications, in order to cover the full cost estimated ex ante for the provision of an infrastructure of a certain capacity23. Graziani (1985) studied the question of a purchase of goods and services by the State, retaining the simplifying assumptions that public expenditure is fully financed by a uniform tax on wages and profits at the rate t. Since by definition the State budget is balanced, there is no new public deficit, nor new public debt. Again, it is assumed that public expenditure does not change the decisions of producers on the level of output and employment and the same remark applies as before that this implies that public investment will be financed ex-post by pre-existing savings. As in the previous case, productivity is assumed to be constant and thus technology is given. To simplify further, it is also assumed that enterprises do not issue debt either, so that all household savings are kept entirely in liquid form and lent by banks to enterprises. In this case relation (3) becomes:

G = twN + t πcNc pc + π INI pI −wN( ) (20)

expressing that public expenditures are financed by a uniform tax on all revenues. The pricing mark-up equations become:

pc = 1− s( ) 1− t( )1− b − t

wπ c

(21) pI = 1− s( ) 1− t( )1− b − t

wπ I

(22)

where unit labour cost do not have anymore the term reflecting interest and where the mark-up reflects also the tax rate. The profit relations become:

Pc = 1− t( ) πcNc pc −wNc( ) (23) PI = 1− t( ) π INI pI −wNI( ) (24)

P = 1− t( )b − s + ts1− b − t

wN (25) Pn = 1− t( )b − s + ts1− b − t

− ibkL i( )⎡ ⎣ ⎢

⎤ ⎦ ⎥ wN (26)

PR =PNpI

=b − s + ts1− b − t

−1− b − t

1− t( ) 1− s( )ibkL i( )

⎡

⎣ ⎢

⎤

⎦ ⎥ π IN (27)

22 Which is consistent with the version of the Kalecki identity outlined in footnote 8. 23 In the case of availability payments, in general the full cost of the infrastructure is paid by the State, with very little paid by the user. In the absence of budgetary ceilings on expenditures, this allows maximising the welfare gains from the use of the infrastructure, as originally demonstrated by Dupuit (1849) in his example of the toll for a bridge, reproduced by Allais (1989[1981], pp. 169-173).

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Relation (23-25) show that taxes increase profits because an expenditure which is this case assumed to be entirely spent on goods and services (public consumption) is substituted to an expenditure that only partially goes to consumption, as the propensity to consume of households is lower than 1. As shown by (26) and (27), in real terms taxes are paid by households only, including in net terms. 2.2.2 The case of an autonomous private and public expenditure: Since in the model of the circuit the level of activity is decided by firms based on their demand and price expectations, a priori there is no reason why this level should coincide with full employment. If public or private expenditure is autonomous, as it is the case when it is not limited by the constraint of budgetary ceilings (and/or linked to a level of activity decided autonomously by the private sector in order to cover the full cost through real tolls), it should influence the rate of activity and thus the level of employment and unemployment and this effect should be taken into account in cost benefit analysis relating to the financing of public infrastructure. When the assumption made in the two sections above is dropped that public expenditure does not influence private sector decisions on the level of output, distribution aspects will depend on whether investment is financed by money creation as discussed in section 2.2.1.1, or taxes, as discussed in section 2.2.1.2. Without developing the relevant algebra, it is interesting to look at the potential effects of increased activity on unemployment with the help of relations (10-11) that describe the effect of activity, which in this Kaleckian model is represented by the investment rate, on the labour market, as illustrated in the chart 1 below:

Chart 1: Labor force, employment and unemployment rate

Labour force, employment and unemployment rate

0

10

20

30

40

50

60

70

80

90

100

110

120

15.0% 17.5% 20.0% 22.5% 25.0% 27.5% 30.0% 32.5% 35.0%

Investment rate b

0%

3%

5%

8%

10%

13%

15%

18%

20%

23%

25%

28%

30%

u,

perc

en

tag

e o

f la

bo

ur

forc

e

Unemployment rate (right) Labour force Employment

u =U

E + U→ u =

92 −69.5 + 56−106( )*b92+ 56*b

≈ 0.2273−0.5248* b

With an investment rate of 30% employment is 100 and unemployment 7%. If the investment rate diminishes, so does the profit rate for an assumed fixed saving ratio. Therefore firms lay out workers and unemployment increases, which tends to reduce the labour force and vice versa when the investment rate increases.

LF = 56*b + 92E = 106*b + 69.5

The chart illustrates sensitivity to exogenous bets on the future profitability of investment and links the steady state investment rate to the labour supply, employment and the unemployment rate. The following numerical parameters have been retained:

LF = 56*b + 92E = 106*b + 69.5U = -0.5248*b+0.2273

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As assumed in relation (11), it is logic to link labour employed to investment undertaken by entreprises. Less obviously, but realistically, one can also link labour supply to the level of activity as it is done in relation (10), because the labour force is attracted by more jobs available, but a lower elasticity is retained in this case.

When the steady state investment rate increases, entreprises increase also investment, reducing unemployment. At the same time new people are attracted into the labour force but less than those newly employed, therefore unemployment decreases. With linear relations linking positively labour supply and labour demand to the investment rate as defined above, the unemployment rate is a quasi-linear negative function of the investment rate. This shows that in a model allowing for the emergence of non-walrasian equilibria, the amounts invested can generate macro-economic effects when for instance public expenditure can influence producers decisions on output and employment. 3. Money creation and mobilisation of existing savings in an accounting model of the circuit The model of the monetary circuit developed by Parguez and Graziani (Halevi and Taouil, 2002), of which the previous section presents a version focusing on public finance, views money as a liability created by the banking system in favour of a borrower in exchange for his promise to repay back a loan24 (Parguez and Seccareccia, 2000). This liability is more liquid and generally accepted by the public than the original promise of paying back the loan by the borrower itself, which in general does not circulate and is not accepted by parties external to the original transaction as a liquid mean of payment. The theory of the monetary circuit can be seen as an illustration of a monetary variant of Post Keynesian analysis that retains an essential element of money endogeneity outlined notably in Kaldor and Trevithick (1981) but goes farer than complete horizontalism (Moore, 1988 and 2005), in the direction of a fully exogenous interest rates (Parguez, 2001)25. This section draws on an accounting model of the circuit developed by Wynne Godley and Marc Lavoie (2007) to follow the time sequence of creation and destruction of monetary assets, which leads at the end of the period of the circuit to the accumulation of financial claims and liabilities as well as to net worth increases tracked by the Kalecki identity discussed above. This allows a detailed comparison of different ways of providing finance for an investment in transport infrastructure. The economy is assumed to comprise four sectors: households (H), non-financial entreprises (E), banks (B) and the Government (G).26 The accounting framework used is that of the Godley–Lavoie transition and balance sheet matrices27, which, provide a consistent way to follow how financial claims and liabilities are accumulated in sequential time in terms of both flows and stocks for the four macroeconomic sectors considered28. The analysis starts with the assumption that household do not save (Sh=0 in relation 1 above). In this context there is no capital market and entreprises’ investment is fully financed by private profits, as originally envisaged by Kalecki (1942). This framework corresponds also to the so-called pure credit economy of Wicksell, where the State is absent and the banking sector is consolidated into a single bank29. If one further assumes that interest paid by banks on households deposits is equal to interest 24 Money is a flow and not a stock. 25 The relations between the circuit and Post Keynesian analyses are discussed in detail in Deleplace and Nell (1996), in Lavoie (1992, ch. 4), in Rochon (1999), Chick (2000) and Graziani (2003). 26 Although extremely simplified, the model explicitly recognizes the presence of money and banks, an original feature of the circuit that is normally neglected by more conventional analyses. 27 For a detailed presentation, see Godley and Lavoie (2007, chapter 2). See also Godley (2004), Lavoie (2005) and Lavoie (2003). 28 Cingolani (2009, section 5.1 pp. 19-26) uses the more intuitive “T accounts” for an introduction to the pure credit economy of Wicksell. 29 This avoids the further complication of introducing a central bank. In a single consolidated bank framework, it is immediate to understand why the economy as a whole has unlimited credit possibilities (Graziani, 1990). In the model of the “pure credit economy” introduced by Wicksell, one of the aspects is that the monetary stock (say M1) is only made of “internal money” created by the banking sector since there is no central bank that can produce “external” or “high-powered” money. Cavalieri (1994 and 1996) has criticised the circuit model, identified with its pure credit variant, precisely for its lack of role for external money, considered an essential feature in a realistic

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paid by entreprises on loans, there are no profits in the banking sector either. To further simplify, it can be assumed that this common interest rate on bank’s loans and deposits is zero. Pure private and pure public financing are examined under this set of assumptions in paragraphs 3.1 and 3.2 respectively and are then compared in paragraph 3.3. The cases of mixed financing, respectively without household savings, with household savings but zero interest rate and with positive household savings and positive interest rates, are examined respectively in paragraphs 3.4, 3.5, 3.6. To facilitate the comparison between the five different cases examined presented in par. 3.7, all variables referred to in paragraph 3.1 to 3.6 have a superscript that goes respectively from A to E. 3.1 Full financing by the user (private sector) 3.1.1 Initial finance30: It is assumed that in the initial phase of the monetary circuit, all sectors have an accumulated net worth (KA

h for households, KAe for enterprises, KA

g for the Government and KAb

for the banking sector) corresponding to their net fixed assets. Firms decide on a certain level of effective demand, establishing at the same time the level of the mark-up and the level of output31. They thus turn to the banking sector and take a loan LA

e to advance the payment of wages and to pre-finance investment32. When the loan is granted, firms are credited by banks of the newly created deposits MA

e. This money creation can be taken as the start of the monetary circuit33. In the Godley-Lavoie simplified transaction matrix34 shown in Table 1, the columns represent the sectors, and each column can be subdivided into current (say income related) and capital items (related to the change in stocks).

Table 1: Transaction matrix phase 1, private finance with no households savings H E G B Total Transaction matrix

Phase 1 Current Capital Current Capital Current Capital Current Capital Change in deposits -MA

e MAe 0

Change in loans LAe -LA

e 0 Total 0 0 0 0 0

Each transaction is registered in the matrix with 4 entries, thus for example to the two entries in the entreprise column that correspond to a loan received, correspond other two entries of opposite sign that appear in the banking sector column, corresponding to the loan granted. The advantage of this type of accounting for transaction flows is that all lines and columns must sum to 0, which provides a description of a monetary economy. However, as argued by Graziani (1995 and 1996) in his replies, the pure credit model is only a simplifying device useful to introduce the circuit with endogenous money, but the circuit can accommodate external money as well, as shown notably in Godley and Lavoie (2007, chapter 4) and as further illustrated below. 30 On the concept of “initial finance” and its descent from Keynes, see Graziani (1985a) and Graziani (1987). 31 The determination of this level of effective demand is discussed in section 4. 32 In line with post-Keynesian endogenous money approach and contrary to the loanable funds doctrine, in the monetary circuit deposits are created by the loans granted by the banks, see for instance the historical review carried out in chapter 1 of Graziani (2003). 33 It is sometimes referred to as the “efflux phase”, a term Seccareccia (1996, p. 403) and Parguez and Seccareccia (2000, p. 101) date back to the banking school. Graziani (1985a p. 166 and 2003) argues that money creation occurs only in the next phase of the circuit, when the payment of wages is done, in line with the definition of the circuit by Schmitt. The same position is expressed by Rochon (1999) However, even in a pure credit economy, from a strict accounting point of view balance sheets change at the time when the loan is granted and the bank account of firms is credited with its proceeds. 34 See Godley and Lavoie (2007, chapter 2). The columns of both the balance sheet and transition matrices represent the sectors of the economy. The balance sheet matrix presents in its rows all the entries of assets and liabilities, with the convention that a positive figure represents an asset and a negative figure represents a liability. To move from one balance sheet matrix to the next one in sequential time, all relevant entries are booked in the transition matrix, which has in the rows all the components of income plus all the changes in financial and real assets and liabilities from one period to another that make the link between the two successive balance sheet positions. Together the two sets of matrices allow integrating fully the real national income accounts and the flow of funds. On the latter Lavoie and Godley (2007) refer to Copeland (1949) and Denizet (1969). In fact the transition matrix resembles very much the social accounting matrix, which was developed initially as an extension of the input-output matrix and has now entered fully into national accounting (Eurostat, 1999). In the following only the lines that are not zero are shown for both transaction and balance sheet matrixes. The complete transaction matrix for instance, would have a line for each element of income and for the variation of each line of the balance sheet matrix.

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way to check for possible errors. Uses (increases in assets or reduction in liabilities) are recorded with a negative sign whereas sources (decreases in assets or increases in liabilities) are booked as positive entries. For entreprises, the loan received from the bank is an increased liability (source) and has thus a positive sign, whereas the money credited by banks is an increased liquid assets (use) and has thus a negative sign. These flows have opposite signs for banks. The results of this first transaction are booked into a second matrix: the economy’s balance sheet matrix shown in Table 2, which records the assets (positive) and the liabilities and net worth (negative) accumulated by the various sectors. In this second matrix, the rows corresponding to the financial claims and liabilities cancel each other out and the corresponding lines sum to zero. This is not the case for fixed assets and net worth, which are net gains for some of the sectors. On the contrary, all columns of the matrix sum to zero. While not always intuitive, the conventions retained for the transaction and the balance sheet matrices provide an integrated treatment of real and financial stocks and flows that reflects the accounting practice35 and allows to check for possible errors through the balancing of rows and columns.

