Some Intuition on the Profit Equation, Courtesy of Kalecki

Kalecki’s profit equation famously shows gross profit, prior to its distribution into various parts (retained earnings, interest, rent, etc.), as a function of aggregate demand. In a simplified model of a closed economy with only capitalists and workers, in which workers in aggregate do not save, it shows that profit is the sum of capitalist consumption and private investment. On first encounter, this is an intriguing relationship. One explanation, which I have discussed previously, is that wages, being spent entirely on consumption items, return to capitalists, whereas capitalist expenditures remain with the capitalist class as a whole. This has been summarized as “workers spend what they get and capitalists get what they spend”. I find this aphorism eye-opening and fascinating, yet, in its own way, also somewhat mysterious if pondered for long. Kalecki provided an alternative way of viewing the situation, which may further aid understanding.

The Profit Equation in a Two-Sector Model

In Kalecki’s simplest model, there are only two broad components of aggregate demand: investment, I, and consumption, C, which Kalecki divides into worker consumption, CW, and capitalist consumption, CP. There are also two broad categories of income, Y: wages, W, and profit, P.

(1) Y = CW + CP + I
(2) Y = W + P

Since all wages are assumed to be spent, we can substitute W for CW in (1), set (1) equal to (2), and upon rearrangement obtain:

P = CP + I

So far this is just an identity, true by definition. Kalecki then introduces his behavioral assumption by noting that capitalists can directly control what they spend (CP + I) but not what they receive as income (P). This implies that the causation runs from investment and capitalist consumption to profit. The more the capitalists spend as a class, the more profit they will make.

Of course, individual capitalists cannot guarantee profit through their own individual spending, because their prospects will depend on the spending decisions of all capitalists, of which they have no control. Instead, individual capitalists must try to anticipate the likely strength of demand conditions in deciding upon their spending levels. Nevertheless, whatever capitalists end up spending in aggregate will determine the profit of their class as a whole.

The Profit Equation in Terms of a Production Schema

In a 1939 paper, “Money and Real Wages”, reprinted in the second volume of his collected works, Kalecki provides an interesting perspective on the profit equation. Reminiscent of Marx’s reproduction schema in volume II of Capital, Kalecki divides the simplified economy into three departments. Departments 1, 2 and 3 produce investment goods, capitalist consumption goods, and worker consumption goods, respectively:

                      Wages          Profit         Income
Dept 1 (I gds)         $2bn           $1bn           $3bn    
Dept 2 (CP gds)        $2bn           $2bn           $4bn
Dept 3 (CW gds)        $6bn           $4bn           $10bn

Kalecki starts by considering department 3, which produces consumption goods for workers. Since workers are assumed not to save in aggregate, the workers employed in department 3 will spend $6 billion on the goods and services produced in their own department. The amount left over, totaling $4 billion, will be consumed by workers in the first two departments. This makes clear that the profit of department 3 is equal to the wages paid by capitalists in the other two departments.

The combined output of departments 1 and 2 is valued at $7 billion ($3bn + $4bn). Of this amount, $3 billion ($1bn + $2bn) is profit going to the capitalists of these departments. The other $4 billion goes to wages, which is a cost to these capitalists, but is matched exactly by the profit going to the capitalists of department 3.

There are two ways to arrive at the figure for total profit. We can simply add up the profit column ($1bn + $2bn + $4bn) to arrive at gross profit of $7 billion for the economy as a whole. Or, by noting that the combined wages of the first two departments make up the profit of the third department, we can instead add up the output values of departments 1 and 2 ($3bn + $4bn) to arrive at the same figure of $7 billion.

But this second method is equivalent to taking the sum of capitalist expenditures. This is because the output of department 1 is total production of investment goods, I, and the output of department 2 is the total production of capitalist consumption items, CP.

