Wages, Materials, and the Markup

In a recent post focusing on inflation and distribution, I touched on the connection between the aggregate markup and income distribution. Here, I thought it might be worth demonstrating the connection explicitly, and then outlining a simple extension that brings out the impact on distribution not only of the markup but also fluctuations in the prices of raw materials. The extension is due to Kalecki, who outlines the argument in the second chapter of his Theory of Economic Dynamics: An Essay on Cyclical and Long-Run Changes in Capitalist Economy, first published in 1954.

In the earlier post, the markup, k, was defined as nominal income divided by the aggregate wage bill:

k = (W + U) / W = PY / W

where P is the price level, Y real income, PY nominal income, W the aggregate wage bill, and U gross profit. Clearly, the share of wages in nominal income, ω, is just the reciprocal of the markup:

ω = 1/k

In other words, an increase in the markup redistributes income from workers to capitalists.

Intuitively, it seems equally clear that the workers’ share in nominal income will be negatively affected if the prices of raw materials rise, since this will push up prices of finished consumer goods relative to wages. In considering distribution, Kalecki takes this additional factor into account.

In his analysis, he assumes that the prices of final goods produced in the dominant manufacturing and services industries are determined, at the micro level, in a different manner than prices of raw materials. He argues that the former are cost based, whereas the latter reflect demand conditions.

In manufacturing and services industries, Kalecki reasons that marginal cost tends to be constant over a fairly wide range of output below full capacity. He assumes that firms set prices as a markup over marginal cost, with the level of output being demand determined. The size of the markup in a given industry is argued to depend on market power, or the ‘degree of monopoly’.

In contrast, the prices of raw materials are assumed to fluctuate positively with demand on the grounds that the supply of raw materials is relatively inelastic.

Although there are differences in the pricing theories of classical, Marxian, Post Keynesian, and Kaleckian economists, the various approaches are all broadly consistent with the notion of cost-based pricing in the dominant manufacturing and services sectors of the economy.

For example, in Marx, competitive conditions – defined as free mobility of money capital – would tend to equalize profit rates across sectors. This is because investment, in the absence of impediments, would be directed into those sectors offering the highest rates of return, the process continuing until prices had gravitated to levels consistent with normal profits. However, to the extent that some industries are monopolistic or oligopolistic, this tendency toward profit-rate equalization in Marx will be hindered in much the same way as a higher ‘degree of monopoly’ results in unequal profit rates in Kalecki’s analysis.

Kalecki considers a broader definition of the markup than was employed above, which at the macro level he defines as the ratio of ‘aggregate proceeds’ to ‘aggregate prime cost’. He can then relate both the markup and material costs to distribution.

Aggregate proceeds in Kalecki’s analysis amount to ‘value added’ plus the cost of materials, M. Here, value added is identical to nominal income or nominal GDP, so aggregate proceeds total U + W + M. Aggregate prime cost is defined as wages plus the cost of materials, or W + M. Since the markup for Kalecki is the ratio of these two sums, we have:

k = (U + W + M) / (W + M)

It is simple enough to arrive at a relationship between this version of the markup and income distribution. Start by equating gross profit with itself and adding and subtracting prime cost to the right-hand side:

U = (U + W + M) – (W + M)

Strictly speaking, Kalecki separates out overheads, which include salaries of management, from the wage bill, since he considers these salaries more akin to profit. I am glossing over this by implicitly including those salaries in gross profit, U, rather than separating the left-hand side of the above identity into profit and overheads.

In the above expression, divide and multiply the first bracketed expression by prime cost:

U = [ (U + W + M) / (W + M) ] (W + M) – (W + M)

The fraction in square brackets is the markup, so we can write:

U = k (W + M) – (W + M) = (k – 1) (W + M)

Recalling that PY = W + U, we can substitute the above expression for U into the wage share out of income:

ω = W / PY = W / [ W + (k – 1) (W + M) ]

Finally, dividing the numerator and denominator of the right-hand side by the wage bill gives:

ω = 1 / [ 1 + (k – 1) (j + 1) ]

where j equals M/W, the ratio of material costs to wages.

This expression shows, as expected, that the workers’ share in nominal income will be negatively related both to the markup and the ratio of material costs to wages. An increase in the prices of raw materials relative to the wage bill will cause the prices of final consumer goods to rise faster than wages.

Kalecki appealed to these relationships to argue that the wage share in nominal income will be broadly stable over the business cycle. His reasoning was that the ‘degree of monopoly’ would tend to increase in a downturn, raising the markup, k, and impacting negatively on the wage share. But, at the same time, prices of raw materials, being positively related to demand, would tend to fall in a downturn relative to wages, at least partially offsetting the effect of the larger markup on the wage share.