Some Intuition on the Profit Equation, Courtesy of Kalecki

Kalecki’s profit equation famously shows realized 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, discussed previously here, 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”. This aphorism is 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 realized profit. The more the capitalists spend as a class, the more profit they will realize.

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

This can be verified 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 specifying a capitalist consumption function. For instance, if CP = A + qP, where A is autonomous consumption and q is the capitalists’ marginal 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 realized profit to be the sum of capitalist expenditures, the government deficit and net exports, minus worker saving. Causation continues to run from the autonomous expenditures to profit.