INTRODUCTION

In underdeveloped countries, for project evaluation and programming, the distribution of factorson the basis of market prices is imperfect because there exist fundamental disequilibria whichis reflected in mass underemployment at existing wage levels, in the deficiency of funds atexisting interest rates and in the scarcity of foreign exchange at the prevalent exchange rate. Insuch a situation, the equilibrium level of wages would be much below the market wage, theequilibrium interest rates would be higher than their market rates, and the equilibrium rate ofexchange would be lower than its market rate. In order to overcome these difficulties J. Tinbergen,H.B. Chenery and K.S. Kretchemer have emphasized the use of shadow or accounting prices.

NEED FOR THE USE OF SHADOW PRICES

The price mechanism operates imperfectly in underdeveloped countries. Market prices do notcorrectly reflect relative scarcities, benefits, and costs. This is because perfect competition isentirely absent; structural changes do not respond to price changes; institutional factors distortthe existence of equilibrium in the product, labour, capital and foreign exchange markets; andprices fail to reflect and transmit the direct and indirect influences on the supply side and thedemand side. Markets are not in equilibrium due to structural rigidities. Labour cannot be

C H A P T E RC H A P T E RC H A P T E RC H A P T E RC H A P T E R

Shadow PricesShadow PricesShadow PricesShadow PricesShadow Prices

72

562 The Economics of Development and Planning

usefully employed because of the shortage of other cooperant factors. The rate of interestunderstates the value of capital to the economy. And disequilibrium persists in the balance ofpayments which cannot be reflected in the official rate of exchange. For instance, in sucheconomies wages are much lower in the non-organized agricultural sector while they are evenhigher than the opportunity cost of labour in the industrial sector where labour is organised instrong trade unions. In capital market; the market rate of interest is much higher than the bankrate, and the current rate of foreign exchange is much lower than in the black market. Thus“market prices, particularly those of the factor of Production form a very imperfect guide toresource allocation in underdeveloped economies, because there exist fundamental disequilibriawhich are reflected in the existence of massive underemployment at present levels of wages,the deficiency of funds at prevailing interest rates and the shortage of foreign exchange at currentrate of foreign exchange.”1 To overcome these problems, the use of shadow prices has beensuggested by economists for the allocation of resources in development planning, for evaluatingprojects and as a device in programming. To conclude with Streeten, “The call for the use ofshadow prices (or accounting prices) in planning for development stems from the obvious factthat actual market prices do not reflect social benefits and social costs. Some are fixed byadministrative fiat. Others are ‘free’, but influenced by restrictive practices or monopolies. Othersagain are influenced by quantitative controls. The shadow price is the price which would prevailif prices were equilibrium prices....”The fixation of shadow price for irrigation water is illustrated inFig. 1. The supply and demand for irrigation water is taken on thehorizontal axis and price in the accounting period is taken on thevertical axis. In the initial accounting period, OQ1 quantity of wateris needed by the farmers of the area. But the government issupplying only OQ2 quantity of water from the irrigation projectat OP1 price. In the next accounting period, the government mayset the price equal to marginal cost or charge the price of irrigationwater too low as part of its strategy of regional development. Afterthe low price OP2 is charged by the government, the demand forirrigation water will exceed its supply. In such a case thegovernment may adopt the policy of rationing of water. It mayask each farmer to limit their land-area for irrigating. In the nextaccounting period, the government uses OPS as the shadow pricewhich is the equilibrium price when OQS of irrigation water issupplied and demanded.

MEANING OF SHADOW PRICES

Shadow prices reflect intrinsic or true value for factors or products. J. Tinbergen defined themfor the first time in 1954 in these words: “Shadow Prices are prices indicating the intrinsic or truevalue of a factor or product in the sense of equilibrium prices. These prices may be different for differenttime periods as well as geographically separate areas and various occupations (in the case of labour).They may deviate from market prices.”2 In 1958, Tinbergen defined shadow prices as those that

1. UN, ECAFE. “Criteria for Allocating Investment Resources among Various Fields of Development inUnderdeveloped Countries,” Economic Bulletin for Asia and Far East, June, 1961.