Table 2: Balance sheet matrix instant 1, private finance with no households savings

Closing Balance Sheet Matrix Phase 1 H E G B Total

Tangible capital net KAh0 KA

e0 KAg0 KA

b0 KAh0+ KA

e0+ KAg0+ KA

b0 Deposits + MA

e - MAe 0

Loans - LAe + LA

e 0 Net worth - KA

h0 - KAe0 - KA

g0 - KAb0 -KA

h0 -KAe0 -KA

g0 -KAb0

Sum 0 0 0 0 0

Prior to the transaction of phase 1, the balance sheet matrix contained only the starting net fixed assets and the net worth of each sector. After this transaction, it includes in addition for firms a debt liability and a current asset in the form of a bank deposit and for banks a claim to the corporate sector and a current liability in the form of a deposit. 3.1.2 Revenue formation: The second phase of the circuit concerns the formation of revenues (wages and profits) for the payment of labour and capital. Wages WA are an advance payment36 by which firms credit household’s accounts by a fraction MA

h of the money MAe raised initially, where

MAh=W. In a model with no intermediate inputs, the fact that firms do not pay as wages the full

amount of money they borrowed (MAh<MA

e), implies that part of the initial monetary creation corresponds to profits, which, with no savings of households, account for the full financing of investment37.

35 Both double entry book-keeping of private accounting and quadruple entry conventions of the flow of funds and national accounting approaches. 36 Graziani (1994) noted that the fact that in the circuit wages are paid at the beginning of the production period is in line with the “classical” tradition, for which, in a non-monetary economy, salaries are paid out of previously accumulated (real) savings, thus providing an explanation for the classical causality of savings on investment. On the contrary for neo-classical authors (except Wicksell), wages are paid at the end of the production period, since only then it is possible to equate them with the marginal productivity of labour. However, at that point, the classical explanation for the causality of savings on investment falls down, since savings are co-determined simultaneously with investment. As a result, contrary to the classics, the neo-classicals cannot really justify the causality of savings on investment within their model. By retaining the “classical” assumption that wages are paid in advance, but introducing the Keynesian finance motive for holding money to allow firms to pre-finance all fixed and circulating capital investment, the circuit provides an explanation for the causality of investment on savings which is exactly symmetrical to the causality of loans on deposits retained by the banking school. It can be reminded that in the UK of the XIX century, the banking school claimed that loans create deposits in contrast with the currency school, which was of the contrary opinion. The modern variant of the Currency School is the quantity theory of money associated with the names of Fisher and Friedman. noted that can be regarded as a forerunner of the Banking School. The banking school view was notably endorsed by Schumpeter, while Kaldor and Trevithick (1981, p. 8) rank Adam Smith amongst its supporters. See also Arena (1985), Graziani (2003, pp. 82-88) and, for a detailed historical review of the debate in the 1990-1940 period, Realfonzo (1996). 37 In the circuit literature there has been an extensive debate on the status of profits and investments, particularly on the question of whether they are realised in money or in kind. If it is assumed that the money created with the new loans finance wage costs only, profits are never monetised. In this case the money circulation in the circuit can be given an interpretation in terms of the Marxist labour theory of value (see Bellofiore 1989). Parguez (2004) has taken position against this “wage postulate”, arguing that in the logic of the circuit profits

- 13 -

In the following, it is assumed that wages paid are not consumed immediately, they thus represent temporary savings for households and enter into their net worth and in their monetary holdings at the end of the phase. In order to balance the rows and the columns of the transaction matrix these savings (and the corresponding dissavings of entreprises) must be entered twice with opposite signs in the corresponding current and capital columns.

Table 3: Transaction matrix phase 2, private finance with no households savings H E G B Transaction matrix

Phase 2 Current Capital Current Capital Current Capital Current Capital Total

Net profits -WA MAh WA -MA

h 0 Wages WA -WA 0 Change in deposits -MA

h MAh 0

Total 0 0 0 0 0 At the end of the second phase of the circuit, which is also the start of the third one, the balance sheet matrix shows that households have money holdings of MA

h, compensated by an equal increase in their net worth38. Entreprises have meanwhile reduced their net worth and money holdings by the same amount MA

h. and they keep their initial debt towards the enterprise sector of LAe.

Table 4: Balance sheet matrix end of phase 2, private finance with no households savings Opening Balance Sheet

Matrix Phase 3 H E G B Total


e0 KAg0 KA

b0 KAh0+KA

e0+KAg0+KA

b0 Deposits + MA

h + MAe - MA

h - MAe

Loans - LAe + LA

e Net worth -KA

h0 - MAh -KA

e0+MAh -KA

g0 -KAb0 -KA

h0-KAe0-KA

g0-KAb0

Sum 0 0 0 0 0 3.1.3 Production and consumption: In the third phase production and consumption take place. Households use their wages to buy from firms the amount of good they need for consumption and their liquid balances disappear in the process. In Table 5, entreprises thus recover from sales the money they paid out as wages in the second phase MA

h. The entreprises sector being consolidated, when it produces and sells the investment to itself it pays and recovers the money amount MA

e-MAh,

realising a profit39 πΑe=MA

e-MAh which self-finances investment IPA. In order to respect the balancing

of the relevant rows and columns, in the transaction matrix profits and investment have been entered with opposite signs as a current and a capital item in the relevant line of entreprises and households.

must necessarily be monetised. Rochon (1999) has taken the same position. The alternative to a monetary financing of profits is either that they have a real counterpart, which represents capital accumulation not realised in money, such as for instance increased inventories, or that their monetary value is included in wages, and later expropriated from workers. The most articulated variant of the wage postulate, labelled “neo-Kaleckian” by Parguez, is that of a two producing sectors economy with a consumption and an investment sector. In the simplifying case where households do not save, wages are paid to workers in both sectors, who spend them entirely. However consumption is equal to production and wages of the consumption sector only. Production and wages of the investment sector correspond to investment and non-monetary profits earned by the entreprise sector. Lavoie (1987) has argued that in a multisectoral model, where corporates are split into one consumption sector and several investment companies organised hierarchically, the two solutions are equivalent, i.e. money creation covers also profits even if loans only cover initially only wages. However Parguez has shown that this case is equivalent to that of the wage postulate and therefore did not retain it, an approach followed also here. Rochon (2005, 2009) and Renaud (2000) are recent contributions that go along the lines of Parguez (2004). Graziani’s position is that at the aggregate level payments internal to the enterprises’ sector must cancel out and that therefore no net money creation is necessary to cover them in a purely macroeconomic model has its logic and is retained in the model of par. 2.2. 38 The separation in phases in somewhat arbitrary and depends from the problem at hand. In the illustration of the pure credit economy given in Cingolani (2009, section 5.1), the second phase ends with household’s consumption (with savings). 39 Although labeled as net profit, because to simplify the example the depreciation of assets is nil, these are to be understood as gross profits.

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In an economy without savings of households profits are always equal to investment, both in real and in money terms (Graziani, 1987). This reflects the so-called “Kalecki principle”, according to which firms gain as profits what they have already spent as investment to acquire newly produced equipment goods (Parguez, 1995).


Phase 3 Current Capital Current Capital Current Capital Current Capital Consumption -CA CA 0 Investment IPA -IPA 0

Net profits CA -MAh -CA-IPA MA

h+πAe 0

Change in deposits MA

h -MAh 0

Total 0 0 0 0 0

At the end of the third phase, the balance sheet matrix in Table 6 shows that entreprises have recovered in their deposits all initially created money Me and this balances the corresponding loan.

Table 6: Balance sheet matrix end of phase 3, private finance with no households savings

Opening Balance Sheet Matrix Phase 4 H E G B Total


e0 + IPA KAg0 KA

b0

Deposits MAe - MA

e 0 Loans - LA

e + LAe 0

Net worth -KAh0 -KA

e0-πAe -KA

g0 -KAb0 -KA

h0 -KAe0-πA

e -KAg0 -KA

b0 Sum 0 0 0 0 0

In addition entreprises have accumulated new fixed assets IP and their net worth was increased by the corresponding profits. 3.1.4 Final finance and closure of the circuit: In the fourth and final phase of the circuit entreprises use their monetary incomes to repay the loan received from banks40. Since households do not save, enterprises can recover the full amount of money created initially, thus destroying fully the money they created at the beginning of the circuit with the loan they requested to banks.


Phase 4 Current Capital Current Capital Current Capital Current Capital Change in deposits MA

e -MAe 0

Change in loans -LAe LA

e 0 Total 0 0 0 0 0

The final balance sheet matrix of Table 8 shows that the net assets of the economy have increased by the amount of the investment realised IPA and its net worth by the corresponding profits πA

e. This marks the closure of the circuit and the appearance of final finance, where savings, in this case only corporate profits, cover investment.

In case in the final phase entreprises would decide to keep a debt liability towards banks to be repaid later and the banks would validate this decision, they would keep the corresponding deposits in their

40 Also called the “reflux phase”.

- 15 -

liquid assets and could use them at the start of the following production phase, for instance as an advance payment to workers. This case is mentioned here for comparison with section 3.2 where at the end of the circuit the State keeps a debt liability towards the banking system. To the extent that in such case not all money initially created is destroyed, this could be interpreted a situation of “monetary disequilibrium” 41.

Table 8: Balance sheet matrix end of phase 4, private finance with no households savings



e0 + IPA KAg0 KA

b0 KAh0+KA

e0 + IPA+KAg0+KA

b0

Net worth -KAh0 -KA

e0-πAe -KA

g0 -KAb0 -KA

h0 -KAe0-πA

e –KAg0 -KA

b0

Sum 0 0 0 0 0

However, the “monetary equilibrium” of the circuit does not coincide with the “real equilibrium” of the walrasian type, which is implied by Hayek. In the circuit a multiplicity of equilibria are possible, depending on the strategies of banks and firms and they are not necessarily stable (Graziani 2003, p. 147). With reference to the model presented in paragraph 2.2, in the case without State intervention (t=0), the walrasian assumption of null profits arises when the propensity to invest is equal to the propensity to save (b=s, see par. 2.2.1, relations 12 and 13). Parguez defines the equilibrium in the circuit as the situation where the plans of the actors are mutually consistent, in particular when the expectations of firms are validated by the banking sector. This means that the money that banks accept to create for firm allows them to fully cover the investment costs and realise the profit necessary for the banks to continue to validate their plans. As noted before, the various steps of the circuit provide an illustration of the monetary explanation for the post Keynesian causality of investment on savings: at the start of the process money is created by the banking sector at the request of producers as a function of their production targets of total investment in fixed and circulating capital. The money that is not destroyed by loan repayment after consumptions and bond issuance by producers remains in the system and “creates” the savings necessary to finance investment in fixed capital (real capital accumulation). It is important to stress the circuit’s conclusion that money created by the banking sector through credit only corresponds to a creation of real wealth once it is transformed into revenues (salaries and profits) that are either consumed or saved (accumulated). In both cases if the agent that got originally into debt recovers the full amount of money that he has injected in the economy he can fully repay the loan to the banking system otherwise he remains with a liability towards the banking system that he can maybe repay in the future. This shows the difference between a good and a bad debt: the good debt creates liquidity matched by a real wealth creation (salaries and profits, corresponding to present and future consumption), whereas a bad debt creates liquidity matched by nothing, which one day the banking system cannot continue to refinance. In this way the circuit provides a monetary explanation for the existence of crises, which seems to fit quite well with recent events. 3.2 Full financing by the State budget With reference to the Kalecki identity given by relation (1), any of the sectors of the economy can be at the origin of the initial money creation determining effective demand, including the State. This section examines the case of pure public sector financing of an investment and is also of relevance for the cases of mixed financing with shadow tolls or availability payments, examined in section 3.3.

41 For instance in the sense of Hayek, who would consider that the permanence of monetary assets backed only by financial claims is by itself an inflationary imbalance.

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3.2.1 Initial finance: As before, in the initial phase of the monetary circuit, all sectors have an accumulated net worth, corresponding to their net fixed assets. Since the suffix B is applied to all variables appearing in this paragraph, it was applied also to the initial capital stock, although one could assume that the initial level of the capital stock is the same as in the previous paragraph. The Government decides to take a loan LB

g from the banking sector to finance capital investment. At the same time entreprises take a loan to finance wages in the consumption sector. When both loans are granted, banks credit the deposits of the Government of an amount MB

g and the deposits of the firms of an amount MB

e and the circuit starts. One can note that at this stage Me

B +MgB ≤ Me

A or MeB +Mg

B ≥ MeA , depending on effective demand expectations in the pure private

financing case, and the level of public investment planned by the State in the case of public financing (see discussion in section 4). The Godley-Lavoie simplified transaction matrix is:

Table 9: Transaction matrix phase 1, pure public financing and no households savings H E G B Total Transaction matrix

Phase 1 Current Capital Current Capital Current Capital Current Capital Change in deposits -MB

e -MBg MB

g+MBe 0

Change in loans LBe LB

g -LBg-LB

e 0 Total 0 0 0 0 0

After this first transaction, the balance sheet of the economy shows that the column of firms includes a new debt liability -LB

e and new liquid asset MBe, that of the Government a new debt liability -LB

g and new liquid asset MB

g, whereas in the column of banks there are new claims to the corporate sector LB

e and to the Government LBg and new current liabilities representing the deposits of firms –MB

e and of the government –MB

g. Table 10: Balance sheet matrix end of phase 1, pure public financing and no households savings


Tangible capital net KBh0 KB

e0 KBg0 KB

b0 KBh0+KB

e0+KBg0+KB

b0 Deposits + MB

e + MBg' -MB

g'-MBe' 0

Loans - LBe - LB

g' LBg'+LB

e' 0 Net worth -KB

h0 -KBe0 -KB

g0 -KBb0 -KB

h0 -KBe0 -KB

g0 -KBb0

Sum 0 0 0 0 0 3.2.2 Revenue formation, production and consumption: This paragraph covers phases 2 and 3 of the previous example of full private sector financing (paragraphs 3.1.2 and 3.1.3)42. First the Government uses the money obtained from banks to pay entreprises for the capital goods to be supplied as shown in Table 11 below. It thus disposes of its bank deposits MB

g to accumulate a work in progress claim -DIBG. The entreprise sector receives the deposits -MB

g and accumulates a corresponding work in progress liability DIBG.


