Worker Utility

1. Worker Utility • Example: Suppose worker utility is given by • The more C and L the happier is the worker

2. Worker Utility • Example: Suppose worker utility is given by • Holding C constant, the more L goes up the happier the worker is

3. Diminishing Marginal Utility • Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal

4. Diminishing Marginal Utility • Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal

5. Diminishing Marginal Utility • Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal

6. Diminishing Marginal Utility • Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal

7. Diminishing Marginal Utility • Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal

8. Indifference Curves • Example: Suppose worker utility is given by • If the worker is indifferent between all market baskets located on an indifference curve, then U is being held constant along it while L and C change

9. Indifference Curves • Example: Indifference curve withU0= 10 U0 = 10

10. Indifference Curves • Example: Indifference curve withU1= 20 U1 = 20 U0 = 10

11. Budget line • C = (w)(H) + A • T = L + H • T – L = H • C = (w)(T – L) + A • C = (wT + A) – w L • Constraints set boundaries on the worker’s opportunity set of all the consumption baskets the worker can afford

12. Budget line • Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) 800 500 100 10 40 80 leisure

13. Budget line • Example: What happens if A increases to 200 ($ per week) 800 500 100 10 40 80 leisure

14. Budget line • Example: What happens if w increases to 12 ($ per hour) 800 500 100 10 40 80 leisure

15. The Hours of Work Decision • Individual will choose consumption and leisure to maximize utility • Optimal consumption is given by the point where the budget line is tangent to the indifference curve • At this point the Marginal Rate of Substitution between consumption and leisure (slope of the indifference curve) equals the wage rate (slope of the budget constraint) • Any other bundle of consumption and leisure given the budget constraint would mean the individual has less utility

16. The Hours of Work Decision • Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) L* = 41 C* = 900 – 10(41) = 490 H* = 80 – 41= 39 500 U2 U1 U0 100 10 40 80 leisure

17. Change in non-earned income • Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) What happens if A increases to 200 ($ per week)? L* = 38 L* = 41 C* = 1000 – 10(38) = 620 C* = 490 H* = 42 H* = 39 500 U1 Leisure is an inferior good since hours of leisure falls 100 10 40 80 leisure

18. Change in non-earned income • Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) What happens if A increases to 200 ($ per week)? L* = 50 L* = 41 C* = 1000 – 10(50) = 500 C* = 490 H* = 30 H* = 39 500 U1 Leisure is a normal good since hours of leisure increases 100 10 40 80 leisure

19. Change in the wage rate • Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) • What happens if w increases to 12 ($ per hour) L* = 40 L* = 41 C* = 1060 – 12(40) = 580 C* = 490 800 H* = 40 H* = 39 500 Since w is the price of Leisure, the law of demand holds An increase in w increases H because SE > IE 100 10 40 80 leisure

20. Change in the wage rate • Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) • What happens if w increases to 12 ($ per hour) L* = 46 L* = 41 C* = 1060 – 12(46) = 508 C* = 490 800 H* = 34 H* = 39 500 An increase in w decreases H because IE > SE 100 10 40 80 leisure

21. Change in the wage rate • When the Income Effect dominates: U1 Consumption ($) U0 SE A IE TE 80 0 40 44 60 Leisure An increase in w decreases H because IE > SE

22. Change in the wage rate • When the Substitution Effect dominates: U1 Consumption ($) U0 SE A IE TE 80 0 35 40 50 Leisure An increase in w increases H because SE > IE

23. The reservation wage • Are the “terms of trade” sufficiently attractive to bribe a worker to enter the labor market? • Reservation wage: the minimum increase in income 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

24. The reservation wage • Initially the individual does not work because w is too low L* = 80 H* = 0 Consumption ($) If w increases a little, H* = 0 If w increases a lot, L* = 70 H* = 10 U2 A U1 U0 Leisure 40 70 80 0

25. Labor Supply • Relationship between hours worked and the wage rate • At wages slightly above the reservation wage, the labor supply curve is positively sloped (the substitution effect dominates) • If the income effect begins to dominate, hours of work decline as wage rates increase (a negatively sloped labor supply curve) • Labor supply elasticity • (% change in hours worked) / (% change in wage rate) • Labor supply elasticity less than 1 means “inelastic” (insensitive) • Labor supply elasticity greater than 1 means “elastic”

26. Labor Supply • Example of backward bending labor supply: Wage Rate ($) IE > SE 27 20 SE > IE 10 0 40 24 30 Hours of Work

27. Female Labor Supply (1960-1980) • Source: Jacob Mincer, “Intercountry Comparisons of Labor Force Trends and of Related Developments: An Overview,” Journal of Labor Economics 3 (January 1985, Part 2): S2, S6.

28. Welfare Programs and Work Incentives Let A = $500 per month, w = $5 per hour, and BRR = –0.5

29. Welfare Programs and Work Incentives • In some states the cash grant is reduced at the “benefit reduction rate”. The BRR acts as a tax on earnings. Consumption ($) L* = 55 L* = 40 BRR = tax = 50% H* = 25 H* = 40 U1 U0 500 Hours of Leisure 0 40 80 55

30. Welfare Programs and Work Incentives • If states choose a BRR equal to 100%, workers will not work because earnings are taxed at a rate of 100%. Consumption ($) BRR = tax = 100% L* = 80 L* = 40 H* = 0 H* = 40 U1 U0 500 Hours of Leisure 0 40 80

31. Welfare Programs and Work Incentives • Choosing a BRR equal to 0%, means the worker will work more than she did when the BRR was equal to 50%. Consumption ($) L* = 55 L* = 40 BRR = tax = 0% H* = 35 H* = 40 U1 U0 500 Hours of Leisure 0 40 45 80

32. Welfare Programs and Work Incentives • The EITC phase in a cash grant at 40% for low-income workers is a wage subsidy (negative tax) of 40%. Consumption ($) L* = 35 L* = 40 EITC = -tax = -40% H* = 45 H* = 40 U1 U0 500 Hours of Leisure 0 40 35 80

33. Welfare Programs and Work Incentives Consumption ($) 33,178 Net wage is 21.06% below the actual wage 17,660 Net wage equals the actual wage 14,490 13,520 Net wage is 40% above the actual wage 10,350 0 110 Leisure