2. Investment Criteria and Economic Growth, (ed.) M. Millikan, 1955.

O Q1 Q

3Q

2

D1

S1

P2

S

PS

E

D

P1

Pri

ce

Fig. 1

Demand and Supply ofIrrigation Water

Shadow Prices 563

correspond to intrinsic values and “that would prevail if: (i) the investment pattern underdiscussion were actually carried out; and (ii) equilibrium existed on the ,markets just mentioned(i.e., labour, capital, foreign exchange markets)”3 This definition is clear and exhaustive, but issilent about the behaviour of accounting prices over time.A UN report defines shadow prices in terms of the opportunity cost of the factor or product.The shadow price of an output such as capital labour or foreign exchange represents its“opportunity cost” or the loss to the economy that would result from a reduction in its supplyby one unit. A factor that is expected to be in short supply should have an accounting pricehigher than its market price, while one that is surplus should have a valuation that is lowerthan its market price.4 A. Qayyum, however, defines shadow prices in terms of the marginalproductivity of factors. In his words, ‘accounting prices are the values of the marginalproductivity of factors when a selection of techniques has been made which produces themaximum possible volume of output, given the availability of resources, the pattern of finaldemand and the technological possibilities of production.’5 It would require the calculation ofthe marginal productivity of factors by the government manipulating the system of subsidyand taxation in such a way that the supply prices of factors to the producers equal the value oftheir marginal productivity. E.J. Mishan gives the simplest definition in these words, “A shadowor accounting price.....is the price the economist attributes to a good or factor on the argumentthat it is more appropriate for the purposes of economic calculation than its existing price ifany.”6 Thus there is hardly any unanimity over defining accounting prices and the differentconcepts present so many difficulties in their calculation that the concept becomes ambiguous.

DETERMINATION OF SHADOW PRICES

The determination of shadow prices can be done through the general equilibrium method orthe partial equilibrium analysis:1. General Equilibrium Method. In the general equilibrium method, equilibrium is establishedamong all factors by taking their final demand and supply. For this, the data relating to thedifferent sectors of the economy is collected and the accounting price of every factor is expressedin algebraic symbols, and added up for the whole economy. A number of simultaneous equationsare required to be solved for which correct and adequate data are not available. Since the shadowprice is the price which would prevail if prices were equilibrium prices, the existence of fullequilibrium is essential for the establishment of an equilibrium price for every factor ofproduction. The evaluation of shadow prices can be done in two ways: one by trial and error,and two, by a systematic method. If the method of trial and error is adopted the evaluation ofaccounting prices may be based on arbitrary values for products, factors and foreign exchange,calculating the priority figures for all investment projects and finding out whether equilibriumhas been attained in the markets or not. If this method fails, a systematic method is requiredwhich consists “in introducing algebraic symbols for each of accounting prices, trying to expresssupplementary demand for the factors and supply of the products concerned, and then equatingtotal demand to total supply.” But the existence of full equilibrium situation for the entireeconomy is not realistic because in order to find out the equilibrium prices, the knowledge of

3. The Design for Development., p., 394. Formulating Industrial Development Programmes, 19615. Theory and Policy of Accounting Prices, 1959.6. Cost-Benefits Analysis, 1971.

564 The Economics of Development and Planning

total demand and supply curves and the production and consumption functions underlyingthem is essential. These functions depend upon the varied social institutions. So thedetermination of accounting or shadow prices through the general equilibrium method is adifficult affair.2. Partial Equilibrium Method. According to the partial equilibrium method, the shadow pricesof capital, labour and foreign exchange are determined separately. This is, therefore, a simpleand correct method of determining shadow prices. We discuss below the determination of theshadow or accounting prices of capital, labour and foreign exchange.(a) Determination of the Accounting Price of Capital. To determine the shadow price of capital orthe accounting rate of interest, it is essential to study the factors which influence the demandand supply of capital. But in underdeveloped countries, the knowledge of these factors isimperfect. Moreover, there is little relationship between the supply of capital and the interestrates prevalent in such economies. There is wide disparity between the prevailing interest ratesin different regions and areas. As such, the accounting or shadow rate of interest can be estimatedon the basis of the interest rates paid by private investors. But while so doing, it is essential tomake allowance or allow discount on different types of loans for differences in risks involved.In the UN Manual of Economic Development Projects, the following formula has been used forcalculating the shadow price of capital.Social return to capital used in the sector Value of output minus cost of materials,

