1. Appendix to Chapter 13 Labor Supply © 2004 Thomson Learning/South-Western

2. 2 Allocation of Time People must choose how to allocate their available fixed time between work and other activities. Table 13A.1 shows the considerable variation in these choices. The study of time allocation allows economists to understand how these decisions adjust to changes in opportunities.

3. 3 TABLE 13A.1: Time Allocation (Percentage of Time during Typical Week) Source: Adapted from F.T. Juster and F.P. Stafford, “The Allocation of Time: Empirical Findings, Behavioral Models and Problems of Measurement,” Journal of Economic Literature (June 1991), Table 1.

4. 4 A Simple Model of Time Use Assume there are only two uses of time, market work or not working. Leisure is time spend in any activity other than market work. Assume utility depends only upon the consumption of market goods (C) and the amount of leisure time (H).

5. 5 A Simple Model of Time Use An indifference curve map for such a utility function is shown in Figure 13A.1. The opportunity cost of leisure – An extra hour of leisure taken by a person costs them the income they could have earned in that hour, their wage rate (w). – Thus, the opportunity cost of leisure is the real wage rate determined in the market.

6. 6 Consumption U1U1 Leisure hours per day 0 U2U2 U3U3 FIGURE 13A.1: Utility-Maximizing Choice of Hours of Leisure and Work

7. 7 APPLICATION 13A.1: The Opportunity Cost of Time Transportation Choices – People consider both time and dollar costs in commuting to work. – Studies suggest that people’s willingness to pay to avoid wait conclude that people value time at about one-half their market wage. – For example, fewer people use the San Francisco transit system because of the time costs involved in reaching train stations.

8. 8 APPLICATION 13A.1: The Opportunity Cost of Time The Economics of Childbearing – One of the most important economic costs of having children is the forgone wages of parents who do not work. Estimates suggest these costs exceed all other childbearing costs combined. – Economists suggest that the higher real wages earned by U.S. women help explain the decline in birthrates.

9. 9 APPLICATION 14A.1: The Opportunity Cost of Time Job Search Theory – Uncertainty in job search necessitates investments in time and resources. – The market wage rate can be used to approximate the hourly search costs. – Higher wages lead to ways to economize on these costs. – Subsidized search (unemployment benefits) prolong search time by up to 10 percent.

10. 10 Utility Maximization If Figure 13A.1, the person can enjoy up to 24 hours of leisure by not working. – This point is the horizontal intercept of the budget constraint. If the person works, he or she can purchase (24·w) in consumption goods. – This point is the vertical intercept. The slope of the constraint equals -w.

11. 11 Consumption U1U1 24w Leisure hours per day 024 U2U2 U3U3 FIGURE 13A.1: Utility-Maximizing Choice of Hours of Leisure and Work

12. 12 Utility Maximization Given the budget constraint, the person maximizes his or her utility at H *, working the rest of the time and consuming C * units of consumption goods. At this point, the slope of the indifference curve, MRS (leisure for consumption) equals the wage rate.

13. 13 Consumption U1U1 C* 24w Leisure hours per day 0H*24 U2U2 U3U3 FIGURE 13A.1: Utility-Maximizing Choice of Hours of Leisure and Work

14. 14 Substitution Effect of a Change in w. The substitution effect of a change in w is the movement along an indifference curve in response to a change in the real wage. – When w rises, the price of leisure becomes higher-- people must give up more in lost wages for each hour of leisure consumed. – A rise in w causes an individual to work more.

15. 15 Income Effect of a Change in w The income effect of a change in w is the movement to a higher indifference curve in response to a rise in the real wage rate. – If leisure is a normal good, the higher income will increase the demand for it. – A rise in the wage rate will cause an individual to work less.

16. 16 A Graphical Analysis With a rise in the wage rate, the substitution effect results in less leisure while the income effect results in more leisure. Whether the person works more, less, or the same depends upon the relative strengths of these two effects. Two cases are illustrated in Figure 13A.2

17. 17 A Graphical Analysis In both graphs, the optimal choices of consumption and leisure before the wage increase (w = w 0 ) are C 0 and H 0. With a wage increase to w 1 the new optimal choices are C 1 and H 1. The substitution effect is shown by the movement along U 0 from H 0 to S. – This reduces the optimal amount of leisure.

18. 18 Consumption U0U0 U1U1 S C0C0 C1C1 Leisure hours per day 0 (a) Rise in Wage Increases Work Wage = w 0 (b) Rise in Wage Decreases Work Wage = w 1 H0H0 Consumption Leisure hours per day 0H0H0 H1H1 H1H1 U1U1 U0U0 S Wage = w 1 Wage = w 0 FIGURE 13A.2: Income and Substitution Effects of a Change in the Real Wage Rate

19. 19 A Graphical Analysis The movement from S to C 1, H 1, is the income effect which increases the consumption of leisure. In Figure 13A.2(a) the substitution effect is stronger than the income effect so the person works more with a wage increase. The income effect dominates in Figure 13A.2(b) so the person works fewer hours.

20. 20 Market Supply Curve for Labor If the substitution effect generally exceeds the income effect, most individual labor supply curves will have positive slopes. A market supply curve is the horizontal summation of these individual supply curves. In addition, the rising wage will induce people to enter the labor force.

21. 21 Market Supply Curve for Labor In Figure 13A.3, this situation is shown with two people. At wages below w 1, no one works so there is no market supply. Between w 1 and w 2 only person 1 works so the market curve is the same as person 1. Above w 2 both work and the market curve reflects the summation of hours supplied.

22. 22 Real wage Hours per week S (a) Person 1 0 (b) Person 2 Total labor supply per week (c) The Market Hours per week w1w1 w2w2 w3w3 Real wage Real wage S1S1 S2S2 FIGURE 13A.3: Construction of the Market Supply Curve for Labor

23. 23 APPLICATION 13A.2: Changing Labor Force Participation for Married Women and Older Men Two important U.S. labor market trends. – Increasing tendency for married women to hold paying jobs. – The decline in the employment of older men. These two trends are shown in Table 1.

24. 24 TABLE 1: Labor Force Participation Rates, 1960 - 2000 Source: Statistical Abstract of the United States at http://www.census.gov/ Table 1 Labor Force Participation Rates, 1960-2000

25. 25 Expanding Female Labor Force Participation The fraction of 25 to 34 year old married women in the labor force doubled between 1960 and 1980. – It continued to rise for the next 15 years. – Economists attribute most of this increase to higher wages. – Sociologist attribute this to changing political and cultural factors.

26. 26 The Case of Older Men Between 1960 and 1985, the labor force participation rate of older married men fell to less than half of its initial level. – At the same time, there have been improvements in health which should have stimulated employment. – Most attribute the trend to increased retirement due to rising Social Security coverage and benefits.