Phase 2 Current Capital Current Capital Current Capital Current Capital Investment DIBG -DIBG 0 Change in deposits -MB

g MBg 0 Total 0 0 0 0 0

The resulting balance sheet matrix is shown in Table 12 below.

42 As mentioned before, the separation between the phases of the circuit is somewhat arbitrary.

- 17 -

Table 12: Balance sheet matrix end of phase 2, pure public financing and no households savings



e0 - DIBG KBg0 + DIBG KB

b0 KBh0+KB

e0+KBg0+KB

b0 Deposits + MB

e + MBg -MB

g-MBe

Loans - LBe - LB

g LBg+LB

e Net worth -KB

h0 -KBe0 -KB

g0 -KBb0 -KB

h0 -KBe0 -KB

g0 -KBb0

Sum 0 0 0 0 0

Next entreprises pay MBh in salaries WB to households as shown in Table 13. Households use it

immediately for consumption -CB so that their deposits disappear in the same phase MBh, while

deposits of the entreprises are credited again by -MBh. The sale of production for consumption and

for capital accumulation generates revenues of CB+IGB for firms.

These revenues correspond to the sum of wages paid and profits retained. The production of the investment good transforms the work in progress liability they had previously accumulated towards the Government –DIBg into a real liability whose delivery to the Government frees the relevant cash MB

g and generates a profit πBe. The work in progress asset of the Government DIBG is thus

transformed into a real asset -IGB. The transaction matrix is presented in the next page in Table 13: Table 13: Transaction matrix phase 3, pure public financing and no households savings

H E G B Total Transaction matrix

Phase 3 Current Capital Current Capital Curr. Capital Curr. Cap. Consumption -CB CB 0 Investment IGB -DIBG -IGB+DIBG 0

Net profits -IGB +πBe 0

Wages WB -WB 0 Change in deposits -MB

h+MBh MB

h-MBh 0

Total 0 0 0 0 0

At the end of this “third phase” of the circuit, the balance sheet of Table 14 shows that the net fixed assets of the Government are augmented by IBG, compensated by a debt of LB

g, whereas all money created MB

e+MBg is in the hands of entreprises, who still owe LB

e to banks. Therefore their net worth has increased by the profits realised πB

e, which correspond to MBg, since the Government fully

financed the capital good. Table 14: Balance sheet matrix end of phase 3, pure public financing and no households savings



e0 KBg0+IGB KB

b0 KBh0+KB

e0+KBg0+IGB+KB

b0 Deposits 0 MB

e+MBg -MB

g-MBe 0

Loans - LBe - LB

g LBg+LB

e 0

Net worth -KBh0 -KB

e0-πBe -KB

g0 -KBb0 -KB

h0 -KBe0-πB

e -KBg0 -KB

b0

Sum 0 0 0 0 0 3.2.3 Final finance and closure of the circuit: In the “reflux phase”, entreprises repay their loans LB

e to banks and destroy the equivalent amount of money MBe. The Government taxes entreprises by

an amount TB, which can be less or equal than MBg, and uses these tax revenues to repay banks, as

shown in the transition matrix of Table 15.

- 18 -

Entreprises reduce their money balances and profits by the amount of taxes paid. The Government uses the money it received in payment of taxes to repay the loan and increases its net worth accordingly. Banks’ loan and deposit balances adjust. In the end, retaining the case where TB<MB

g, that part of the money created by the Government that was recovered in the form of taxes is destroyed, but not the part that corresponds to the debt the government keeps towards the banking system.


Phase 4 Current Capital Current Capital Current Capital Current Capital Net profits TB -TB -TB TB 0 Taxes - transfers -TB TB 0 Change in deposits MB

e+TB -TB-MBe 0

Change in loans -LBe -TB LB

e+TB 0 Total 0 0 0 0 0

This illustrates one of the basic properties of the monetary circuit, whereby taxes do not finance public expenditure, because they appear at the closing end of the circuit when public expenditure has already been financed. Intervening in the reflux phase, taxes destroy the money created at the start of the circuit (efflux phase)43. The closing balance sheet of Table 16 at the end of the circuit shows that the Government has increased its fixed assets by the amount of the fixed investment IG and kept a debt of Lg-T, increasing its net worth by the amount of taxes repaid.

Firms realised a profit equal to the debt remained in the liabilities of the Government. They have a deposit balance equal to Mg-T, which corresponds to their increase in net worth. This illustrates another neat result of the monetary circuit approach, valid in general in a closed economy: Government’s debt is net wealth for the private sector. In this example it was assumed that private profits from the Government deficit were accumulated in the entreprise sector only, that is also the only sector taxed in this example, but they could have been also redistributed to the households, if the latter had been assumed to hold all fixed net assets in the economy in the beginning44.

Table 16: Balance sheet matrix end of phase 4, pure public financing and no households savings



e0 KBg0+IGB KB

b0 KBh0+KB

e0+KBg0+IBG+KB

b0 Deposits 0 MB

g-TB 0 -MBg+TB 0

Loans 0 -LBg+TB LB

g-TB 0 Net worth -KB

h0 -KBe0-pB

e+TB -KBg0 - TB -KB

b0 -KBh0 -KB

e0-pBe -KB

g0 -KBb0

Sum 0 0 0 0 0

Overall the economy net assets have increased again by the amount of the fixed investment. This corresponds also to the final net worth of the economy, where however, to the extent that not all Government debt is repaid, the increase in net worth is shared between the Government and the entreprises. By hypothesis, the period of the circuit has been closed here with a partial money

43 See Parguez (2002) or Gnos and Seccareccia (2002). 44 This assumption is retained for instance in the BMW model of chapter 7 of Godley-Lavoie (2007).

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destruction. To the extent that some agents keep financial claims to others through the next period, the economy can be seen as being in disequilibrium (with respect to the definition of equilibrium of the neo-classical model). 3.3 Comparison of pure private and pure public financing The case where households do not save and banks do not generate profits simplifies substantially the discussion of the main aspects of private and public financing and it is worth being discussed in detail. As discussed below in paragraphs 3.5 and 3.6, its main results extend to the more complex cases where both household and banks are assumed to realise monetary surpluses. Let’s refer as before to the cases examined of pure private and public sector financing with the subscripts A and B respectively. The table 18 below compares the main variables involved in the sequences of the circuit in these two cases.

Table 18: Comparison of pure public and private financing

A (Private) B (public) Initial money creation MA

0 = MA

h+πAe MB

0 = MB

e+MBg

Change in net worth πA = πAe = MA

e-WA πB = πBe = MB

g Firms πA = Me - Mh πB = MB

g - TB Government 0 TB

End of period debt of the investor 0 0 or LBg - TB

Change in fixed assets (Kalecki identity) IPAe = πA

e IGB= πBe+ TB

Money not destroyed at the end of the circuit MA1 = MA

e MB

1 = MB

e+MBg

or MB1

= MBe+MB

g –TB

The amount of money created as initial finance (MA and MB) corresponds in the two cases to the sum

of wages and the investment cost. The difference is that with full private financing money is only created at the request of firms, whereas with public financing it is created in part at the request of firms and in part at the request of the Government, respectively for the payment of wages or for the financing of investment. With private financing, profits cover the entire cost of investment, so that the Kalecki relation (1) reduces to SE − I( )= 0 . With public financing, since it is assumed that part of the State debt created to finance the public investment is repaid by taxes, firms’ profits correspond at the end of the circuit only to the debt remaining in the balance sheet of the Government πΒ

e-TB. The rest of the investment cost, once repaid by taxes, becomes a net worth for the Government (TB). However, at the level of the overall economy, profits are the sum of these two components, and are thus equal to πΒ. In this case the Kalecki identity SE − I( ) + T −G( )= 0 illustrates that in a closed economy, the public deficit increases corporate profits45. In principle the solutions of pure private financing and pure public finance could bring to the same outcome, except for the distribution of the property and of the debt on the asset financed. This is the case if the private sector and the public sector plan the same level of effective demand based on expected traffic (for instance if QSBO=QBE in the chart 3 in par. 4.2.1) and if the surplus extracted by the private sector is equal to the inefficiency rent of the public sector ( rB

q = π A + π Ae , in relation 34 in

par. 4.3.4). In that case the initial money creation will be the same MA0 = MB

0 and will generate the

45 An anti-Barro result of the circuit, which derives originally from Kalecki (1990 [1935], pp. 193-195)

- 20 -

same investment value (IP=IG), which will in turn provide by assumption the same level of service (say QBE), at the same cost. 3.4 The case of mixed financing with no households savings and zero interest rate 3.4.1 This case corresponds to a highway financed in part by the Government and in part by the private sector, with real and shadow tolls (or availability payments), under what is called public-private partnership46. When willingness to pay is low, it is similar to the case of public financing, with the notable difference that national accounting rules allow in some cases liabilities to be incurred by the State for shadow tolls or availability payments to be booked in the balance sheet of the corporate sector (see for instance discussion in Sawyer, 2009, pp. 4-8). The developments up to 3.1.1 included are the same as before. The starting situation is thus the same as at the end of 3.1.2, with entreprises having already paid wages for an amount MC

h to households, but where households have not yet started to consume, as shown by the balance sheet matrix in Table 19.

Table 19: Balance sheet matrix end of phase 2, mixed financing with no households savings Opening Balance Sheet


Tangible capital net KCh0 KC

e0 KCg0 KC

b0 KCh0+KC

e0+KCg0+KC

b0 Deposits + MC

h + MCe - MC

h - MCe

Loans - LCe + LC

e Net worth -KC

h0 - MCh -KC

e0+MCh -KC

g0 -KCb0 -KC

h0-KCe0-KC

g0-KCb0

Sum 0 0 0 0 0

What changes from there on is that in the phase of production and consumption, part of consumption comes from the Government. It is supposed that the Government finances this consumption by a loan from banks. Banks credit the deposit account of the Government, who accumulates a debt liability –LC

g. When this money is credited to entreprises, the Government decreases its net worth by the amount corresponding to the “current” State deficit DC

g, as shown by the transaction matrix of Table 20.

Table 20: Transaction matrix phase 3, mixed financing with no households savings H E G B Total Transaction

matrix Phase 3 Current Capital Current Capital Current Capital Curr. Capital Consumption -CPC CPC+CGC-CGC -CGC 0 Investment IPC+IGC -IPC-IGC' 0 Net profits CPC -MC

h' -CPC-IPC MCh +pC

e CGC -DCg 0

Change in deposits MC

h -MCh-MC

g -MCg+MC

g MCg 0

Change in loans LC

g -LCg 0

Total 0 0 0 0 0

Entreprises receive revenues from both Government and households in payment for their consumption CPC+CGC and self-finance private investment IPC through monetised profits. Government’s consumption represents the amount that the Government has contractually agreed to cover every year for the provision of capital services by the private sector. The latter remains owner

46 The case of availability payments can be assimilated to that of shadow tolls by fixing the subsidy coming from the Government at the same aggregate level than the revenue that, given traffic, would be perceived with shadow tolls.

- 21 -

of the infrastructure until the end of the contract and public consumption is capitalised in the balance sheet of entreprises.

As shown by the balance sheet matrix in Table 21, at the end of this phase entreprises have money holdings equal to MC

e+MCg, i.e. money created by the banks to cover their needs plus money created

to cover those of the State. Their assets have increased by the amount of investment realised and their net worth as well. They still owe to banks the loan contracted in the first phase. The Government has a debt liability, compensated by a decrease of its net worth. The banks have in their balance sheet the money created and the loan granted to both sectors.

Table 21: Balance sheet matrix end of phase 3, mixed financing with no households savings



e0 +IPC+IGC KCg0 KC

b0 KCh0+KC

e0 +IPC+IGC +KCg0+KC

b0

Deposits + MCe+MC

g +MCg-MC

g - MCe - MCg 0

Loans - LCe - LC

g + LCg 0

Net worth -KCh0 -KC

e0-MCg-πC

e -KCg0+DC

g -KCb0 -KC

h0 -KCe0-MC

g-πCe -KC

g0+DCg -KC

b0

Sum 0 0 0 0 0 3.4.2 In the last phase of the circuit it is assumed that all money created for firms is destroyed, but, as in paragraph 3.2.3, not all the money created for the Government is destroyed, because Government taxes profits less than for the full amount of the loan created. This is shown in the transaction matrix in Table 22 in the next page:

Table 22: Transaction matrix phase 4, mixed financing with no households savings H E G B Total Transaction matrix

Phase 4 Curr. Cap. Current Capital Current Capital Current Capital Net profits TC -TC -TC +TC 0 Taxes - transfers -TC TC 0 Change in deposits MC

e+TC -TC+TC -MCe-TC 0

Change in loans -LCe -TC LC

e+TC 0 Total 0 0 0 0 0

The final balance sheet matrix of Table 23 shows once again that net worth of the economy has increased by the amount of the investment realised, now IPC+IGC, corresponding to firm’s profits πC

e. Table 23: Balance sheet matrix end of phase 3, mixed financing with no households savings



e0+IPC+IGC KCg0 KC

b0 KCh0+KC

e0+IPC+IGC+KCg0+KC

b0 Deposits +MC

g-TC -MCg+TC

Loans - LCg + TC LC

g-TC Net worth -KC

h0 -KCe0-pC

e-MCg+TC -KC

g0+DCg-TC -KC

b0 -KCh0-KC

e0-pCe-KC

g0-KCb0

Sum 0 0 0 0 0

It can be noted that firm’s profit are higher than total investment realised by the amount of the Government’s debt remained in the balance sheet of the State. The latter is lower than the initial money creation and debt as an amount T was destroyed with the payment of taxes.

