Profit Maximization

We can use the diagram also to understand why VMP=wage is the diagnostic that tells us the profit is at a maximum. Suppose the labor input is less than 500 -- for example, suppose labor input is 200. Than an additional labor-day of labor will add about 7.8 units to output, and about $780 to the firm's sales revenue, but only $500 to the firm's costs, adding roughly $220 to profits. So it is profitable to increase the labor input from 200, or, by the same reasoning, from any labor input less than $500.

This difference between the VMP and the wage is the increase or decrease in profits from adding or subtracting one unit of labor. It is sometimes called the marginal profit and (as we observed in studying consumers' marginal benefits) the absolute value of the marginal profits is a measure of unrealized potential profits. That's why the businessman wants to adjust the labor input so that VMP-wage=0.

Let's try one more example. Suppose the labor input is 800 labor-days per week. If the firm "downsizes" to 799 labor-days, it reduces its output by just about 1.2 units and its sales revenue by about $120, but it reduces its labor cost by $500, increasing profits by about $380. Thus a movement toward the VMP=wage again increases profits by realizing some unrealized potential profit.

The formula VMP=wage is a diagnostic for maximum profits because it tells us that there is no further potential to increase the profits by adjusting the labor input -- marginal profit is zero.

The marginal productivity rule is the key to maximization of profits in the short run. But now let's take a look at the long run perspective.

A Long Run Perspective