Labor Supply. Ch. 2: 3-8

Transcription

1 Labor Supply Ch. 2: 3-8

2 Introduction to Labor Supply We saw some facts. How do we explain them? Outline: Microeconomic foundations of the labor supply decision. Extensive margin: To work, or not to work? Participation decision. Intensive margin: How hard to work? Hours of work decision McGraw-Hill Education. All Rights Reserved. 3

3 Utility Function Neo-Classical Model of Labor-Leisure Choice Measure of satisfaction individuals receive from consumption (C) of goods and leisure (L). U = f(c, L) U is an index. The higher is U, the happier is the person McGraw-Hill Education. All Rights Reserved. 11

4 Indifference Curves Downward sloping captures the tradeoff between the two goods: consumption and leisure. Higher curve = higher utility (Fig. 2-2) Do not intersect (Fig. 2-3) Convex to the origin, indicating that opportunity costs increase. Differences in preferences (Fig. 2-4) 2016 McGraw-Hill Education. All Rights Reserved. 12

5 Indifference Curves Fig. 2-2 Consumption ($) ,000 Utils 25,000 Utils Hours of Leisure 2016 McGraw-Hill Education. All Rights Reserved. 13

6 Indifference curves do not cross! If they did, higher curve = higher utility condition would be violated 2016 McGraw-Hill Education. All Rights Reserved. 6

7 Differences in Preferences Fig. 2-3 Consumption ($) Consumption ($) U 1 U 1 U U 0 0 Hours of Leisure Hours of Leisure Workers with steeper indifference curves value their leisure relatively more than workers with shallower indifference curves McGraw-Hill Education. All Rights Reserved. 14

8 C = wh + V The Budget Constraint Consumption equals earnings from work (wages hours of work) plus nonlabor income (V). The budget constraint defines the worker s opportunity set: all of the consumption leisure combinations the worker can afford. Endowment of worker: (V, T) To discover the budget line, use h = T L. As h = T L, can rewrite C = w(t L) + V. (Fig. 2-5) 2016 McGraw-Hill Education. All Rights Reserved. 15

9 The Budget Constraint Fig. 2-5 Consumption ($) wt+v V 0 Budget Line T E C = w(t L) + V (1) Set L = T (no work): Defines minimum C. E = endowment point (2) Set L = 0 (no leisure): Defines maximum C. Y = wt + V = full income (3) Take derivative w.r.t. L: dc/dl = -w Hours of Leisure 2016 McGraw-Hill Education. All Rights Reserved. 16

10 The Hours of Work Decision Individuals choose consumption and leisure to maximize utility. Optimal consumption is given by the point where the budget line is tangent to the indifference curve (Fig. 2-6). At this point the marginal rate of substitution (MRS) between consumption and leisure equals the wage. Any other consumption leisure bundle on the budget constraint would give the individual less utility McGraw-Hill Education. All Rights Reserved. 17

11 Optimal Consumption and Leisure Fig. 2-6 $1,200 $1,100 A Y $500 P U 1 U* $ E U 0 Hours of Leisure Hours of Work 2016 McGraw-Hill Education. All Rights Reserved. 18

12 Slope of an indifference curve U = U(C, L); Marginal utility = the change in utility associated with a unit change in a good consumed. Let MMMM LL = / CC kkkkkkkk cccccccccccccccc MMMM CC = / CC LL kkkkkkkk cccccccccccccccc UU = LL MMMM LL + CC MMMM CC. Utility is constant on an indifference curve. 0 = LL MMMM LL + CC MMMM CC CC = MMMM LL < 0. LL UU cccccccccccccccc MMMM CC 2016 McGraw-Hill Education. All Rights Reserved. 12

13 Marginal Rate of Substitution (MRS) MRS = MMMM LL MMMM CC < 0 Holding utility constant, to get more of one good, need to give up the other suppose CC > 0, then LL < 0! Some textbooks define MRS as the absolute value of the ratio of the marginal utilities McGraw-Hill Education. All Rights Reserved. 13

14 The tangency condition Slope of the indifference curve = slope of the budget line (both slopes are negative!) MMMM LL MMMM CC = ww The rate at which a person is willing to trade leisure for consumption (MRS) = wage rate McGraw-Hill Education. All Rights Reserved. 14

15 The tangency condition Leisure is priced at w ($/hr). Opportunity cost of an extra hour of leisure = w. Rewrite tangency condition as MMMM LL ww = MMMM CC Marginal utility of a dollar s worth of leisure = marginal utility of a dollar s worth of consumption McGraw-Hill Education. All Rights Reserved. 15

16 Changes in the optimal bundle Let (C*, L*) denote the optimal bundle. How does the optimal bundle respond to changes in: (1) Nonlabor income (V)? (2) Wage (w)? The answer depends on individual preferences (the indifference map). We will use graphs to answer the questions McGraw-Hill Education. All Rights Reserved. 16

