Suppose wages rise. The higher wage increases the price of leisure. We saw in the chapter on consumer choice that consumers substitute more of other goods for a good whose price has risen. The substitution effect of a higher wage causes the consumer to substitute labor for leisure. To put it another way,the higher wage induces the individual to supply a greater quantity of labor. We can see the logic of this substitution effect in terms of the marginal decision rule. Suppose an individual is considering a choice between extra leisure and the additional income from more work. Let MULe denote the marginal utility of an extra hour of leisure. What is the price of an extra hour of leisure? It is the wage W that the individual forgoes by not working for an hour. The extra utility of $1 worth of leisure is thus given by MULe/W. Suppose, for example, that the marginal utility of an extra hour of leisure is 20 and the wage is $10 per hour. Then MULe/W equals 20/10, or 2. That means that the individual gains 2 units of utility by spending an additional $1 worth of time on leisure. For a person facing a wage of $10 per hour, $1 worth of leisure would be the equivalent of 6 minutes of leisure time. Let MUY be the marginal utility of an additional $1 of income (Y is the abbreviation economists generally assign to income). The price of $1 of income is just $1, so the price of income PY is always $1. Utility is maximized by allocating time between work and leisure so that:
EQUATION 12.5
Now suppose the wage rises from W to W’. That reduces the marginal utility of $1 worth of leisure, MULe/W, so that the extra utility of earning $1 will now be greater than the extra utility of $1 worth of leisure:
EQUATION 12.6
Faced with the inequality in Equation 12.6, an individual will give up some leisure time and spend more time working. As the individual does so, however, the marginal utility of the remaining leisure time rises and the marginal utility of the income earned will fall. The individual will continue to make the substitution until the two sides of the equation are again equal. For a worker, the substitution effect of a wage increase always reduces the amount of leisure time consumed and increases the amount of time spent working. A higher wage thus produces a positive substitution effect on labor supply.
But the higher wage also has an income effect. An increased wage means a higher income, and since leisure is a normal good, the quantity of leisure demanded will go up. And that means a reduction in the quantity of labor supplied.
For labor supply problems, then, the substitution effect is always positive; a higher wage induces a greater quantity of labor supplied. But the income effect is always negative; a higher wage implies a higher income, and a higher income implies a greater demand for leisure, and more leisure means a lower quantity of labor supplied. With the substitution and income effects working in opposite directions,it is not clear whether a wage increase will increase or decrease the quantity of labor supplied—or leave it unchanged.
Figure 12.5 illustrates the opposite pull of the substitution and income effects of a wage change facing an individual worker. A janitor, Meredith Wilson, earns $10 per hour. She now works 42 hours per week, on average, earning $420.
The substitution and income effects influence Meredith Wilson’s supply of labor when she gets a pay raise. At a wage of $10 per hour, she supplies 42 hours of work per week (point A). At $15 per hour, the substitution effect pulls in the direction of an increased quantity of labor supplied, and the income
Now suppose Ms. Wilson receives a $5 raise to $15 per hour. As shown in Figure 12.5, the substitution effect of the wage change induces her to increase the quantity of labor she supplies; she substitutes some of her leisure time for additional hours of work. But she is richer now; she can afford more leisure. At a wage of $10 per hour, she was earning $420 per week. She could earn that same amount at the higher wage in just 28 hours. With her higher income, she can certainly afford more leisure time. The income effect of the wage change is thus negative; the quantity of labor supplied falls. The effect of the wage increase on the quantity of labor Ms. Wilson actually supplies depends on the relative strength of the substitution and income effects of the wage change. We will see what Ms. Wilson decides to do in the next section.
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