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3.5 Mixed financing with household savings and zero interest rates When the possibility to save part of the revenues of households is reintroduced, the traditional final finance of investment by pre-existing savings comes back into the picture. The first and second steps of the circuit are the same as in section 3.1: entreprises take a loan from banks and advance wages to households. The balance sheet matrix at the start of the third phase in Table 24 is thus the same as at the end of paragraph 3.1.2.

Table 24: Balance sheet matrix beginning of phase 3, mixed financing with savings of households Opening Balance Sheet


Tangible capital net KDh0 KD

e0 KDg0 KD

b0 KDh0+KD

e0 +KDg0+KD

b0 Deposits +MD

h +MDe-MD

h -MDe

Loans -LDe +LD

e Net worth -KD

h0-MDh -KD

e0+MDh -KD

g0 -KDb0 -KD

h0-KDe0 -KD

g0-KDb0

Sum 0 0 0 0 0

In phase 3, households keep part of their wage in the form of deposits, consumption is therefore lower than wages by an amount MD

h- CPD, corresponding to households’ savings SDh. Therefore

revenues of entreprises are now also lower than in par. 3.1.3, as not all the wages WD paid during the previous phase are recovered by firms. At the same time, in line with paragraph 3.4.1, firms also receive payments from the Government for what the latter books as consumption. It is supposed again that the Government finances this consumption by a loan from banks. Banks credit the deposit account of the Government, who accumulates a debt liability –LD

g. When this money is credited to entreprises, the Government decreases its net worth by the amount corresponding to the “current” State deficit DD

g. Entreprises receive revenues from both Government and households in payment for their consumption and self-finance private investment through monetised profits as before. Government’s consumption represents the amount that the Government has contractually agreed to cover every year for the provision of capital services by the private sector. Again, the latter remains owner of the infrastructure until the end of the contract and public consumption is capitalised in the balance sheet of entreprises. The transaction matrix in Table 25 is therefore:

Table 25: Transaction matrix phase 3, mixed financing with savings of households


Phase 3 Current Capital Current Capital Curren

t Capital Curr. Cap. Consumption -CPD CPD+CGD-CGD -CGD 0 Investment IPD+IGD -IPD-IGD 0 Net profits CPD -MD

h+SDh -CPD-IPD MD

h -SDh'''+pD

e CGD -DgD 0 Change in deposits MD

h-SDh -MD

h+SDh-MgD -MD

g+MDg MD

g 0 Total 0 0 0 0 0

At the end of this third phase, the balance sheet matrix in Table 26 shows that the net worth of households has increased by the amount they saved SD

h, whereas that of the entreprises is now lower by the same amount. Households deposits have also increased by SD

h. This time money holdings of entreprises are less than those of paragraph 3.4.1 as they are diminished by savings and equal to MD

e-MD

g-SD

h.

- 23 -

As before enterprises assets have increased by the amount of investment realised IPD+IGD, but their net worth has increased by this amount less the savings remained in the hands of households -KD

e0 +SD

h-πDe. They still owe to banks the loan contracted in the first phase -LD

e. The Government has a debt liability -LD

g, compensated by a decrease of its net worth by DDg. As shown by the balance sheet

matrix in Table 26, the banks have in their balance sheet the money created -MDe-MD

g and the loan granted to both sectors LD

e+LDg.

Table 26: Balance sheet matrix end of phase 3, mixed financing with with savings of households Opening Balance

Sheet Matrix Phase 4 H E G B Total


e0+IPD+IGD KDg0 KD

b0 KDh0+KD

e0+IPD+IGD +KDg0+KD

b0 Deposits SD

h' +MDe-SD

h+MDg +MD

g-MDg -MD

e-MDg 0

Loans -LDe -LD

g +LDe+LD

g 0 Net worth -KD

h0-SDh -KD

e0 +SDh-pD

e -KDg0+DD

g -KDb0 -KD

h0 -KDe0 -pD

e -KDg0+DD

g -KDb0

Sum 0 0 0 0 0 In the last phase of the circuit it is assumed as before that not all the money created by the Government is destroyed by the payment of taxes, in symmetry with paragraphs 3.2.3 and 3.4.2. The main difference with paragraph 3.4.2 is however that entreprises cannot repay all the loans they received, but only that part they recovered from sales. Either entreprises are able to absorb the liquidity remained in the hands of households by an emission of bonds, which is difficult since the interest rate was assumed nil, or they end up with a liability to the banking sector. The latter case is portrayed in the transaction matrix in Table 27 in the next page:

Table 27: Transaction matrix phase 4, mixed financing with savings of households H E G B Total Transaction matrix

Phase 4 Curr. Cap. Current Capital Current Capital Current Capital Net profits TD -TD -TD +TD 0 Taxes - transfers -TD TD 0 Change in deposits MD

e -SDh+TD -TD+TD -MD

e +SDh -TD 0

Change in loans -LDe+SD

h -TD LDe -SD

h +TD 0 Total 0 0 0 0 0

The final balance sheet matrix in Table 28 shows once again that net worth of the economy has increased by the amount of the investment realised, now IDP+IDG corresponding to firm’s profits. As before firm’s profit are higher than total investment realised by the amount of the Government’s debt remained in the balance sheet of the State, but reduced this time by household’s savings. Entreprises keep a debt towards the banking system equal to the savings of the households sector, assumed to remain liquid. As before Government debt is lower than the initial money creation as an amount T was destroyed.

Table 28: Balance sheet matrix end of phase 4, mixed financing with savings of households Opening Balance



e0+IPD+IGD KDg0 KD

b0 KDh0+KD

e0+IPD+IGD+KDg0+KD

b0 Deposits SD

h +MDg-TD -MD

g-SDh+TD

Loans -SDh -LD

g+T LDg+SD

h -TD

Net worth -KDh0-SD

h -KDe0+SD

h-πDe+TD -KD

g0+DDg-TD -KD

b0 -KDh0-KD

e0-πDe-KD

g0-KDb0

Sum 0 0 0 0 0

- 24 -

Assume now that Government debt is limited exogenously, so that entreprises bet that Government would be able to finance only less than IGD. In that case they will not raise initial finance in the amount full amount of MD

e. At the limit, when users’ willingness to pay is very low, the only finance they can count on is final finance, therefore, with household’s savings, the only investment realised during the year even under mixed financing will be precisely the amount of households’ savings SD

h. 3.6 Mixed financing with household saving and interest The assumption that is withdrawn in this section is that of zero or equal active and passive interest rates. In that case the version of the Kalecki identity to be kept as a background reference includes a term for the banking sector surplus as in footnote 5 where bank profits are separated from the profits of the non-financial corporates: SNFE − I( ) + PFI + T − G( ) + M − X( ) + SH − H( ) = 0 , with PFI as the banks profits 3.6.1 Also in this case the sequence of the circuit is followed from the moment a loan is granted to firms, after which the economy’s balance sheet matrix of Table 29 is, as in paragraph 3.1.1:

Table 29: Balance sheet matrix end of phase 1, mixed financing, with savings and interest Opening Balance


Tangible capital net KEh0 KE

e0 KEg0 KE

b0 KEh0+KE

e0+KEg0+KE

b0 Deposits +ME

e -MEe 0

Loans -LEe +LE

e 0 Net worth -KE

h0 -KEe0 -KE

g0 -KEb0 -KE

h0 -KEe0 -KE

g0 -KEb0

Sum 0 0 0 0 0

As shown by the transaction matrix in Table 30, during the second phase entreprises pay wages WE to households. At the same time they pay interest to banks at the rate of interest re on the loan LE

e

they received in the previous phase, paid out of the loan itself (cf. Renaud, 2000). Banks remunerate deposits ME

e at the rate rd. To the extent that interest earned on loans exceeds interest paid on

deposits, the banks realise a profit (re-rd)*LEe.47

Table 30: Transaction matrix phase 2, mixed financing, with savings and interest

H E G B Total Transaction

matrix Phase 2 Curr. Cap. Current Capital Current Capital

Net profits -WE MEh WE-rd*ME

e+re*MEe -ME

h+rd*MEe-re*ME

e -re*MEe+rd*ME

e''' re* MEe-rd*ME

e 0 Wages WE -WE 0 Loan interest -re*ME

e +re*MEe 0

Deposit interest +rd*MEe -rd*ME

e 0

Δ deposits -MEh ME

h-rd*MEe+re*ME

e -re*MEe+rd*ME

e 0

Total 0 0 0 0 0

The balance sheet matrix in Table 31 shows that firms retained profits are now lower than in the case without interest and the difference is the net interest flow.

47 Which is of course nil when rd=re, corresponding to the case without interest examined in par. 3.5

- 25 -



Tangible capital net KEh0 KE

e0 KEg0 KE

b0 KEh0+KE

e0+KEg0+KE

b0 Deposits +ME

h +MEe*(1+rd-re)-ME

h -MEe*(1+rd-re)

Loans -LEe +LE

e Net worth -KE

h0-MEh -KE

e0+MEh+(re-rd)*ME

e -KEg0 -KE

b0 +(rd -re)*MEe -KE

h0-KEe0-KE

g0-KEb0

Sum 0 0 0 0 0 3.6.2 In the third phase described by the transaction matrix in Table 32 below, households decide the allocation of their monetary revenues between private consumption and savings as before. The difference is that in this section it is assumed that the Government finances its consumption CGE by a deficit covered by the issuance of a bond BE

g paying the rate rg and entirely bought by households. The latter thus have now a new possibility to have their savings better remunerated if they invest them into the acquisition of this Government’s bond. This means that CGE, which is in fact that part of public investment booked on the Government accounts of the current year, is now financed out of household’s savings and not from new credits from the banking sector. It is thus financed as final finance and not initial one and entails no new money creation. As before deposit interest at a rate rd is paid on previous period’s households’ deposits ME

h, whereas part of deposit interest remunerates also entreprises’ savings ME

e-MEh. Firms continue to pay interest

re on the money borrowed from banks Me. Table 32: Transaction matrix phase 3, mixed financing, with savings and interest


Phase 3 Current Capital Current Capital Current Capital Current Capital

Consumption -CPE CPE+CGE-CGE -CGE 0

Investment IPE+IGE -IPE-IGE 0

Net profits CPE-rd*ME

h

-MEh+SE

h-SE

h+rd*MEh

+DEg

-CPE-IPE

+re*MEe -

rd*MEe

+rd*MEh

MEh-SE

h +pEe

-re*MEe +

rd*MEe -

rd*MEh+SE

h

CGE -DEg

+rd*MEe-

re*MEe

-rd*ME

e+re*MEe

0

Loan interest -re*MEe re*ME

e 0 Deposit interest rd*ME

h rd*MEe-

rd*MEh

-rd*MEe 0

Change in deposits ME

h-rd*MEh

-MEh+SE

h-SE

h+re*MEe-

rd*MEe+rd*ME

h -

SEh+SE

h rd*ME

e-re*MEe 0

Change in loans/bonds -BE

g BEg 0

Total 0 0 0 0 0 As shown in Table 33, at the end of the third phase households have deposits equal to the interest revenues they perceived on their holdings during the previous period, which correspond to an equal increase in their net worth. Households have allocated their savings to the acquisition of financial asset BE

g representing a claim on the Government. Firms have accumulated investment in their net fixed assets. Their deposits include all revenues they recovered from their sales to households and to the Government, i.e, all money created by them plus the interest revenues accumulated on their holdings of deposits. Firm’s net worth is adjusted

- 26 -

accordingly. The Government has a debt liability towards households, which is compensated by a decrease in its net worth. Banks have claims towards the entreprises compensated by the corresponding deposits. The latter are adjusted by net interest earned, which also accumulate in the banks’ net worth.


