Appendix toChapter 13

Labor Supply

© 2004 Thomson Learning/South-Western

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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.

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TABLE 13A.1: Time Allocation (Percentage of Time during Typical Week)

Men Women U.S. Japa

n Russia U.S. Japa

n Russia

Market work 28.3%

33.6%

35.1% 15.4% 15.3%

25.4%

Housework 8.2 2.1 7.1 18.2 18.5 16.1 Personal care and sleep

40.6 43.1 40.4 42.6 42.9 41.6

Leisure and other 22.9 21.2 17.4 23.8 23.3 16.9

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.

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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).

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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.

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Consumption

U1

Leisure hoursper day

0

U2

U3

FIGURE 13A.1: Utility-Maximizing Choice of Hours of Leisure and Work

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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.

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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.

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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.

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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.

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Consumption

U1

24w

Leisure hoursper day

0 24

U2

U3

FIGURE 13A.1: Utility-Maximizing Choice of Hours of Leisure and Work

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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.

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Consumption

U1

C*

24w

Leisure hoursper day

0 H* 24

U2

U3

FIGURE 13A.1: Utility-Maximizing Choice of Hours of Leisure and Work

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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.

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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.

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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

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A Graphical Analysis

In both graphs, the optimal choices of consumption and leisure before the wage increase (w = w0) are C0 and H0.

With a wage increase to w1 the new optimal choices are C1 and H1.

The substitution effect is shown by the movement along U0 from H0 to S.– This reduces the optimal amount of leisure.

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Consumption

U0

U1

S

C0

C1

Leisure hoursper day

0

(a) Rise in Wage Increases Work

Wage = w0

(b) Rise in Wage Decreases Work

Wage = w1

H0

Consumption

Leisure hoursper day

0 H0H1H1

U1U0

S

Wage = w1

Wage = w0

FIGURE 13A.2: Income and Substitution Effects of a Change in the Real Wage Rate

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A Graphical Analysis

The movement from S to C1, H1, 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.

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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.

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Market Supply Curve for Labor

In Figure 13A.3, this situation is shown with two people.

At wages below w1, no one works so there is no market supply.

Between w1 and w2 only person 1 works so the market curve is the same as person 1.

Above w2 both work and the market curve reflects the summation of hours supplied.

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Realwage

Hoursper week

S

(a) Person 1

0

(b) Person 2

Total labor supplyper week

(c) The Market

Hoursper week

w1

w2

w3

Realwage

Realwage

S1

S2

FIGURE 13A.3: Construction of the Market Supply Curve for Labor

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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.

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TABLE 1: Labor Force Participation Rates, 1960 - 2000

Source: Statistical Abstract of the United States at http://www.census.gov/

Year Femalesage 25-34

Males age 65and over

1960 35.2 33.91970 43.1 27.71975 53.7 21.61980 65.5 191985 69.4 15.81990 73.5 16.31995 74.9 16.82000 76.3 17.5

Table 1 Labor Force Participation Rates, 1960-2000

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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.

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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.