Labor

To produce goods and services, a firm uses raw materials, labor, and capital. We will now look at the market for labor. The workers sell their labor, or alternatively the sell their leisure time, for a wage, and their supply depends on their valuations of leisure and wage, respectively. From the firm’s perspective, it buys labor as long as that gives a positive contribution to its profit. The firm’s cost of labor is the wage, and its revenue of labor is the price at which they can sell the goods. The firm will consequently hire workers until the last produced unit of the good costs as much to produce as the firm is paid for it.

This means that the structure in the output market, i.e. the market where the firm sells its goods, will also affect what the firm will be willing to pay in wages, since it is in the output market that the price is set. We will study the cases when the output market is a perfectly competitive market and when it is a monopoly market. Furthermore, the structure of the labor market also affects the outcome. We study cases in which either the firm, or the workers, or both of them are in a monopoly position or in a perfectly competitive situation.

The Supply of Labor

We will assume that the workers prefer leisure to work and that they work for, and only for, the wage. There are 24 hours in a day, which sets an upper bound for how much labor a worker can sell. To analyze the supply of labor, it is useful to redefine the question: Instead of studying the supply of labor, we will study the demand for leisure. The supply of work will then be 24 minus the amount of leisure. Then, we can analyze the situation as in Figure 16.1. As we are studying the consumption of two goods, leisure and wage (where, again, it is useful to think of money, the wage, as “all other goods than leisure”), increases and decreases in wage will have both substitution- and income effects. Note that one can view an increase in wage as a decrease in the price of “all other goods.” The budget line will then rotate around a fixed point at 24 (as a day has exactly 24 hours) on the X-axis and intersect the Y-axis at different points depending on the wage. (However, note one thing: Here, the price of the other good changes (i.e. wage, not leisure), not the price of the one we are analyzing.)

In Figure 16.1, we have drawn four budget lines, corresponding to four different levels of income, w (for wage), and four indifference curves. The indifference curves, as always, indicate combinations of the two goods that the individual is indifferent between, and she strives to maximize her utility given the budget restriction. As before, the point of maximization occurs where an indifference curve just barely touches a budget line. We have indicated four such points of tangency in the figure, and then connected them to a curve. That curve corresponds to the individual’s demand for leisure, and indirectly (if you take 24 minus her demand for leisure) to her supply of labor. The odd thing about the supply curve for labor is that it slopes back again at high wages. Remember that the effect of a price change can be divided into a substitution effect and an income effect . At initially low wages, an increase in the wage often leads to an increase in the labor supplied. That is due to the substitution effect dominating over the income effect. The substitution effect makes the wage more attractive relative eisure, whereas the income effect makes the individual wealthier. The increase in wealth can lead to an increased consumption of both “other goods” (the wage) and of leisure.

The higher the wage is, the more important the income effect will be, until finally it will start to dominate over the substitution effect. If a well-paid individual has her wage increased even further, she may choose to work less than she used to. This is what makes the supply curve for labor bend backwards for high wages.

The Marginal Revenue Product of Labor

we studied the firm’s production, and we defined the production function as a function of labor, L, and capital, K, such that q = f(L,K). In the long run, both L and K are variable, in the short run only L is variable. If the firm buys one more unit (for instance, one more hour) of labor, how will that affect the profit? Remember that we defined the marginal product of labor, MP_L. In words, MP_L is how much more of the good that will be produced if we increase labor by a small amount (say, one more unit), given that everything else is held constant. When the firm decides whether to buy more labor, it first asks how large the value of the extra production is, i.e. how valuable is MP_L? We can express this value mathematically as

Here, MRP_L, is the marginal revenue product of labor. It corresponds to how much total revenue, TR, changes because of a small increase in L. In the third step above, we have divided and multiplied by Δq in order to show that

MRP_L = MR*MP_L. In other words, if we hire one more unit of labor, the value added is how many additional units of the good is produced during that hour (MP_L) times at which price can we sell each additional unit (MR). That value added is called the marginal revenue product of labor.

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