Sheet Matrix Phase 4

H E G B Total

Tangible capital net KE

h0 KEe0+IPE+IGE KE

g0 KEb0 KE

h0+KEe0+EIPE+IGE+KE

g0+KEb0

Deposits +rd*MEh

+MEe*(1+2rd-2re) -rd*ME

h -ME

e*(1+2rd-2re) 0

Loans/bonds +BEg -LE

e -BEg +LE

e 0

Net worth -KE

h0

-rd*MEh -

DEg

-KEe0+(2re-2rd)*ME

e-pE

e+rd*MEh

-KEg0

+DEg

-KEb0

+(2rd -2re)*MEe

-KEh0-KE

e0-pEe-KE

g0-EKEb0

Sum 0 0 0 0 0 3.6.3 As before the final phase of the circuit described in Table 34 is that of the reflux, when all credit money repaid to banks is destroyed. The Government taxes firms profits by TE, but this time uses this amount to reduce its debt towards households, to whom it pays also interest at the rate rg. Firms repay all money they recovered from sales to households and the Government, i.e. ME

e. Table 34: Transaction matrix phase 4, mixed financing, with savings and interest


Phase 4 Current Capital Current Capital Current Capital Current Capital

Net profits -rd*rd *MEh

-rg*BEg

rd*rd* MEh

+rg*BEg

TE+re* ME

e-rd*DE(3)

-TE

-re*MEe

+rd*DE(3)

-TE+rg *LE

g +TE

-rg*BEg

-re*MEe

+rd*DE(3)+rd*rd *ME

h

re*MEe

-rd*DE(3)

-rd*rd *MEh

0

Loan/bond interest rg*BE

g -re*MEe -rg*BE

g re*MEe 0

Deposit interest rd*rd*ME

h rd*DE(3) -rd*DE(3)-rd*rd*ME

h 0

Taxes - transfers -TE TE 0

Change in deposits

-rd*rd* ME

h -rg*BE

g-TE

MEe+TE

+re*MEe

-rd*DE(3)

-TE+TE+r

g*BEg

-MEe

-re*MEe

+rd*DE(3)+rd*rd *ME

h

0

Change in bonds/loans TE -LE

e -TE LEe 0

Total 0 0 0 0 0

Banks pay interest on households’ and firms’ holdings of deposits during the previous period, the latter are noted DE(3) to shorten notations. Firms and the Government pay interest on their loans for the last time.

As shown by the balance sheet matrix in Table 35, at the end of this fourth phase households have in their deposits the amount of the bond repaid by the Government, together with accumulated interest received and keep as asset that part of the bond BE

g-TE not yet repaid. Firms have repaid all their debt to the banks but have their net worth decreased by the amount of household’s savings kept in

- 27 -

the form of deposits, including mainly TE. The Government kept a debt liability towards households equal to part of the loan not repaid through taxes. At the level of the overall economy a net wealth corresponding to the amount invested has been created, which is also equal to firms profits gross of household’s savings.


Sheet Matrix Phase 5

H E G B Total

Tangible capital net KE

h0 KEe0+IPE+IGE KE

g0 KEb0

KEh0+KE

e0+IPE+IGE

+KEg0+KE

b0

Deposits +rd*(1+rd)*ME

h

+rg*BEg+TE

+MEe*(2rd-3re)

-rd*MEh

-TE+rd*DE(3) -rg*BE

g -ME

e*(2rd-2re)-rd*DE(3)+re*ME

e-rd*rd*ME

h 0

Loans +BEg-TE -LE

e+LEe -BE

g+TE +LEe-LE

e 0

Net worth -KE

h0

-rd*(1+rd)*MEh

-DEg-rg*BE

g

-KEe0+(3re

-2rd)*MEe

-pEe+TE

+rd*MEh-rd*DE(3)

-KEg0

+DEg

-TE

+rg*LEg

-KEb0+(2rd-3re)*ME

e +rd*DE(3)+rd*rd*ME

h -KE

h0-KEe0-pE

e

-KEg0-KE

b0

Sum 0 0 0 0 0 3.7 Final remarks In the last three cases examined in section 3, the circuit illustrated the possibility to take financial liabilities out of the balance sheet of the Government through mixed financing (3.4) and, more importantly, the influence of households’ savings as a leakage from the circuit (3.5), which can in part be countered by a deficit of the Government (3.6)48. The difference between initial and final finance appears in the comparison between paragraphs 3.1.1 and 3.2.1 on the one hand and paragraph 3.1.4 and 3.2.3 on the other. When one considers the effect on the net worth of the economy, the results obtained show a formal similarity but cover different realities. This is shown in the Table 36 in below, summarising the main outcomes in the 5 cases considered.

Table 36: Comparison of different mixes of financing with and without savings and interest

Pure Private

Pure Public Mixed Mixed with

savings

Mixed with savings and

interest Net change in assets IPA IGB IPC+IGC IPD+IGD IPE+IGE

Corporates IPA 0 IPC IPD IPE

State 0 IGB IGC IGD IGE

Net change in net worth πAe πB

e πCe πD

e πEe

Corporates πAe πB

e–TB πCe+MC

g-TC πDe-SD

h-TD πEe-TE-NIEe

State 0 TB TC-DCg TD-DD

G TE-DEg-NIEg

Households 0 0 0 SDh DE

g+NIEh Debt (end of the circuit) 0 0 0 0 0

Corporates 0 0 0 -SDh 0

Banks 0 -LBg+TB LC

g-TC LDg+SD-TD 0

State 0 -LBg+TB -LC

g+TC -LDg+TD -BE

g+TE Households 0 0 0 0 +BE

g-TE

48 Or private corporate debt if private firms are sufficiently optimistic to accept to keep a debt to households at the end of the period.

- 28 -

To facilitate comparison, let’s first make the hypothesis that the volume of investment financed, corresponding to the change in net assets of the whole economy is the same in all cases in both real and nominal terms and thus corresponds to an equal increase in real net worth. Then Table 36 shows that in the case of pure private financing this is financed only by revenues collected from the users in such a way as to accumulate the corresponding profits in the net worth of the corporate sector, who also has the full amount of the investment in its net assets. In the example studied, no sector remains indebted at the end of the circuit. The case of pure public financing is symmetric for what concerns investment, which is booked entirely in the balance sheet of the Government. However, to the extent that it was assumed that the Government finances part of the investment by a deficit, it keeps a debt at the end of the circuit, corresponding to the initial money creation less the amount of money destroyed by the payment of taxes. This balance remains as a profit in the balance sheet of the corporate sector.

In the case of mixed financing it was assumed that the investment could be booked in the balance sheet of the corporate sector, which finances it in part with the user revenues and in part with a contribution from the State. The latter is financed by deficit, but this is going to be initially lower than in the case of pure public financing because it only concerns the current expenditures of the year, not the full amount of the investment to be financed49. At the end of the circuit, the State will have increased its total debt by the full amount of the investment not covered by user revenues (IG).

In the case of mixed financing with savings, the difference with the previous case is that now the corporate sector remains indebted towards the banks at the end of the circuit by the amount that households keep in the form of deposits. This is one of the nice illustrations of the circuit, showing that as long as household save in liquid form, enterprises cannot recover all the money initially put into circulations and must therefore remain indebted towards banks or towards household at the end of the circuit. Finally in the case with interest, the previous results change due to the presence of positive interest rates that illustrate the competition for households’ savings between the rate of interest paid by banks and the rate of interest paid by the State50. This allows the State to collect part of the households savings that were kept in liquid form in the previous case and therefore illustrates the case of part financing of investment by accumulated savings, the counterpart of which is the accumulation of debt of the State towards households, which was not there previously. It can be observed that in any case interest rates represent a net drain of resources from the banking sector to the rest of the economy, summarised in Table 36 by the acronym NI that stands for Net Interest. This shows the importance of including the banking sector in the Kalecki relation examined in relation 1 above. The discussion above showed that in principle it would be possible that the real and nominal volume of investment financed could be exactly the same in all cases and that, according to the case, the distribution of assets and liabilities in the economy would be different with more or less of the investment and debt booked in the balance sheet of the private sector and/or of the State. However, both the nominal and the real amount of the investment financed depend on the expectations of firms about costs and demand and would differ according to the way the investment is financed. As argued in par. 4.3.2, if the private producer will fix capacity at the level that maximises his expected profits, he will equate marginal cost with expected marginal revenue and not with expected

49 The effect on the state budget is similar to that that would be obtained in case public investment would be accrued to the years when it is in activity. 50 The model of section 2 was simplified by assuming either debt finance sold to the central bank or financing by taxes. Therefore most of the discussion is developed with the help of a single interest rate, which is the one paid by enterprises on bonds to households. However, for the calculation of net and real profits, the interest paid by enterprises to banks was also taken into account.

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price. This means that the prices will differ by the monopoly margin from their pure competition level even for a given capacity. In addition, as argued in 4.3.1, normal profits of the private sector alone can be strictly higher than inefficiency rents of the public sector when the private sector takes the traffic risk and the latter is high and can be better diversified by the public sector. From the welfare point of view, when the investment cost of private sector provision is higher, either for good (with reference to the symbols used in paragraph 4.3, because of a high πe) or not so good reasons (high πM), pure public provision of infrastructure is preferable, although sometimes this choice is precluded due to exogenous budgetary constraints. Even if there is no difference in unit costs, i.e. ( rB

q = π A + π Ae , in relation 34 in par. 4.3.4) the private

producer can in any case do no better than covering his full costs (investment plus operation and maintenance), whereas the State can implement the solution where price just covers short-term variable costs, which entails a much higher demand (in chart 3 of paragraph 4.2.1 QSBO versus QBE).51 In particular if, given a certain affordable level fixed for the toll, which will depend on average revenues and their distribution (and on the relevant value of time), expected traffic is below the break-even level, the project would not be fully undertaken under private financing and therefore pure or mixed financing by the public sector should be considered. With a toll and an expected traffic below the break-even level, private investors would however bet only on an investment level that can be covered by the revenues they can generate. Therefore one would have in any case IPA<IGB when Q<QBE. Thus, total money created in the case of private financing would be less than that created by public financing and the same would be true for investment. Finally one can mention the possibility that the unit cost of investment by the private sector is lower than that of the public sector (see relation 34 in par. 4.3.4). This implies that the “inefficiency rent” of the public sector is higher than profits of the private sector. This case represents the standard justification for the private sector involvement in the provision of infrastructure. From the cost-benefit point of view, when the investment cost of private sector provision is lower, private provision is better if estimated traffic is high enough. The cost of public provision could instead be lower if the public sector had superior knowledge of future demand, which could be the case when several parallel investment are undertaken that modify the traffic patterns, such as in the case of the development of a full new network. It results from the above discussion that the parameters involved in the comparison between pure public and pure private provision of infrastructure are expected traffic demand, actual traffic demand, normal profits, inefficiency rents and monopoly profits. The case for full public financing of infrastructure appears more solid than usually thought. Apart from the case where the two solutions have equivalent unit costs, only when private sector traffic expectations are correct and validated by the banking sector and inefficiency rents exceed private sector profits (including the remuneration for traffic risk) private provision of infrastructure is preferable. Otherwise the private sector will either invest at a higher unit cost or invest less in absolute terms (or both). It is clear that in the New Member States, where traffic demand is particularly uncertain given the development phase in which most networks are, income and willingness to pay are low and generally non competitive market structures prevail, all conditions are there a priori for the pure private provision of infrastructure to be an inferior solution. Nonetheless, essentially for ideological reasons, including variations on the theme of Maastricht fiscal constraints, private financing of transport infrastructure is frequently proposed in these countries as the general panacea for solving the transport infrastructure gap, at “no cost” for the State.

51 Despite it is not the case in theory, de facto in cost-benefit analysis, the case of null profits is the reference case to which all other cases are compared (See discussion in Cingolani, 2009, section 2). In the example of par. 4.2, the conditions for this reference case to emerge are that expected traffic is exactly equal to actual traffic and to the break-even traffic level QBE and that firm’s expectations are validated by banks, otherwise either firms would not invest as much as the Government when expected traffic is below QBE, or they could realise monopoly profits and one would not be in the reference case anymore.

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4. Producers’ expectations of the monetary cost of output and their welfare comparison The circuit is a sequential scheme of analysis where the initial causal factor is given by firms’ expectations of monetary costs to be incurred to supply for different levels of household’s demand. The component of expected profits feed the “animal spirits” that, through the demand for credit addressed to the banking sector in the first phase of the monetary circuit, ultimately determines the level of effective demand. The latter, expressed in monetary terms, has an impact on welfare both through its price and its volume components. The analysis of these welfare aspects, to be developed in particular in the light of the efficiency criteria, implies a comparison between the neoclassical equilibrium, where maximum efficiency implies the zero profit condition, and a larger set of non-neoclassical equilibria, where this condition is not fulfilled. Since monetary equilibria are undetermined and therefore do not allow for an obvious definition of efficiency (Graziani, 1987b), one can use the neoclassical equilibrium as a tool to measure efficiency. If one assumes that the banking sector supports the bets of enterprises implicit in their production plans, there is no obstacle for enterprises to realize their plans in the monetary circuit. In this sense, enterprises plans reflect an equilibrium. In comparing two different suboptimal equilibria with different levels of expected demand, one can thus compare the level of the monetary costs expected at the beginning of the production process, and particularly the level of expected profits (which will be realised as long as banks supports entreprises’ plans), to the level of profits that would prevail under a neoclassical perfect competition equilibrium. 4.1 Expected profits: equilibrium and disequilibrium In the neo-classical tradition, equilibrium is defined as a point of maximum efficiency, like point OE in the first figure in Chart 2 below.

Chart 2: Marginal and structural change

"Marginal" change

Individual 1

Ind

ivid

ual

2

E1

E2

OE

"Structural" change

Individual 1

Ind

ivid

ual

2

D1

D2

OD

OE

If in equilibrium the conditions of maximum efficiency prevail, the economy finds itself on the utility

possibility frontier. In any of these points, noted OE in the first chart, any change can at best achieve the same level of utility prevailing before the change. The real economy normally does not reach these ideal equilibrium conditions (for instance at OE and on any point on the frontier profits are stable at zero). 52

Suppose the real economy is in E1. A marginal change moves the economy from E1 to say E2. The project is profitable although E2 is not on the frontier. E2 is better than E1 because both individuals consume more. Nothing changes on the utility possibility set of the economy.

A structural change can impact on the utility possibility set and moves it outwards. The economy moves from the (“sub-optimal”) equilibrium D1 to the (“sub-optimal”) equilibrium D2. Again the project is profitable because D2 is better than D1. D2, although “sub-optimal” with respect to OD, is better than OE.