= depreciation and labour

InvestmentIn this, the costs of materials, labour, foreign exchange and other inputs are valued at accountingprices, and to calculate the return on capital invested (rate of interest) these costs are deductedfrom the value of output. Thus the accounting price of capital can be known for a sector. Tinbergenopines that it is better to take a higher price of capital than interest rates at which limited sumscan be borrowed under certain conditions in underdeveloped countries. He, therefore, suggestsan interest rate of 10 per cent for underdeveloped countries on the plea that even some of thedeveloped countries were having an interest rate of 7 to 8 per cent till recently, whereas personalloans are being made now at an interest rate of 25 to 30 per cent in the former.Its Difficulties. But there are certain difficulties in the calculation of the shadow rate of interestin underdeveloped countries.First, to base the shadow rate of interest on what is paid by private investors understates thevalue of capital to the economy because an integrated development programme may raise theinterest rate over the long run.Second, the calculation of the marginal product of capital as the basis of the shadow rate ofinterest for the whole economy is not easy when projects of higher and lower capital intensityare started, and there is considerable waste of capital in substituting capital for labour in movingthings about, in the handling of materials inside the factory, in packaging, in moving earth, inmining, in building and construction, and their failure to develop an appropriate technology inkeeping with their factor endowments.7

Third, in the shadow rate of interest ‘double index number ambiguity’ is present which makesits use somewhat dubious. The rate of interest is both a stock and flow concept. The shadow

7. W.A Lewis, Development Planning, 1966.

Shadow Prices 565

rate of interest is thus not a single measure but is concerned with relations between stock andflow. In fact, in a developing economy there is a very large variety of stocks with differentdegrees of durability. Thus the calculation of the shadow rate of interest becomes verycomplicated.

RG

SP

PSp

y

yw

=+

−1

However, the appropriate formula for the calculation of the shadow rate of interest for theeconomy is: where, R is the shadow rate of interest, G is the rate of growth, Sp is the savings rateof profit receivers, Py is the share of profit in total income, and Sw is the savings rate of the wageearners.Assuming G = 5 per cent, Sp = 25 per cent, Py = 50 per cent, and Sw = 5 per cent, the shadow rateof interest will be:

R=+ − ×

= =5

0 251 0 5

0 50 05

5

0 316 6

..

.. .

. per cent

(b) Determination of the Price of Labour. Determination of the shadow price of labour is a difficultproblem because labourer differ in efficiency. Therefore, shadow price of labour cannot be thesame for both the unskilled and skilled labour and for different types of skilled labour. Therehas to be a different shadow price for different types of labour because labour is not like otherfactors. In underdeveloped countries there is surplus labour in the rural areas having almostzero marginal product. But its shadow price cannot be assumed to be zero, it should be positiveand provide a minimum subsistence level when such labour is employed on construction works.“But even if the marginal product of labour is less than the wage (or subsidized income), it doesnot necessarily follow that one should use a shadow price for labour lower than the wage. Thisis because wage earners tend to consume most or all the wages which they are paid. Thus thepayment of wages constitutes a real cost to the economy, even if there is no alternativeemployment for labour.” Therefore, some economists are of the view that the accounting pricefor labour can be fixed anywhere above the zero marginal product of labour, and with theincrease in the marginal product of labour its accounting price can also be raised. But, accordingto UN experts, assuming no surplus of skilled labour but ample supplies of agricultural andunskilled labour the accounting prices of different kinds of skilled labour can be based on thecost of moving workers from villages to industrial areas, providing them with houses andother facilities, and training them.8

(c) Determination of the Rate of Foreign Exchange. The shadow price of foreign exchange is essentialfor underdeveloped countries suffering from balance of payments difficulties. An artificialequilibrium is achieved in the balance of payments by fixing a higher shadow rate of exchangethan the official rate of excnange. “In an optimum development plan, the accounting price offoreign exchange would be equal both to the incremental cost of earning foreign exchangethrough exports and to the incremental cost of saving foreign exchange through importsubstitution. The former may be easier to estimate in many cases because there are relativelyfew potential exports, at least in the near future in underdeveloped countries.” For this, weight

