PRICES AND COSTS: Corrections to the Labor-Share Measure of Real Marginal Cost 4

One reason might be monopsony power in the labor market. Suppose that each firm faces an upward-sloping firm-specific labor supply curve, and takes this into account in its hiring and production decisions. (The wage that the firm must pay may also depend upon other variables such as the overall level of employment in the economy, but these factors are taken as given by the individual firm, and can simply be treated as time-variation in the location of the firm-specific labor supply curve.)
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If w(H) is the wage that the firm must pay if it hires H hours of work, then W(H) = Hw(H), and ш = 1 + 6#^, where is the elasticity of the firm-specific labor supply curve. This might be either increasing or decreasing with increases in hours hired by the firm. The most plausible assumption, however, would probably be that the elasticity of labor supply decreases as the hours hired by the firm increase (it is hard to induce people to work more than a certain number of hours, even at very high wages, while on the other hand the opportunity cost of their time tends not to fall below a certain level even when the number of hours worked is small). Under this assumption, the factor oj is an increasing function of Я, and (2.9) again holds, with b
Alternatively, one might imagine that firms first hire a certain number of employees, and that they initially contract with them about a wage schedule which determines the wage as a function of hours worked. Subsequently, perhaps after receiving additional information about current demand conditions, the firms determine the hours of work. If all employees are asked to work the same number of hours at this stage, we may interpret W{H) in (2.11) as the wage schedule negotiated with each employee.

Now if the number of employees is chosen ex ante so as to minimize the cost of the number of hours that the firm expects to use, then ex ante expected hours per worker will be the level H* that minimizes the average wage W(H)/H22 At this point, the marginal wage should equal the average wage, and (assuming a unique minimum) in the case of small fluctuations in H around the value H*, to should be increasing in H. Again this would imply markups more countercyclical than would be suggested by (2.5).

Most observed wage contracts do not involve wages that increase continuously with the number of hours that the employee is asked to work. On the other hand, if one supposes that contractual wages are not the true shadow price of additional labor to a firm, because of the presence of implicit contracts of the kind assumed, for example, by Hall (1980), then one might suppose that the true cost to the firm rises in proportion to the employee’s disutility of working, even if the wages that are paid in the current period do not. This would be a reason to expect the effective wage schedule W(H) to be convex, so that the above analysis would apply.