52 Different ways have been followed to define this distance Allais (1989 [1981]), see discussion in section (2) of Cingolani (2009), which draws on.

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For ease of reference, any point below the possibility frontier such as E1 could be qualified as a disequilibrium, although as long as there is no demonstration of the stability of the neoclassical equilibrium, these “disequilibria” could also be seen as “points of rest” of unspecified dynamic processes and could thus be retained under a more general definition of equilibrium (Cingolani, 2009, section 2). For instance, Massé (1954, p. 87) argued that points below the possibility frontier are relevant for Keynesian analysis, which is logical, since these are points of unemployment and suboptimal capacity utilization, possible equilibrium outcomes for Keynesian analysis, including in the long-term. These suboptimal points are necessarily associated to prices, which, by definition, must also be different from the ones that would guarantee the neoclassical optimum. In the formation of producers expectations on the level of monetary demand, welfare aspects concerns not only prices, but also quantities, which can be above or below their full employment level53. These “non-equilibrium” prices imply also a level of remuneration of the factors of production that is different from the neoclassical one, as it is implicit in Kahn (1935). Therefore, below the possibility curve, one should expect profits to diverge from their neoclassical “equilibrium level”. Indeed, interpreting the charts above as a map of the possible production choices open at the time when producers form their expectations, the walrasian deterministic case of a competitive industry with free entry, is characterized by the fact that in the long-term profits would tend to zero, a condition of maximum efficiency. If uncertainty is considered, expected profits should include a risk component covering random fluctuations in both costs and demand factors. Massé (1949, p. 193) noted that that in the neo-classical equilibrium, the rate of profit (marginal efficiency of investment) should be equal to the rate of interest (equal to the marginal rate of time preference) and to the marginal liquidity premium. The equilibrium rate of interest should thus reflect both a remuneration for abstinence and a reward for liquidity renunciation. Irrespective of the presence or absence of risk, the level of profits that producers would expect in choosing a point below the maximum efficiency curve, could be taken as a rough indicator of the distance from neoclassical equilibrium. Even in a deterministic context, in a “classical” long-term competitive equilibrium, profit will set at a positive level π, which is equalized for all sectors (“normal profit”) but may be different from zero and, in a dynamic context, could exceed also the expected cost of investment (Petri, 1989). In the cost expectations of producers there could thus be an element that reflects their capacity to extract monopoly or other types of rents, a point that is sometimes neglected in welfare analysis and that seems important in the context of a discussion on PPP, all the more if one retains the versions of the circuit where expected profits can be monetized, as done in section 3 above (Renaud, 2000). In the following, an attempt is made to discuss the factors shaping producers’ expectations, distinguishing price and volume effects, in order to give a judgment from the welfare point of view on the level of effective demand generated under different financing schemes. It is assumed that producers expectations of household’s demand depend on their expected revenues and their distribution and on expected unit production costs. The resulting level of monetary output supplied I is decomposed into its price p and quantity Q elements: I = pQ , where, in line with the asymmetric position of producers and consumers retained in the circuit, producers, who are the one having access to credit, decide both p and Q.

53 A policy of promotion of public investment may increase the possibilities for expanding output as perceived by the producers if for instance there is confidence that the Government can finance it sustainably. In addition, technical process brought by the investment will change the technical parameters of the economy, bringing to a productivity increase simply by the replacement of old equipment with new one. For instance, in the case of transport, even if technology is constant, by reducing transport input costs. In these cases of “structural change” the possibility frontier is not fixed but it can move as a result of the decision to invest, as illustrated in the second figure in chart2 above.

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If two ways of financing infrastructure are compared, for instance A (say private) and B (say public), breaking dow the associated levels of effective demand into a price and a demand component, 9 cases are possible in principle, as illustrated by table 37 below. Based on the efficiency criteria, in cases (1), (7) and (8), mode A is preferred to mode B54(tan colour) because the quantity supplied with A is higher or equal than B or because the price is lower or equal, but only in case (8) effective demand, which is the product of the two, is higher for A than for B, implying both a larger real amount of investment and a higher unit cost.

Table 37: Effective demand: possible cases of price and quantity combinations

QA = QB QA < QB QA > QB

pA < pB (1) A f B

(IA < IB) (4) ?

(IA < IB) (7) A f B

(IA ? IB)

pA = pB (2) A ≈ B

(IA = IB) (5) A p B

(IA < IB)

(8) A f B (IA > IB)

pA > pB (3) A p B

(IA > IB)

(6) A p B (IA ? IB)

(9) ? (IA > IB)

In case (1) the cost of A is lower because the price is lower, although the quantity supplied is the same. Therefore A is preferred because it entails a higher efficiency55. The same is true for case (7) where both the quantity supplied is higher and the price is lower. As discussed below in section 3.1.4, this illustrates the fact that although in the circuit the argument is generally developed at “constant efficiency”, in fact, real effects count and any monetary creation which is not backed by a creation of real value (real revenues consumed or accumulated) is only bringing to an accumulation of financial or inflationary unbalances. In a similar way, irrespective of the total cost, in cases (3), (5) and (6) in yellow, mode B is preferred to A. In cases (4) and (9) in green, nothing can be said without making assumptions on preferences, in case (2) in turquoise, the two modes are indifferent. To discuss the merits of different financing modes in the above cases, one can rely on a partial equilibrium framework, a simplifying assumption that appears acceptable in the context of the formation of producer’s expectations. In such context, it is convenient to focus first on the determination of the quantity supplied (par. 4.2), which would apply for instance when considering the financing of a full programme of road construction, focusing first on the case of pure real toll PPPt (4.2.1) and derive the more general case after (4.2.2). The price comparison for the case of a fixed quantity (par. 4.3), would be relevant instead for the case where it was already decided that a certain road section is to be built and the question is how to procure this section at the lowest cost. In this case, the argument applies equally to all cases of PPP: real or shadow tolls, as well as availability payments. 4.2. Variable capacity supply When the amount of infrastructure to be built is not decided yet, capacity is variable, as in the cases (4) to (9) in Table 37. In these cases, the quantity supplied will depend from the costs and the way they can be recovered by the revenues generated by the investment. One can develop separately and in more detail the option of PPP financing through a pure toll PPP, where the investment costs must be covered entirely by revenues coming from the users, from the other main options of mixed

.54 The symbols f and p in the table indicate respectively “preferred to” and “not preferred to” and the symbol ~ “indifferent to”. 55 Graziani (1987) discusses the notion of efficiency in the context of the monetary circuit.

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financing with Government support, with real or shadow tolls or availability payments, where the revenues covering the project cost come in majority from the State budget. 4.2.1 A pure toll PPP: Focusing on the particular case of pure toll PPP, the amount of infrastructure that a private entrepreneur is willing to supply can be discussed in a partial equilibrium setting, since most producers will take decisions mainly based en expected developments in their specific sector. In particular the amount supplied will depend on the producer’s expectations of the revenues he can extract from the users. The latter will depend on its expectations of the average incomes of the population concerned and their distribution. To elaborate on demand, one can rely on the analysis of René Roy (1930, 1933), who used the Pareto distribution in his econometric analyses of the links between market demand and income. This allowed him to develop a demand theory based on the idea that consumers establish a hierarchy amongst their needs, allocating their income first to the classes of goods of first necessity and then to the other classes of goods. This theory provides an alternative to the standard neoclassical treatment of demand and is seen by authors such as Lavoie (2005) as a forerunner of the “lexicographic” approaches to consumption choice retained in the post Keynesian literature. Assume with Roy that for all individuals in the population there is a single and same quantity ql that represents the satiation level for a certain good. Then if income follows the Pareto distribution, with parameters (A,α) (see relation (1) of the Annex), taking ρ as the revenue spent on “first necessity goods”, it can be shown56 that the market demand function for a superior goods, linking the quantity sold Q to price P, is given by:

Q =A

α −11

ρα−11P

1−1

1+qlρ

P⎛

⎝ ⎜

⎞

⎠ ⎟

α−1

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥

(28)

Roy derived the price elasticity of this demand function (see relation 15 in Annex I), which he showed to be comprised between 0 and 1, implying by construction a price inelastic demand. While this restriction may appear arbitrary, it reflects Roy’s (1930, pp. 146-151) econometric findings on the tariffs on urban transport in France in the 1920s and is a result not unusual in more recent studies on transport (see for instance Oum, Waters and Young, 1990). Concerning costs aspects, it can be assumed that total long term marginal costs are made of two constant components, a long-run variable and a long run fixed cost IC, depending on capacity Q. Assume variable costs are linear as a function of installed capacity. If variable costs are VC, unit variable costs are UVC=VC/Q then the long-run marginal cost μ can be approximated by:

μ =VCQ

+α ICQ

r 1+ r( )N

1+ r( )N −1 (29)

where r is the discount rate and N the life length of the equipment in years (see Annex II). The curves (28) and (29) have been illustrated in the quantity-price plane, respectively in red and blue in the chart 3 in the next page. The parameters used to draw the curves are shown in the box appearing on the charts. Taking α=1.6, r0 = 0.6, and the scale parameter = 950, they imply a population of 2151 with a total revenue of 3442. Average income is 1.6, whereas the median income is 0.93. The satiation level is supposed to be attained for a consumption of 150 trips (it is assumed that 1 km of

56 Roy (1930). Given that the argument is technically interesting and the review in which it was published is not available in standard electronic library packages, its main steps have been summarised in Annex I.

- 34 -

motorway is built), which corresponds to a price of 0.4 cents. The income level starting from which the consumer starts buying non-necessary goods is 1.57

Chart 3: Partial equilibrium with inelastic demand Transport demand and marginal costs with Pareto distribution of incomes

QBE=12824

QBL=26647QSBO=51503

0

0.025

0.05

0.075

0.1

0.125

0.15

0.175

0.2

4000 8000 12000 16000 20000 24000 28000 32000 36000 40000 44000 48000 52000 56000 60000Traffic in vehicles per day

Tarif

f and

mar

gina

l cos

t in

EUR

per

km

Demand: R=P*Q Marginal Cost LT Marginal Cost ST

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+

−−

=−

−

1

1 1111

α

α ρρ

ρα PqPAQ

l

Demand ParameteA = 950α = 1.6r0 = 0.6Pop = 2,151Gini = 2.67Y = 3,442yavg = 1.60ymedian = 0.93ql = 150ρ = 1Incr = 0.00421Pl = 0.00400

μ=VCQ

+γICQ

r 1+r( )N

1+r( )N −1

Cost parametersMaintenance (CV) 150000 EUR per yearInvestment (C0) 3000000 1 lane (<15000) EUR

7000000 2 lanes (<35000) EUR12000000 3 lanes (>50000) EUR

r 3% %N 25 YearsQ 25000 Vpdd/year 365 days/yearCV/Q 0.016438 EUR/VPD Vpy

Assuming that conditions for pure competition prevail and that profit maximization prevails58, a PPP financed entirely by real tolls will be dimensioned by the private sector for a traffic level of QBE, corresponding to the equality of price with expected long term marginal cost. With the parameters retained in the chart, this implies a traffic of some 12,000 vehicles per day and a toll of PBE equal to EUR 10 cents per km. The amount of effective demand generated is shown in the chart by the green dotted box. 4.2.2 Adding Government support: When Government support is available and capacity is variable, the private sector will dimension the investment taking into account not only of the expected revenues it can collect from the users, but also of those he can expect to come from the Government. In the case of real or shadow tolls, these depend on the money that the government has agreed to spend on each traffic unit and on demand. In the case of availability payments there is no relation with demand and revenues depend only on Government expenditures per unit of traffic. At the limit, if the public sector undertakes the project only with own funds, it can opt for the capacity corresponding to the level of demand that equals price to “short-term marginal cost”, an optimality rule often encountered in the second best literature (Jansson, 2000, pp. 183-185). With the parameters retained in the chart 3, this second best optimum, which can be seen as a “full capacity” level, corresponds to a traffic QSBO of 51500 vpd, with a long-term marginal cost of CSBO= 4 EUR cents per km. The Government can either cover this cost entirely or decide to give a traffic subsidy of 57 The charts refers to 1 km of motorway and income can be considered as hourly income. Then minimum income corresponds to EUR 96 per month, median income to EUR 149 per month and average income to EUR 256 per month. 58 Retaining profit maximisation may seem peculiar in a post Keynesian context, however the point concerns here the formation of expectations, where this may be accepted as a first approximation. Retaining profit maximisation allows comparing an ideal case of pure competition to other possible market outcomes, including pure monopoly. The reality will be somewhere between the extremes. In Cingolani (2006) a similar example is developed assuming cost coverage only (not profit maximisation). It brings to the same conclusion that under reasonable values of the parameters, cost coverage implies that a toll motorway should be priced at a toll per km several times above the corresponding average value of time.

