The labor market differs somewhat from the market for goods and services because labor demand is a derived demand; labor is not desired for its own sake but rather because it aids in producing output. Firms determine their demand for labor through a lens of profit maximization, ultimately seeking to produce the optimum level of output and the lowest possible cost.
Labor Market Equilibrium
In order to find the equilibrium quantity and price of labor, economists generally make several assumptions:
- The marginal product of labor (MPL) is decreasing;
- Firms are price-takers in the goods market (cannot affect the price of output) as well as in the labor market (cannot affect the wage rate);
- The supply of labor is elastic and increases with the wage rate (upward sloping supply); and
- Firms are profit-maximizers.
The marginal revenue product of labor (MRPL) is equal to the MPL multiplied by the price of output. The MRPL represents the additional revenue that a firm can expect to gain from employing one additional unit of labor - it is the marginal benefit to the firm from labor. Under the above assumptions, the MRPL is decreasing as the quantity of labor increases, and firms can increase profit by hiring more labor if the MRPL is greater than the marginal cost of that additional unit of labor - the wage rate. Thus, firms will hire more labor when the MRPL is greater than the wage rate, and stop hiring as soon as the two values are equal. The point at which the MRPL equals the prevailing wage rate is the labor market equilibrium.
Optimal Demand for Labor
The optimal demand for labor is located where the marginal product equals the real wage rate. The curved line represents the falling marginal product of labor, the y-axis is the marginal product/wage rate, and the x-axis is the quantity of labor.
Optimizing Capital and Labor
In the long run, firms maximize profit by choosing the optimal combination of labor and capital to produce a given amount of output. It's possible that an automobile company could manufacture 1,000 cars using only expensive, technologically advanced robots and machinery (capital) that do not require any human participation. It's also possible that the company could produce the same number of vehicles using only employee work (labor), without any assistance from machines or technology. For most industries, however, relying solely on capital or solely on labor is more expensive than using some combination of the two .
Factory Worker
Most firms need a combination of both labor and capital in order to produce their product.
Firms use the marginal decision rule in order to decide what combination of labor, capital, and other factors of production to use in the creation of output. The marginal decision rule says that a firm will shift spending among factors of production as long as the marginal benefit of such a shift exceeds the marginal cost. Imagine that a firm must decide whether to spend an additional dollar on labor. To determine the marginal benefit of that dollar, we divide the marginal product of labor (MPL) by it's price (the wage rate, PL): MPL/PL. If capital and labor are the only factors of production, then spending an additional $1 on labor while holding the total cost constant means taking $1 out of capital. The cost of that action will be the output lost from cutting back on capital, which is the ratio of the marginal product of capital (MPK) to the price of capital (the rental rate, PK). Thus, the cost of cutting back on capital is MPK/PK.
If the marginal benefit of additional labor, MPL/PL, exceeds the marginal cost, MPK/PK, then the firm will be better off by spending more on labor and less on capital. On the other hand, if MPK/PK is greater than MPL/PL, the firm will be better off spending more on capital and less on labor. The equilibrium - the point at which the firm is producing the maximum amount of output at a given cost - occurs where MPL/PL=MPK/PK.