PRICES AND COSTS: Corrections to the Labor-Share Measure of Real Marginal Cost 3

Indeed, Hall (1988) finds (using stock market returns to construct a user cost for capital) that pure profits in U.S. industry are close to zero. It furthermore makes sense that profits should be zero in the steady state, due to entry, which one should expect to eliminate persistent profits in the long run, even if entry does not respond quickly enough to eliminate cyclical fluctuations in profits. If we assume this, we can impose p = /i, so that there is only a single parameter to calibrate, that describes both the degree of returns to scale and the degree of market power. With fi = 1.25 and a labor share of .7, the parameters b is then ~A. Table 2 shows that, even letting a equal zero, such a value of b leads to markups that are strongly countercyclical though the correlations with lagged output remain higher in absolute value.
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The significance that one attaches to such findings obviously depends upon the size of the average markup (or degree of returns to scale) that one is willing to assume. Here it is worth remarking that a value of /i equal to 1.6 need not mean that any individual firm marks up its costs by 60%. The reason for this is that firms do not just mark up their labor costs but also their materials cost. To see what this implies about the markup, suppose that, as in Rotemberg and Woodford (1995), materials are a fixed proportion sM of aggregate output while value added constitutes only a fraction (1 — sm) of total costs. The marginal cost of producing one unit of gross output is then

where fiVA is the “value-added markup” that satisfies (2.2). If the materials share equals 0.6 (as is typical of U.S. manufacturing), then а fiVA of 1.6 (the “baseline case” of Rotemberg and Woodford. 1991) requires that the typical firm’s price be only 18% higher than its marginal cost.

A related correction would assume, instead of overhead labor, a “setup cost” for each employee, as is considered in Basu and Kimball (1994). Suppose that the production function is Y = F(K, z(h-h)N)), where now N represents the number of employees and h the number of hours worked by each. We again assume that F is homogeneous of degree one; the “set-up cost” h > 0 represents a sort of per-employee fixed cost. (The observed preference for fulltime employees observed in many lines of work makes the existence of such costs plausible.20 )

If we consider the marginal cost of increasing output solely on the employment margin (holding fixed hours per week), we again obtain (2.8), but with H and H replaced by h and h in the first factor. Wre correspondingly again obtain (2.9), but with H replaced by h. Since hours per employee are also a strongly procyclical variable, the first factor in (2.8) is again a source of further countercyclical movement in implied markups. Basu and Kimball suggest that s0 = .25 should be an upper bound on the importance of such set-up costs (as full-time wage premia should otherwise be larger); but this value would still allow the elasticity in (2.9) to be as large as b = —0.3.

Marginal Wage Not Equal to the Average

Thus far, we have assumed wage-taking behavior on the part of firms, meaning that they regard themselves as being able to hire additional hours of work, at the margin, at a wage which is also the wage paid for each of the hours that they do hire – so that the relevant marginal wage is also the average wage that is paid. Suppose, however, that this is not true, and that the firm’s wage bill is W(H), a function that is increasing, but not necessarily linear in Я 21 In this case, marginal cost depends upon the marginal wage, W'(H), so that