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CSBO-PSBO= EUR 3.2 cents per km, letting the difference being recovered by a concessionaire as a real toll. At this level of traffic, effective demand is given by the dotted box in orange Always under perfect competition, with shadow tolls or availability payments, depending on the toll level, any level of demand between QBE and QSBO can be satisfied. If however there is a budget limit at CBL, then only a level of demand lower than QBL=CBL/PST is viable59, generating a level of effective demand given by the dotted box in brown. We thus have less effective demand with the private sector provision combined with a budget ceiling, a conclusion that has macroeconomic consequences for employment and thus for the welfare comparison of the various funding modes. 4.3 The supply of a fixed capacity When a fixed capacity is to be supplied by the private sector, the possible cases are (1), (2) and (3) in Table (37). In these cases, the comparison about the cost of alternative financing modes depends only on price. This allows to extend the discussion to the case of “non-competitive” pricing behaviour. The revenues deriving from the sale of any good will always be equal to costs, which, for a given quantity produced, will cover the “equilibrium” remuneration of the various production factors. If land, capital and labour, and their “competitive” remuneration r, i60 and w, are considered, the price of any good can be decomposed into:

p = r + i + w + m (30)

where m is a “margin” over purely competitive factor remuneration, which can in principle be appropriated by any of the three factors of production61. If in addition to its “normal” profit remuneration, the entrepreneur can exert some market power, he will find himself in a position to sell at a price that generates an extra-profit πe even in the long run. Moreover, in a dynamic context, various forms of quasi-rents rq can emerge. Therefore the margin m in (30) can be seen as comprising “normal” profits, extra-profits and quasi-rents62:

m = π + π e + rq (31)

Assuming competitive markets for labour, credit and land, r, i and w will be the same for an infrastructure financed from the private or from the public sector. Therefore, when the quantity to be supplied is fixed, the comparison of prices or costs between private or public provision of infrastructure reduces to a comparison between the margins over the competitive production factor remuneration in the two cases: mA and mB.

mA >=<

mB → π A + π Ae + rA

q >=<

π B + π Be + rB

q (32)

The following paragraphs discuss each component of relation (32). 4.3.1 Normal profit component (π) : “Normal” rates of profits sought by a private sector investor entering into the business of infrastructure provision could be considered to be of the order of at least 59 As noted above, the case of availability payments can be assimilated to that of shadow tolls by fixing the subsidy coming from the Government at the same aggregate level than the revenue that, given traffic, would be perceived with shadow tolls. 60 Capital remuneration i comprises an interest rate element covering the cost of borrowing. In the long-run and with free entry with no uncertainty this capital remuneration would tend to the interest rate (zero profit condition). 61 See the discussion on vertically integrated sectors in par. 6.1 of Cingolani (2009). One of the interesting points discussed by the theory of the circuit is the extent to which this margin can be monetized (see Renaud, 2000 and, above, paragraph 3.1.2). 62 As mentioned above, in a static framework of analysis, the distance of a particular situation from the “walrasian” optimum can be approximated by the distance of this margin from zero. This departure from perfect competition likely implies that other competitive equilibrium conditions will not be fulfilled either, in particular the condition for full employment. Indees, when the rate of profit diverges from the competitive free-entry level, which in the long-term is zero, other Pareto optimal conditions are also broken (Lipsey and Lancaster, 1956-57).

- 36 -

some 25%. In principle the public sector is non-profit. Therefore if A is the private sector and B is the public sector one should expect πA>πB, an inequality that remains true whatever the form of PPP that is considered. However, in the case of toll-motorways and with shadow tolls where traffic risk is transferred to the concessionaire, there is another factor that is quantitatively more important. It results from the fact that when the private sector becomes concessionaire of a single element of infrastructure it must cover traffic risk on that piece of infrastructure, whereas the State can diversify this risk over the whole network. This is the classical argument of Arrow and Kurz(1970)63. Based on the risk model retained by Quinet (1998, Annex 6.2), Cingolani (2006, p. 16, section 4.2 and p. 36, Annex 4) calculates that, under reasonable assumptions for the parameters involved, covering traffic risk for a 20% traffic dispersion (standard error/mean) can require a margin that could easily represent 40% of the cost of the project. This cost element would be on the contrary diversified away in case the project is undertaken by the State who can spread the risk on the whole network. 4.3.2 Extra-profit component (πe): In the case of a toll motorway, the users have in general no other choice than paying the toll if they want to use it. Therefore a toll motorway can be assimilated to a case of pure monopoly (Ragazzi, 2008, p. 16), in which by definition price will exceed marginal cost and the quantity supplied will be less than the quantity prevailing in a fully competitive equilibrium. It is known that in this case under profit maximization the monopoly equilibrium will imply that the percentage difference between the price P and marginal cost μ that would prevail under competitive conditions is equal to the inverse of the price elasticity of demand λ (cf. Lerner (1934), or, for a more recent treatment, for instance Picard (1998, p. 358)).

P − μμ

= −1λ

(33)

To give some examples, for a price elasticity of -0.5 the monopoly mark-up is equal to 100% of the marginal cost, for a price elasticity of -2, it is 50%, for -3 it is 33% etc. This corresponds to the usual equilibrium condition for a monopoly, which equals marginal revenue to marginal cost. The inverse of the price elasticity of demand measures the ”extra-profit” mark-up under pure monopoly. For the demand relation (28), Roy derived the price elasticity of demand, but, as noted, the demand curve (28) is inelastic by construction (λ<1), reflecting the peculiarities of the transport sector. In general in these cases the marginal revenue is always negative and cannot be set equal to the long-term marginal cost. The monopoly would thus have an interest in always increasing the tariff up to infinite values (Van Ommeslaghe, 1980-81, p. 25). However, in order to illustrate the choices implied by (33), what would be the monopoly equilibrium QM under an elastic demand, could be compared to the competitive solution QBE, as the former can be seen as an upper bound for demand (or a floor for price) given that with an inelastic demand price will probably be higher. The chart 4 in the next page, illustrates this comparison. It shows that, out of competitive conditions, which are in fact difficult to be realized in a natural monopoly, the price will be higher and the quantity supplied lower (QM) than what would a private producer supply under competitive conditions (QBE), which was seen to be lower than what the public sector may supply (QSBO). Therefore a toll PPP will be priced by the private sector with a monopoly mark-up on marginal cost whose size will depend on the elasticity of demand. The quantity supplied will be lower the higher this

63 See also Ragazzi and Rothengatter (2005) as well as the papers presented at the EIBURS meeting on Traffic Risk in Concession Projects, EIB Luxembourg, 13th June 2008.

- 37 -

margin. In the cases of shadow tolls and availability payments, the monopoly extra-profit would presumably be lower but is likely to be still positive.

Chart 4: Partial equilibrium with elastic demand

Elastic demand and cost

QM=2000 QBE=11000

QSBO=57000

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

0.3

0 10000 20000 30000 40000 50000 60000

Demand and capacity in vehicles per day

Pri

ce a

nd

co

st in

EU

R p

er

km

LT Marginal cost Demand Marginal revenue Series4

Demand ParametA = 550α = 1.5

Cost ParametersTraffic (Vpd) Fixed cost (EUR

1000 600,000 5000 2,500,000 7000 3,500,000

10000 5,000,000 15000 6,000,000 20000 7,500,000 30000 8,000,000 40000 10,000,000 60000 12,000,000

Maintenance (EUR/KM)200000

P =QA

⎛ ⎝ ⎜

⎞ ⎠ ⎟ −

1α

To conclude on this point, it can be noted that in a pure public sector solution, the assumption that the Government is “no-profit” would imply that it should also be “no-extra-profit”, therefore in principle also for the extra-profit price component one would expect that πe

A>πeB.

As emphasized by Ragazzi and Rothengatter (2005), from the point of view of the public sector and of the State budget, the choice on the level of tolls to be required from the users appears much as a question of deciding whether tolls should be considered taxes, in case they are set in order to cover costs or more, or tariffs, to be set in order to reach a social optimum. 4.3.3 Quasi-rent component (rq): This component of the mark-up can be seen as including any other element not included in par. 4.3.1 and 4.3.2 above. For instance it can cover any cost due to the X-inefficiency associated with the provision of services by the public sector, but also, for instance, “corruption costs”. The latter are normally thought to be higher when the public sector tenders works or maintenance services to provide directly the infrastructure, although they can in principle arise also in a private concession. However, since there are no reliable estimates for these potential element of costs, which relate to the black economy, they will be assumed to be either zero or equal in the two cases. Therefore, due mainly to X-inefficiency factors, which can be expected to be lower with private sector provision (be it real tolls, shadow tolls or availability payments), in general for the “quasi-rent” component of the margin, one can assume that rq

A<rqB.

4.3.4 Summary: Retaining thus the simplifying assumption that rq

A=πB=πeB=0, the price/cost

comparison between public and private provision of infrastructure given fixed quantities to be supplied depends on whether the quasi-rent of the public sector exceeds or is inferior to the sum of the profits and extra-profits of the private sector.

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rBq>=<

π A + π Ae (34)

If one retains for example 20-50% for πA, depending on the type of PPP, and 20-30% for πeA, than

one can provisionally conclude that the public sector must be really inefficient to be preferable to the private sector, because it must have an rq

B in excess of 40-80%. As emphasized by the literature on Government failures in the provision of large projects, the component rq

B could be expected to be in general lower, of the order of 20% (Flyvbjerg, Bruzelius and Rothengatter, 2003). Therefore one would expect that on average private provision of infrastructure through PPP structures should be slightly more costly than with pure public provision when the quantity is fixed, which confirms the skepticism expressed by Sawyer (2005 and 2009). 4.4 Final remarks If the comparison between private and public support for the provision of transport infrastructure in the road sector is seen as a contrast between two sub-optimal states of the economy, in each case before and after the investment, then the resulting outcome in each case can be compared indirectly through a comparison with the neoclassical optimum. If the latter is recognised to entail a zero profit condition, then the mark-up expected under private of public financing could be taken as a first rough approximation of the distance of each result from the optimum. The discussion developed above in a partial equilibrium setting showed that one should rationally expect this mark-up to be higher under private infrastructure provision. This higher mark-up would logically be associated to a lower level of capacity supplied, either because of the negative slope of the demand function, (and/) or because of the difference between the competitive market outcome and the second best social optimum. In any event, whereas in the case of a fixed amount of infrastructure to be provided, the distortion brought by PPP is likely to concern only monopolistic pricing elements and is thus possibly of the second order, when the financing of a full programme of road transport infrastructure provision is considered, the scope of the programme that can be realized through PPP financing is limited by the amount of effective demand that the private sector can be expected to generate through its projected expenditures, and the latter is lower than desirable in the presence of budgetary ceilings on public expenditures, irrespective of whether PPP are realized with real tolls, shadow tolls or availability payments. This is because the amount of investment depends on expectations, and these integrate in turn the existing budgetary constraints. Therefore, in general, although in theory the comparison made in Table 36 could bring to the same amount of infrastructure financed at the same cost in each case, in practice this will not be the case, and in general infrastructure provision would be lower or equal under private financing than under public financing, particularly when budget ceilings are put on public expenditures. 5. Summary and conclusions This contribution examined the welfare implications of private and public support for the financing of road infrastructure when conditions for neoclassical equilibrium are not fulfilled. In this context, in line with post Keynesian theory, expectations should be considered as exogenous to the model and causal factors of its dynamics (Davidson, 1982-83). In particular, there is no guarantee that the expectations of the private institutional sectors of the economy (households, firms, banks), would be consistent amongst each other, and that they would result in equilibria of full employment and/or of

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full capacity utilization (expectational market failure emphasized by Massé, 1991[1965]; Guesnerie, 2000 and 2005; Parguez, 2008). In the macroeconomic model of the monetary circuit, the definition retained for money and banks provides a very simple explanation for the alleged causality of investment on savings, showing why, out of neoclassical barter equilibrium, investment can be financed either out savings created by the investment itself or out of previously accumulated financial surpluses. Several equilibria are possible depending on the debt levels and economic policy can play a positive role in discriminating between them (Graziani, 2003). The Kalecki identity confirms that the Government deficit increases private sector profits, in line with the circuit’s result that when investment is financed out of new monetary creation, Government financing can create the necessary savings in the private sector, that would not be created otherwise, when it can change the private sector’s expectations. Public investment can thus be seen as an exogenous and stabilizing source of autonomous expenditure that can help reducing the unemployment gap, in a way that goes in the direction of functional finance (Lerner, 1943). The above general macroeconomic principles, discussed in section 2, can be investigated in more detail with the help of an accounting model of the monetary circuit. This framework, examined in section 3, allows going further in the description of how the realization of a road infrastructure financed through a public private partnership impacts on the net worth position of each macroeconomic sector in the economy through the creation of real and financial assets and liabilities. The analysis is developed keeping a distinction between the three main cases of mixed financing by the private and the public sector of PPP with real tolls, shadow tolls and availability payments. Focusing on the main comparison between pure private and public financing (par 3.7), the conditions for the amount and cost of infrastructure supplied to be the same under private and public sector financing (IP=IG) are very restrictive. When the private sector does not anticipate sufficient profits from the investments to be undertaken, either the Government creates a deficit that will validate the expectations needed to undertake the necessary expenditures to restore the compatibility between the private sector expectations and the social needs, or the level of investment will be lower than in the case of pure public financing. This result is immediate in a model where households do not save, and it is reinforced by the presence of savings, which in fact create a leakage in the firm’s circuit of revenues. In the extreme case where Government focuses on compensating for the savings leakage only and not more, the solution with public financing of investment is equivalent to pure final financing by the private sector and the level of investment undertaken will depend on the private sector expectations of demand, i.e. could be lower than desired. In the cases of mixed financing, these results are independent of whether debt is booked inside or outside of the Government’s accounts. Since the net worth change will depend in the end on the expectations of the various institutional sectors and the way they combine, the different level of infrastructure that would be supplied under alternative financing modes can be further clarified with the help of the partial equilibrium analysis developed in section 4, based on realistic microeconomic configurations of costs and transport demand parameters. This analysis concerns the decision to be taken by producers and/or the pubic sector in the beginning of the circuit, which fixes the amount of infrastructure provided (and the level of economic activity) as well as its cost. It is argued that it is unlikely that PPP financing is preferable to straight public financing from a welfare point of view, the more so that the local regional income levels are low.

