A MARK-UP APPROACH TO THE DISTRIBUTION OF AGGREGATE PROFITS*

ROBERT DIXON

University of Melbourne

It is important (especially in the context of Kalecki’s writings) to distinguish between theories of the level of profits in the economy as a whole (i.e. the macro-theory of profits) and theories which pertain to the share of profits in the value-added in an individual industry. However, whilst they are logically distinct, the two theories are related in that models of industry price-cost relationships may be used to account for the distribution of the aggregate profits-fund between industries.

The paper begins with a very brief restatement of the macro-theory of the aggregate profits-fund. This will be followed by an exposition of the determinants of the level of firm’(or industry) profits, as suggested by different “cost-plus” pricing models. In the final section we will identify the “proximate” determinants of the share of an individual firm (or industry) in total profits.’

I. THE MACROECONOMICS THEORY OF PROFITS

This section is devoted to an extremely brief re-capitulation of the macroeconomic theory of profits. (More detailed expositions will be found in Asimakopulos [ 13 and Kalecki [5 ] . )

We will deal with the case of a closed, two-sector economy. We assume that all profits are saved and that all wages are spent on consumer goods.

To the extent that workers employed in the consumption sector spend their wages on consumer goods, the firms in that sector (taken together) will be receiving back as revenue no more than they already paid out as a cost of production. In order for these firms to receive monies as revenue in excess of the wages they have paid out (i.e. in order for revenue to exceed costs of production), there must be some spending on their products which is over and above the spending which is undertaken by their own workers. Given the classical savings assumptions, it is the spending (on consumer goods) of wages earnt in industries outside the consumption sector which is the (proximate) source of the profits of the firms in the consumption sector. This is one of the insights which form the basis for the macro-theory of profits.

A second insight concerns the proposition that “There can only be profits in the aggregate if money which has not already been entered into business accounts as a cost

*I am grateful to an anonymous referee for extremely incisive and helpful comments. ‘For a model based upon equalisation of the rate of profit in (von Neumann) growth equilibrium see Dixon [3].

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1983 DISTRIBUTION OF AGGREGATE PROFITS 449

of production is spent on goods.” (Eltis [4], p. 73). In the classical two-sector model, the only spending which does not simply return to firms as revenue what has previously been paid out as a cost of production (that is, the only non-wage spending) is the expenditure by firms or individuals on (newly produced) investment goods. We may demonstrate this as follows. Suppose that firms or individual capitalists in the economy borrow or use their retained earnings to finance investment expenditure. The revenue received from the sale of capital goods will be divided, within the capital- goods sector, between profits and wages. In this way part of the investment expenditure yields profits directly to the firms producing capital goods. That part which does not constitute the profits of the firms producing capital goods will (under our assumption of full integration) constitute the wages paid to the workers in the capital goods sector. It will be recalled from our earlier discussion that it is the wages of the workers in the capital-goods sector which, when they are spent on the products of the consumption sector, generates revenue in that sector (i.e. the consumption sector) in excess of its costs of production. In other words, it is the (direct) wages component of investment expenditure which becomes the profits of the firms in the consumption sector. In summary, we may say that a given value of investment expenditure generates an equivalent value of profits in the economy as a whole because part of it generates profits directly in the capital goods sector itself and the remaining part of it (i.e. the wages paid to workers in the capital goods sector) will indirectly generate profits in the consumer-goods industries. A neat way of summarising this result is provided by the maxim: “workers spend what they get, and capitalists get what they spend”.

11. THE LEVEL OF A FIRM’S PROFITS UNDER COST-PLUS

In this section we deal with the proximate determinants of the level of a firm’s (or an industry’s) profits under different “cost-plus” price setting regimes. We will make a number of simplifying assumptions. First, we will deal with the price-cost equation for a “representative” (or average) firm in the industry.* Secondly, we will assume that labour costs are the only prime cost.3 Thirdly, we will take the mark-up parameters to be exogenous. Fourthly, we will assume that the money wage is the same in all industries.