8. UN. ECAFE.

566 The Economics of Development and Planning

is attached to the cost of foreign exchange in the project. If say, “the accounting price of foreignexchange is 50 per cent higher than its market value, the net effect of a project on the balance ofpayments should be given a weight of .5 in addition to the effect on the national income. This isequivalent to valuing all foreign exchange costs and earnings at a price of 1.5.”9 According toDr. Little, Israel is the only developing country in which the accounting price of foreign exchangeis estimated in this way.10 It is not essential that every project should be weighted equally becausethe foreign exchange component of each project is different.As an alternative, it is suggested that the demand for and the supply of foreign exchange shouldbe computed which should then determine the rate where the two equilibrate. But this procedureis not practicable in developing economies where the foreign exchange requirements differsector-wise and project-wise. Further, a single shadow rate of exchange cannot be applied overtime. It will have to be reviewed and raised at different points of time on the basis of the ‘black’and ‘free’ rates of exchange, because the market for some important international currencieslike the dollar and the sterling is imperfect. Professor Tinbergen suggests the calculation of theshadow rate of foreign exchange based on the ‘black’ and ‘free’ rates of exchange. If the official(free) exchange rate is Rs. 7.5 a dollar and the black rate is Rs. 15 a dollar and the conversion ofthe official rate is four times as great as that at the black rate, then the shadow rate would be theweighted average

4 7 5 1 15

59

× + × =.

Rs. 9 per dollar would then be the most serviceable shadow rate instead of the official rate ofRs. 7.5.

DIFFICULTIES OF SHADOW PRICE

Apart from certain difficulties already mentioned in the determination of shadow price forcapital, labour and foreign exchange, there are other difficulties of a general nature.First, the calculation of shadow prices pre-supposes the availability of data. But adequate datais not easily available in less developed countries.Second, in order to establish the intrinsic value of a factor or product requires the existence offull equilibrium in all market. In an underdeveloped economy which is characterized by anumber of fundamental disequilibria, the knowledge of full equilibrium conditions for theentire economy is not possible. Thus the notion of shadow prices corresponding to intrinsicvalues is arbitrary.Third, the assumption of full employment equilibrium in the whole economy makes the conceptof shadow prices indeterminate. It requires a complete knowledge of demand and supplyfunctions which are based on the existing social institutions in the economy. “Land prices willdepend upon the system of land tenure and on agricultural policy generally. The supply priceof labour will depend upon the motivation and education of potential workers, on acceptabilityof employing women and on the attitudes to different kinds of work. The price of capital willdepend upon degrees of monopoly in the economy.”11 Thus shadow prices are difficult toascertain under the existing institutional framework of underdeveloped countries.Fourth, another difficulty arises with regard to the time dimension. The concept of shadow prices

9. Ibid.,10. I.M.D. Little, “Project Analysis in Relation to Planning in a Mixed Economy,” in Development Problems.

OECD, Paris, 1967.11. W.A. Lewis, op. cit.

Shadow Prices 567

is static and timeless, for shadow prices are used to overcome the difficulties involved in projectevaluation and programming when factor prices change over time. All inputs and outputs arevalued at fixed shadow prices in such cases. This is not realistic because, as Tinbergen himselfpointed out, “the realization of investment pattern will itself influence these intrinsic values, butonly after some time, since investment processes are essentially time-consuming.”12 Ifaccordingly, labour, capital, foreign exchange and other products are assigned different, theymay give contradictory results in accordance with the time-period considered. Hence the conceptof shadow prices remains essentially a static one.Fifth, if shadow prices are calculated in terms of Qayyum’s definition, they require the calculationof marginal productivity of factors by the government and the manipulation of the system ofsubsidy and taxation in such a way as to equate the supply prices of factors to the value of theirmarginal productivity. But it is not easy to calculate the marginal productivity of factors(especially of capital and labour), and producers’ response to changes in taxes and subsidies.Thus, the shadow prices based on marginal productivity are also indeterminate.Sixth, another practical difficulty that arises is that of using shadow prices in the economywhere the private enterprises buy inputs and sell outputs at market price. The government, onthe other hand, uses shadow prices for the evaluation of its projects but buys all inputs atmarket prices and sells outputs at competitive market prices where she does not possess amonopoly.Seventh, the determination of shadow prices is difficult in the case of projects with high capital-intensity and which are substitutes and complementary to each other. Suppose there are twoprojects in which the input of one is the output of the other, and vice-versa. In such cases thedetermination of the accounting prices of the inputs of labour, capital and foreign exchangewill not only be difficult but impossible because the decision about the construction plans ofthe two projects cannot be the same.Eighth, often prices of such services as electricity and transport are regulated by the government,and are not fixed on the basis of social opportunity cost. “For example, the prices of electricityused in feasibility studies of industrial projects in many developing countries are derived as anaverage charge of a two-part tariff. Since a two-part tariff charges a consumer according to hisindividual demand, rather than the system peak demand, it will fail to reflect the long-runincremental cost (hence the social opportunity cost of electricity).”13