17 The Effect of a Change in Nonlabor Income on Hours of Work -- Fig. 2-7 (a) Consumption ($) F 1 F 0 P 1 U 1 $200 P 0 U 0 E 1 $100 E Hours of Leisure An increase in nonlabor income leads to a parallel, upward shift in the budget line, moving the worker from point P 0 to point P 1. If leisure is a normal good, hours of work fall McGraw-Hill Education. All Rights Reserved. 19

18 The Effect of a Change in Nonlabor Income on Hours of Work Fig. 2-7 (b) Consumption ($) F 1 F 0 P 1 U 1 $200 P 0 U 0 E 1 $100 E An increase in nonlabor income leads to a parallel, upward shift in the budget line, moving the worker from point P 0 to point P 1. If leisure is inferior, hours of work increase McGraw-Hill Education. All Rights Reserved. 20

19 Change in wages Wage change rotation of the budget line around the endowment point. The slope of the budget line changes! Full income changes! It is useful to decompose the effect of a wage increase into Income effect (utility preserving parallel shift in non-labor income) Substitution effect (movement along an indifference curve) 2016 McGraw-Hill Education. All Rights Reserved. 19

20 More Leisure at a Higher Wage When the income effect dominates the substitution effect, the worker increases hours of leisure in response to an increase in the wage. Consumption ($) G U 1 D R Q F U 0 P D V E Hours of Leisure 2016 McGraw-Hill Education. All Rights Reserved. 21

21 More Work at a Higher Wage When the substitution effect dominates the income effect, the worker decreases hours of leisure in response to an increase in the wage. Consumption ($) G U 1 D U 0 R Q D F P V E Hours of Leisure 2016 McGraw-Hill Education. All Rights Reserved. 22

22 To Work or Not to Work? Are the terms of trade sufficiently attractive to bribe a worker to enter the labor market? Reservation wage: the lowest wage rate that would make the person indifferent between working and not working. Rule 1: if the market wage is less than the reservation wage, then the person will not work. Rule 2: the reservation wage increases as nonlabor income increases 2016 McGraw-Hill Education. All Rights Reserved. 22

23 The Reservation Wage Consumption ($) H Has Slope -w high ww = MMMM LL MMMM CC Reservation wage: G X Y E U H ww = MMMM LL MMMM CC LL=TT CC=VV MRS at point E U 0 0 T Has Slope - ww Hours of Leisure 2016 McGraw-Hill Education. All Rights Reserved. 24

24 Labor Supply Curve Relationship between hours worked and the wage rate: h ii = h ii ww. At wages slightly above the reservation wage, the labor supply curve is positively sloped. Over a wide range of wage increases, the substitution effect typically dominates the income effect. When wages rise a lot, the income effect may dominate the substitution effect. Then hours of work declines as the wage rate increases (a negatively sloped labor supply curve). 24

25 Individual labor supply Fig Labor supply: h ii = h ii ww ; hours a function of wages. Here the inverted function, ww = ww(h ii ) has been graphed. 25

26 The Backward Bending Labor Supply Curve The substitution effect typically dominates the income effect over the range of «low» wages, but the reverse may be true when wages are very high. Wage Rate ($) Hours of Work 2016 McGraw-Hill Education. All Rights Reserved. 26

27 Labor Supply Elasticity The labor supply elasticity (σ) measures responsiveness in hours worked to changes in the wage rate. σ = Percent change in hours worked divided by the percent change in wage rate. Labor supply elasticity less than 1 is inelastic as hours of work respond proportionally less than the change in wages. Labor supply elasticity greater than 1 is elastic as hours of work respond proportionally more than the change in wages McGraw-Hill Education. All Rights Reserved. 27

28 Labor supply: two individuals Alice has a higher labor supply elasticity than Brenda. After the kink the joint labor supply curve is shallower in the w-h space, because a given wage increase is associated with a lower total hours response. 28

29 Aggregate Labor Supply Curve When wages are in the ($10, $20) range, aggregate labor supply has the usual slope. If wages rise beyond that, more and more people cut back on hours. Wage Rate ($) Hours of Work 29

30 Estimates of the Labor Supply Elasticity Typical model used by economists: h ii = αα + ββww ii + γγvv ii + ooooooooo vvvvvvvvvvvvvvvvvv h ii = hours of work ww ii = oooooo wwwwwwww VV ii = nnnnnn llllllllll iiiiiiiiiiii ββ < 0 if income effect dominates, ββ > 0 otherwise; γγ < 0 if leisure is a normal good. Took Econ 311 and curious? Borjas 2.8 reviews empirical estimates 30