We consider first a very simple case where prices are set by “marking-up” actual unit labour costs. For the representative firm;

p = ( w a ) ( l + 7 ) (1 )

where:p =price per unit of output.

w = average money earnings per worker.

21 use the notion of “representative” in exactly the same fashion as Kalecki (p. 480. In what follows I shall use the word “firm” as standing for “representative firm” and I shall take it as given that statements made in relation to the profits of that firm will also apply (albeit on a higher scale, depending on the number of firms) to the industry taken as a whole.

”he addition of materials and other costs neitheradds to, nor detracts from, the substantive argument to be developed here.

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a =amount of labour required per unit of output.

T =mark up.

Gross4 money profits per unit of output (r) will equal the difference between average revenue per unit of output (assumed, for the moment, to equal sales) and unit labour costs,

7T=p-(WU) = ( W U ) ( T ) (2)

P = ( w a ) ( 7) Q (3)

Total money profits received (i.e. on all output) ( P ) will therefore equal:

where Q = quantity produced.

which is to say that the level of (money) profits received by the firm will reflect its unit labour costs, the size of the mark-up, and the quantity sold.

There is a growing body of evidence which suggests that firms mark-up “expected” or “normal” costs per unit of output rather than actual costs per unit of output. We will also allow, in what follows, for there to be a difference between the quantity produced (which influences cost) and the quantity sold (which influences revenue). For the representative firm we may assert that:

p =(w‘ae) ( k ) (4)

where: an ‘e’ superscript indicates an expected or normalised value of the variable, and

k = ( 1 + T )

Multiplying both sides of (4) by the quantity of output which is actually sold ( S ) , yields an expression for gross sales revenue as;

ps= (wear) ( k ) S ( 5 )

Let us define “profits” to equal the difference between gross sales revenue (equal to gross selling price per unit multiplied by the quantity sold) and the total (prime) costs of producing output currently (equal to the actual dollar costs per unit of current output times the quantity which has been produced in the current period (Q)) .5

Total (operating) profits will therefore equal:

P = p S - ( wa)Q= [(w‘u‘) ( k ) S ] - [ ( w a ) Q ]

Equation (6) allows for the possibility that actual operating profits may be (say) below what they were expected (or targeted) to be because actual unit labour costs were greater than they were expected to be and/or output (Q) exceeded sales (S).

41n what follows I will neglect overheads, depreciation, taxes, erc. There are various definitions which are all plausible, and which may be distinguished according to their treatment of the valuation of changes in the stocks of finished goods. The definition I have adopted here seems to me to be that which is both consistent with the macro-theory of profits and is likely to have interesting dynamic implications.

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We may define:

t = (( w‘a‘)/ (wa)) (7) i.e. t is the ratio of expected to actual unit labour costs and therefore measures the (proportional) extent to which the firm was over-estimating ( t > I ) o r under- estimating ( t < I ) unit costs.

and

= ( S / Q ) (8)

i.e. 0 is the ratio of sales volume to actual output. Assuming that actual output can be regarded as being equal to desired or expected sales the 0 ratio measures the extent to which expected sales were a n over, or under-estimate.

Substitution of (7) and (8) into (6) yields an expression for the total gross profit

P=(wa)[t(k)e- I I Q (9)

which expresses gross profit in terms of realised unit labour costs, the mark-up parameters, the level of output, and our two coefficients ( E and 0 ) which measure the (proportional) inaccuracy of the firms expectations of unit costs and sales.6

111. THE DISTRIBUTION ALGORITHM

In this section we will consider the implications of “cost-plus” models for the determination of the share of aggregate profits which will be received by each firm or industry. In what follows we will denote the level of profits accruing to the representative firm 0 in any given industry as Pr and the total level of profits accruing to all firms and industries in the economy as a whole as P.

Under the classical savings assumptions total profits accruing to all firms and industries (P) will equal the value of investment expenditure currently being undertaken in the economy, i.e.

