# PRICES AND COSTS: Corrections to the Labor-Share Measure of Real Marginal Cost 8

In the data, however, employment variations and variations in total person-hours are not the same, even if they are highly correlated at business-cycle frequencies. This leads us to suppose that firms can vary both employment N and hours per employee h, with output given by F(K, zhN), and that costs of adjusting employment in period t are given by KtNt(f){Nt/Nt-i). If, however, there are no costs of adjusting hours, and wage costs are linear in the number of person-hours hired Nh, firms will have no need ever to change their number of employees (which is clearly not the case). If, then, one is not to assume costs of adjusting hours per employee, one needs to assume some other motive for smoothing hours per employee, such as the sort of non-linear wage schedule discussed above. We thus assume that a firm’s wage costs are equal to W(h)N, where W(h) is an increasing, convex function as above.

One can then again compute the marginal cost of increased output at some date, assuming that it is achieved through an increase in employment at that date only, holding fixed the number of hours per employee h at all dates, as well as other inputs. One again obtains (2.12), except that the definition of Q in (2.13) must be modified to replace 7я by 7/v, the growth rate of employment, throughout. (In the modified (2.13), w now refers to the average wage, W(h)/h.) Correspondingly, (2.15) is unchanged.

# PRICES AND COSTS: Corrections to the Labor-Share Measure of Real Marginal Cost 7 The intuition for this result is that high lagged levels of hours imply that the current cost of producing an additional unit is relatively low (because adjustment costs are low) so that current markups must be relatively high. Since, as we showed earlier, the labor share is more positively correlated with lags of hours (and more negatively correlated with leads of hours) this correction tends to make computed markup fluctuations more nearly coincident with fluctuations in hours.

To put this differently, consider the peak of the business cycle where hours are still rising but expected future hours are low. This correction suggests that marginal cost are particular high at this time because there is little future benefit from the hours that are currently being added.