Minimum Wage laws that reduce labor costs

Abstract

It may seem obvious that minimum wage laws raise labor costs. Yet, what seems obvious is not necessarily so, especially in efficiency wage models. In these models, firms choose to set wages higher than the opportunity costs of labor to induce greater effort, reduce tumover, or in other ways lower costs or raise efficiency (effective labor input per worker). Let reducing turnover be the motivation. Turnover likely falls as either the wage (w) or unemployment rate (u) rises. Either of these raises the attractiveness of the job relative to its alternative, quitting to search for a new job. A fall in turnover raises the average worker's efficiency (E), either because the average worker is more experienced or because less time is spent training new hires. Mathematically, E =E(w, u). To maximize profits, the firm chooses the wage that minimizes effective labor costs (w/E). The first-order condition for minimization is (0 [w/E]/Ow) = 0. This is another form of the Solow condition [Lai and Chang, AEJ, 1993, p. 57]. Once the firm has found its minimum w/E, it chooses the profit-maximizing output level. Of course, output is a decreasing function of the effective labor cost. Now, consider the effects of a minimum wage law that mandates only a small increase in the wage above the firm-chosen wage (for a very large increase, the results of this paper may not hold). There is no direct effect of the higher wage on w/E, since (O[w/E]/Ow) = 0. If there were no change in unemployment, costs would be constant and so output would be constant. But, constant output with greater worker productivity implies fewer workers. Thus, unemployment must rise. With more unemployment, turnover falls further. Lower turnover implies greater efficiency and therefore lower effective labor costs. Costs fall because efficiency rises twice. The direct effect through wages raises efficiency by the same proportion that the wage rises. This leaves costs constant. The indirect effect, due to unemployment, raises it even more. This lowers costs. The indirect effect works like a positive firm-to-firm externality, Atomistic firms do not take it into account when setting wages; one firm's wage cannot significantly change the unemployment rate. However, when the minimum wage forces all firms to pay more, they all reduce employment and they all profit through reduced turnover. Combining the direct and indirect effects, productivity rises more than the wage does; labor costs fall. More complete models yield the same result (derivations are available from the author on request). Although the result may be counter-intuitive, it is not new. Webb [JPE, 1912, p. 990] wrote: "To put it plumply, if the employers paid more, the labor would be worth more. In so far as this proves to be the case, the legal minimum wage would have raised the Standard of Life without the loss of trade, without cost to the employer, and without disadvantage to the community."