P= I (10)

We have seen that where prices are set by marking up expected unit costs that the level of profits accruing to a representative firm in a n industry will equal:’

Pf= (wa/) [ c f (k f ) e f - 1 1 Q/ (9) Noting that (wu,.)Q, will equal the actual wages-bill paid out by the firm (wL,.) our

(1 1)

expression for gross profit accruing to the firm will equal:

Pj= (wL/) [E/(kr)e/- 1 1 where L=numbers employed.

6CIearly the two may be related. ’If we are interested in the industry, we merely have to substitute the level ofindustry output for the level of firm’s output (Qf) in what follows.

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Dividing (1 1) by (lo), and dividing both the numerator and denominator by the money wage (w)* yields an expression for the firm’s share of profits in terms of current investment measured in wage units, as:

( P / / P ) = [ ( L / ( t f ( k /W/ - l)) /(I/w)l (12)

which is to say that the firm’s (or industry’s) share of total profits will depend upon its degree of monopoly ( k ) , its “size” (L ) , the extent to which its expectations of unit cost and sales are realised, and the aggregate rate of accumulation measured in wage units. It is important to note that even leaving the fulfilment or otherwise of expectations to one side, at least one other important determinant of the firms share of profits, namely the rate of accumulation, is out of the control of a single firm. Whatever the market form, the single firm cannot effect (at least in a significant way) the aggregate of other firms investment decision^.^

In the special case where all expectations are realised (i.e. t = 8 = 1) this collapses to: 10

(Pfl P) = [ ( T / L / ) / ( I / w ) 1 (13) which is to say that the firm’s share of total profits will depend upon its mark-up parameter, its size (i.e. its level of employment) and the rate of accumulation (measured in wage units) being undertaken in the economy as a whole. Again, we note that the latter determinant is not subject to the control of the firm.

Note also that the value of investment in current prices (Z) will equal the price per unit @/) times the quantity of investment sold. If mark-up pricing is being pursued in that sector we may say that:ll

P I = (h’a,) (1 + 7 1 )

Given that the money value of investment expenditure (Z) is equal to the price of newly produced capital-goods @,) times the quantity produced and sold (Q,), it follows that

( I / w ) = ( @ I Q / ) / = [a / ( 1 T/)Q/I Since a/= ( L J QI) the above may be rewritten as:

I / M’ = ( 1 + T / ) L / (14)

where L,= numbers employed in the capital-goods sector.

So that in the case where all expectations are realised the distribution algorithm (13) reduces to:

(P// P) = kf/ ( 1 + 7,) ) (Lf/ (L,) 1 (15)

which is to say that the distribution of aggregate profits depends upon the size of the

8It will be recalled that we are assuming that the money wage is the same in all industries and firms. 9I am especially indebted to a referee for drawing my attention to the need to stress this.

1°It will be recalled that k = ( I + r ) . “In what follows we will restrict ourselves to the case where e,=O,= I .

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mark-up in the firm or industry under consideration relative to (unity plus) the mark- up co-efficient in the capital-goods sector, and upon the numbers employed in the firm or industry under consideration, relative to employment in the capital-goods sector.

It is clear from the foregoing that Kalecki’s theories of “cost-plus” pricing, (associated also with his theory of the distribution of value added within an industry between profits and wages) may be coupled with his macro-theory of profits, to yield a comprehensive theory of the level and distribution of aggregate profits and also the possibility of a dynamic macro-micro theory incorporating both Kaleckian and Keynesian insights.

First version received 16th June, 1982 Final version accepted 16th August, 1982

(Editors)

REFERENCES 1.

2. 3.

4. 5.

A. Asimakopulos, “Themes in a Post-Keynesian Theory of Income Distribution”, Journal of Posr Keynesian Economics, vol. 3, 1981. R . Dixon, “A Model of Distribution”, Journal of Posr Keynesian Economics, vol. 3. 1981. R. Dixon, “A Classical Model of the Distribution of Aggregate Profits”, mimeo, University of Melbourne, 1982. W. Eltis, Growth and Distribution (London: Macmillan. 1973). M. Kalecki, Selected Essays on the Dvnamics of rhe Capitalisf Economy (Cambridge: Cambridge University Press. 1971).