Conclusion. Prof. Myrdal in his “Asian Drama” regards shadow prices as “utterly unreal andother worldly in concept, particularly in underdeveloped countries like those in South Asia...as it is recognised that they cannot be definitely ascertained.... This abstract and metaphysicalconcept cannot help to solve the theoretical and practical problems facing South Asian planners.It stands out as a typical example of the pseudo-knowledge, given a learned and occasionallymathematical form, that unfortunately has formed a major part of the contribution of Westerneconomies to the important tasks of ascertaining the facts in underdeveloped countries andcreating a framework for policies designed to engender and direct development.”14

USES OF SHADOW PRICES

Despite these difficulties shadow prices possess the following uses:1. In Project Evaluation. The use of market mechanism for the determination of product andfactor prices is not a perfect and correct method because it leads to a wrong allocation of

12. Tinbergen. op. cit. Italics mine.13. Ajit K. Dasgupta, op. cit., p. 92.14. Asian Drama— An Enquiry into the Poverty of Nations, pp. 168-69. Italics mine.

568 The Economics of Development and Planning

resources. In underdeveloped countries, the market mechanism operates imperfectly due to anumber of economic and social obstacles. Therefore, it is not possible to have project evaluationon this basis. Even otherwise, the rise in prices being inevitable during the process of planning,it is therefore not possible to correctly assess the costs and benefits of a project. “Accountingprices are a convenient tool for evaluating investment projects in different sectors of theeconomy....A factor that is expected to be in short supply should have an accounting pricehigher than its market price, while one that is surplus should have a valuation that is lowerthan its market price.”’15

Thus shadow prices are used for evaluating the effects of a project on the national incomewhich are also termed as external effects. This is often done on the basis of the profitabilitycriterion or cost-benefit analysis where both costs and benefits are calculated at accountingprices. Sometimes even rough estimates of shadow prices also help. “They may, for example,show how sensitive the priority figures of a number of projects are to changes in such accountingprices. They may enable us to classify products in groups that are attractive under certainspecified emergency circumstances...It may nevertheless have a rough guide for emergencycases.”16

2. In Public Policy. The success of development planning depends upon the correct operationof public policy. Shadow prices are intrinsic prices on whose correct determination dependsthe success of a plan to a considerable extent. In a mixed economy, the public sector cannot bedeveloped unless the prices of labour, capital, foreign exchange and other inputs are determinedin accordance with shadow prices. Though very often shadow prices are rough estimates, yetthe state should try to bring market prices close to the shadow prices of products and factorsthrough fiscal, monetary and other measures for the successful implementation of the plans.3. In Programming. Shadow prices have the greatest importance in programming. Programmingis the working of the economy in a rational, consistent and co ordinated manner. The main aimis to maximise the national income through time. For this, it makes an optimum use of theamount and composition of investment, and adopts public investment, fiscal, monetary andcommercial policies. In the context of under developed countries, programming implies theoptimum use of investment whereby there is no difficulty in the production process. But inreality, the difficulties of supplies of factors, rise in market prices and the scarcity of foreignexchange is apparent in such economies. All such difficulties are overcome with the help ofshadow prices, and fiscal, monetary and other policies help in bringing the market prices offactors, products and foreign exchange in conformity with their shadow prices and thus makeprogramming a success.In the case of linear programming for a wide class of problems, the variables in the dual solutioncan be interpreted as shadow prices or accounting prices, in as much as they are the ‘correct’input prices being consistent with the maximum value of the primal objective function.... Whenthese shadow prices are imputed to the given inputs, the value of the dual objective function isminimised. It can then be interpreted as the minimum input cost, subject to the constraints, andto the requirement that no profits be made. These shadow prices are, therefore, not differentfrom the factor prices that would emerge in perfectly competitive equilibrium in which productprices are exogenously determined.”17

Thus the technique of shadow prices serves as a useful computational shorthand in devising arelatively efficient system of project evaluation and helps in achieving success in programmingand public policy.

15. UN, ECAFE. op. cit.16. J. Tinbergen, op. cit.17. J. Mishan, op. cit. Italics mine.