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Assuming that the capacity to be supplied is variable, as it is the case for instance when a programme of road infrastructure is planned, the comparison between various forms of possible PPP support depends on both unit cost and quantities, in particular expected profit margins and demand, which can be considered at the same time as expectations and realisations as long as the banking sector endorses the producers’ bets on the future. For instance, when the cost of infrastructure is fully borne by the user, such as in a pure toll PPP, the capacity that will be supplied by the private sector will depend from its expectations on solvent traffic and the latter will depend on the expected level of income of the users and its distribution (or, what in a first approximation is the same, the expected value of time of the users and its distribution)64. This points to an important policy conclusion of the circuit model retained, where profits can be financed ex ante by monetary creation and when these can exceed an “equilibrium “ level. In this case, private sector costs can increase and the capacity supplied be reduced compared to a public sector provision. In the event that private financing mobilizes existing savings that could also be mobilised by the Government, in principle at a lower cost, the capacity supplied and the effective demand created will be at best the same. When the length of the motorway to be built is fixed, as it is the case when financing is considered for a new project whose construction is already decided, the welfare comparison between the various PPP cases depends only from the unit costs of the private and of the public sector and/or from the way they combine. In general, under private financing, it could be expected that unit costs include a monopoly markup. It could thus be concluded that in the road sector PPP play essentially a role in mobilising part of the passively accumulated savings that the State is forbidden to attract directly because of debt ceilings. They have a softening effect on the Government debt constraints similar to that that could be reached if the Government was allowed to accrue investment like the private sector, but are a less transparent solution, because the relevant debt is not necessarily recognized in the balance sheet that services it and the budgetary ceilings remain in any case binding. Thus, contrary to a widely held view that PPP help removing existing constraints on public expenditures, they do not add anything to the level of effective demand, being in fact the other flip of the coin of restrictive budgetary policies. Debt and expenditure ceilings and the associated restrictive fiscal policies have effects on all sectors of public investment, and the lack of budget resources has been a permanent feature of European policies in the last 30 years, particularly in the transport field (See Cingolani, 2009, Chart p.34). This restrictive fiscal policy stance has been severely criticized by many post Keynesian observers including notably Arestis, Mc Cauley and Sawyer (2001), Halevi and Kriesler (2004), Parguez and Bliek (2007), and Parguez (2009), who pointed out that it does not take into account the need for managing long-term effective demand at macroeconomic level and that it tends to create a level of “natural unemployment” that keeps wage growth below that of productivity, perpetuating a policy induced long term stagnation of economic activity. The view taken here is that these policies, and the systematic use of PPP they imply in the road sector, can find a temporary justification until the transfer of the macroeconomic instruments to the EU continental level that started with the Monetary Union is brought to completion. In such case, the loss due to passive fiscal policies imposed temporarily at national level with restrictive fiscal arrangements linked to the Monetary Union can be more than compensated by the gains from the transfer of fiscal activism at continental level, where the fiscal instrument is notoriously more effective. However, if these policies become a permanent

64 Since the average value of time in the EU12 (NMS) is expected to be lower than in EU15 and the inequality of revenues higher, this implies that ceteris paribus the margin realised on an infrastructure built in EU12 will be higher and the quantity supplied lower.

- 41 -

arrangement, they can result indeed in “long-term stagnation” (Steindl, 1979), as confirmed by the growth experience of Europe in the last 20 years. PPP in the road sector could thus be viewed as a temporary and expensive mean to alleviate some of the effects of restrictive fiscal policies, whereas they should be replaced in the future by better and more active forms of coordination of public investment, an idea that will be developed in forthcoming research.

_________________________________________

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ANNEX 1: Expected demand when revenues are Pareto distributed Assume a certain population of N persons where income x is distributed according to the Pareto distribution65. This distribution is known to fit reasonably well the highest incomes and has been used notably by Roy (1930, 1933) in theoretical discussions of demand, because it is practical to handle in calculations. Pareto observed that the number of people earning a revenue equal or in excess of a certain amount x could be approximated by a hyperbolic function:

N x( ) = n x( )x

∞

∫ dx = Ax−α (1)

where α>0. From (1) it follows immediately that the total number of people in a given income class (comprised between x1 and x2, x1 ≤ x2) is:

N12 = N (x1) −N (x2) = Ax1

−α − Ax2−α (2)

By taking x1=r0 as the minimum income and x2 = ∞, (2) gives total population as:

N = Ar0−α −

A∞→0{

= Ar0−α (3)

To derive from (1) the more usual expression of a statistical distribution function, one starts from the population with an income lower or equal than a certain level x, which is:

NP ε ≤ x( )= N −N (x) = Ar0−α − Ax−α (4)

dividing by total population, one obtains the Pareto cumulative distribution function, where y is the percentage of population earning an income less or equal than x and r0 is the minimal income. The Pareto distribution is thus defined by:

F y( )= P ε ≤ x( )=N −N (x)

N= 1−

Ax−α

Ar0−α = 1−

xr0

⎛

⎝ ⎜

⎞

⎠ ⎟ −α

if x > r0 ; F y( )= P ε ≤ x( )= 0 if x ≤ r0 (5)

Its density, or frequency function, is:

f y( )=dF y( )

dy= −

xr0

⎛

⎝ ⎜

⎞

⎠ ⎟ −α−1

if x > r0 ; f y( )=dF y( )

dy= 0 if x ≤ r0 (6)

The Pareto distribution implies that the total revenue earned by people in an income class comprised between x1 and x2, x1 < x2, is given by:

xdNx1

x 2

∫ = −A αα −1

1x

2

α−1 −1

x1α−1

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥ (7)

Assume again that x1=r0 is the minimum income and calculating (7) for x2 = ∞, the total revenue of the whole population is given by:

R = xdNr0

∞

∫ = −A αα −1

1x

2

α−1

→0{

−1

x1α−1

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

= A αα −1

1r0

α−1 (8)

65 Pareto Vilfredo (1965), see also Steindl (1990 [1978]). Pareto actually proposed 3 different distributions of increasing complexity to fit his data on fiscal declarations, although only the first one, more practical to handle in calculations, is usually referred to as the “Pareto law” for the distribution of income. Enjoyable portraits of Pareto and other great economists of the past can be found in Ruffolo (2000). See in particular pp. 213-232, “Pareto lo sprezzante”.

- 46 -

Dividing (8) by (3), the average income of the same population is given by:

x =α

α −1r0 (9)

an expression that links the average income x to the minimum income and the inequality of revenues measured by the ratio α/(α—1), which is actually the Gini coefficient for the Pareto distribution, a well-known index of revenue concentration. One can note that income inequality increases with α/(α—1), or with 1/α, not with α, as Pareto originally thought (Roy, 1965). The median income xM can be obtained by solving:

AxM−α =

Ar0

−α

2→ xM

−α( )−1α =

r0

−α

2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

−1α

(10)

thus:

xM =r

0

−α

2

⎛

⎝ ⎜

⎞

⎠ ⎟

−1α

= 21α r0 (11)

The ratio between the mean revenue and the median one is thus:

xxM

= 2−1α

αα −1

(12)

Since α is assumed to exceed 1 to obtain the convergence of the integral in (6), and since it is often found to be below 2, the level starting from which the distribution has a finite variance66, (12) illustrates how unequal is the income distribution given by (6) 67. For the parameter α=1.5, which was originally calculated by Pareto as fitting well the data on fiscal declarations he had available, (12) implies that the mean is about the double of the median, or that 50% of total population earn less than half the average income. Assume with Roy (1930) that for all individuals in the population there is a single and same quantity ql that represents the satiation level for a certain good. Then it can be shown that, if income follows the Pareto distribution, the market demand function for goods of “first necessity”, linking the quantity sold Q to its price P, is given by where (A,α) are the parameters of (1)68:

Q =A

α −1α

r0α−1

1P

−1

qlα−1

1Pα

⎡

⎣ ⎢ ⎤

⎦ ⎥ (13)

Taking ρ as the revenue spent on “first necessity goods”, demand for the superior goods is given by:

Q =A

α −11

ρα−11P

1−1

1+qlρ

P⎛

⎝ ⎜

⎞

⎠ ⎟

α−1

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥

(14)

66 Following Levy, Mandelbrot(1960) popularized the class of distributions where the right-end tail is given by (1) as the Levy-Pareto distributions. The L-stability implied by α≤2, played a role in the development of fractals through the concept of the self-similarity. 67 Dubbed naïve “from a modern statistical standpoint” by W. Feller (1971 p. 50, Vol. II), a judgment to which Mandelbrot (1961) apparently did not pay too much attention. Since Pareto believed that each factor of production is paid according to its marginal productivity, he interpreted the results of his empirical studies on the distribution of income as evidence of the great inequality existing in the distribution of talents (or intellectual capacities) in the population. This led him to dismiss the redistributive policies proposed at the time by the socialists. 68 This expression is valid for P greater than Pl=r0/ql, see Roy (1930 p. 123). If P falls below this limit, the minimum revenue ensures satiation for all individuals. The limit value Ql is given by: Ql = qlAro

−α .

- 47 -

Graphically (13) and (14) are two functions with negative slope in the quantity-price plane, with the demand for necessary goods (in blue in the chart) having a less steeper slope and showing an inflexion point relatively close to the minimum price, where it becomes inelastic to price.

Demand for first necessity (QFN) and other goods (QOG) as a function of price assuming Pareto income distribution

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

220000

240000

0.01 0.05 0.09 0.13 0.17 0.21 0.25 0.29 0.33 0.37 0.41 0.45 0.49 0.53 0.57

Price

QFNQOG

Demand ParametersA = 950.0 α = 1.6 r0 = 0.60 Pop = 2,151 Gini = 2.67 Y = 3,442 yavg = 1.60 ymedian = 0.93 ql = 150.0 Rho = 1.0 Incr = 0.0042 P0 = 0.00400

The parameters used to draw the curves in the chart above are shown in the box appearing on the same chart. Taking α=1.5, r0 = 2, and the scale parameter = 650, they imply a population of 230 with a total revenue of 1378. Average income is 6, whereas the median income is 3.2. The satiation level is supposed to be attained for a consumption of 100 trips (in the example it is assumed that 1 km of motorway is built), which corresponds to a price of two cents. The income spent on necessary goods is assumed to be 50% of the minimum income. In the case of a toll motorway one can assume that the relevant specification for the demand function is that for the non-necessary good, since in principle the alternative always exists to take a normal non-toll highway. This specification is thus retained. Roy (1930) showed that this elasticity could be derived as:

λ =Q −QS

Q=

α Pqlr0

⎛

⎝ ⎜

⎞

⎠ ⎟ α−1

−α

α Pqlr0

⎛

⎝ ⎜

⎞

⎠ ⎟ α−1

−1

=αxα−1 −ααxα−1 −1

(15)

where QS is the total consumption of the part of population whose revenue exceeds qlP (those that are satiated of this product), which can be expressed in the two cases by.

QS =d QP( )

dP= ql n r( )dr

ql P

∞

∫First necessity goods

1 2 4 4 3 4 4

= ql n r( )drρ +ql P

∞

∫Other goods

1 2 4 4 3 4 4

(16)

The term x in (15) represents the ratio between the price index P and the index of minimum (or limit) price Pl=r0/ql. As (13) shows, it can also be seen as the share of the minimum income that it is

- 48 -

necessary to allocate to the good in question in order to attain satiation at price P. The price elasticity becomes nil for x=1, i.e. when the market price is equal to the limit price Pl (or when the minimum income allows to obtain satiation). It increases up to 1 when the price increases above the limit level Pl. Intuitively, elasticity thus appears to increase with inequality: the more people are revenue constrained, i.e. the less they are able to achieve satiation, the more demand is price elastic. Roy (1930) also showed that the price elasticity of demand could be interpreted as the ratio of “constrained consumption” to total consumption, and would thus be comprised between 0 and 1. Annex II Long-term marginal cost To represent the cost aspects, assume that total long term costs are made of two constant components, a long-run variable and a long run fixed cost IC, depending on capacity. Assume variable costs are linear as a function of installed capacity. If variable costs are VC, unit variable costs are UVC=VC/Q and total costs will be given by (Babusiaux, 1990, pp. 166-178):

LTC =UVC * Q +r 1+ r( )N

1+ r( )N −1IC Q( ) (18)

where r is the discount rate and N the number of years. The long term marginal cost μ will then be:

μ =d LTC( )d Q( )

=VCQ

+r 1+ r( )N

1+ r( )N −1

d IC( )d Q( )

(19)

If the investment cost increases linearly with capacity according to:

ICIC0

=QQ0

⎛

⎝ ⎜

⎞

⎠ ⎟

α

→ d IC( )d Q( )

= α ICQ

(20)

then the long-run marginal cost can be approximated by:

μ =VCQ

+α ICQ

r 1+ r( )N

1+ r( )N −1 (21)

In a pure competitive market price will be equal to this marginal cost. In pure monopoly, price will be equal to the marginal revenue. This can be obtained from the total revenue R=PQ taking the total differential and dividing by R:

1 ⎟⎠⎞

⎜⎝⎛ −

=−

+=+=→+=λ

λλ

PQQ

PPQdQdPP

dQdRdPQPdQdR (22)

where the definition of price elasticity of demand was used: λ = −dQdP

PQ

→ dQQ

= −λ dPP

. In a

monopolistic market, the marginal cost will thus be set in order to equal (22).

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