We can verify this algebraically by calling the wages of the three departments W1, W2, W3, the profits P1, P2, P3, and outputs (incomes) Y1 = I, Y2 = CP, Y3 = CW:

                      Wages         Profit         Income
Dept 1 (I gds)          W1            P1            Y1 = I   
Dept 2 (CP gds)         W2            P2            Y2 = CP
Dept 3 (CW gds)         W3            P3            Y3 = CW

Total profit for the economy can be found by summing the incomes of the separate departments and subtracting wages:

P = (Y1 + Y2 + Y3) – (W1 + W2 + W3)

Recalling that P3 = W1 + W2, this becomes:

P = Y1 + Y2 + Y3 – P3 – W3

Here, Y3 – P3 = W3, so:

P = Y1 + Y2 + W3 – W3 = Y1 + Y2 = I + CP

Implications of the Profit Equation

For Kalecki, the profit equation makes clear that “fluctuations in production and profits depend on the fluctuations in capitalists’ consumption and investment”.

He illustrates this in terms of the three departments by considering the impact of an increase in optimism among capitalists. The initial effect will be felt in department 1 as capitalists step up investment-goods production. This increased production of investment goods will bring with it an increase in employment and wages in department 1.

Since workers are assumed to spend what they get in wages, demand for worker consumption items will increase. Capitalists in department 3 will step up production in response, resulting in higher employment and wages in that department as well.

With production and profit rising in the investment-goods and worker-consumption-goods departments, it is also possible that capitalists will increase their own consumption of items produced in department 2. If so, employment and wages will increase in that department, having further spillover effects on demand for worker-consumption goods, and employment and wages in department 3.

Kalecki is implicitly describing a multiplier process in which “production will be finally pushed up to the point where the increase in profits will be equal to the increase in expenditure on investment and capitalist consumption”.

This can be made explicit by assuming a form for the capitalists’ consumption function. For instance, if CP = A + qP, where A is autonomous consumption and q is the capitalists’ propensity to consume out of profit, we can obtain P = (A + I)/(1 – q).

The logic can be extended to a more elaborate model that includes government, worker saving and an external sector. Kalecki’s profit equation in that case shows that profit will be the sum of capitalist expenditures, the budget deficit and net exports, minus worker saving. Causation, for Kalecki, will run from the autonomous expenditures to profit.

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4 thoughts on “Some Intuition on the Profit Equation, Courtesy of Kalecki

  1. Pretty much what I wrote the other day…never read Kalecki, it’s simple arithmetic/chain of logic within a closed system with leakages without all of the added complexity.

    Minsky wrote something similar…

    https://dl.dropbox.com/u/33741/wp74.pdf

    …starting with “The financial instability hypothesis…” bottom of page 5.

  2. Thanks for the link. In a way, this post was a bit of a coincidence. I consulted “Money and Real Wages” — as the title may suggest — with the idea of a follow-up on a recent post, “Raise the Minimum Wage”, then got sidetracked — because of the recent discussion you initiated — by a page or two discussing the three departments and profit equation.

    By the way, as an engineer you might enjoy Kalecki. According to wikipedia he started out studying engineering, then had to do military service and get various jobs due to his father’s circumstances. He returned briefly to uni after becoming interested in economics, but had to leave again for monetary reasons, ending up in a job relating to economics where he began to develop his macro ideas.

    Wikipedia Entry on Michael Kalecki

  3. In this model it is assumed that W = C[w], therefore, any exogenous change in demand must be due to capitalists only.

    However, in the business media one often sees consumer demand in general (meaning combined capitalists’ and workers’ demand) characterized as driving the economy.

    In the context of the model, can the above assumption be relaxed to account for this or is the business media necessarily mistaken?

  4. Yes, if workers are allowed to save (or dissave) in aggregate, P = CP + I – SW, where SW is worker saving.

    If workers’ consumption exceeds wages (e.g. through credit-fueled consumption), worker dissaving will add to profit. Conversely, if workers save in aggregate, profit will be reduced by the same amount.

    To get this result, equate (1) and (2) from the post:

    CW + CP + I = W + P

    Rearranging:

    P = CP + I – (W – CW)

    Here, W – CW is worker saving out of wages, SW.

    It would also be possible to specify a worker consumption function with autonomous and induced components, analogous to the capitalist consumption function mentioned in the post.

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