1. Example: Suppose worker utility is given by The more C and L the happier is the worker Worker Utility C ($) L (hours) U (utils) 000 1001031.6 2002063.3 3003094.9 40040126.5 50050158.1

2. Example: Suppose worker utility is given by Holding C constant, the more L goes up the happier the worker is C ($) L (hours) U (utils) 30000 1054.8 3002077.5 3003094.9 30040109.5 30050122.5 Worker Utility

3. Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal C ($) L (hours) U (utils) 30000 1054.8 3002077.5 3003094.9 30040109.5 30050122.5 Diminishing Marginal Utility

4. Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal C ($) L (hours) U (utils) 30000 1054.8 3002077.5 3003094.9 30040109.5 30050122.5 Diminishing Marginal Utility

5. Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal C ($) L (hours) U (utils) 30000 1054.8 3002077.5 3003094.9 30040109.5 30050122.5 Diminishing Marginal Utility

6. Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal C ($) L (hours) U (utils) 30000 1054.8 3002077.5 3003094.9 30040109.5 30050122.5 Diminishing Marginal Utility

7. Marginal utility (MU) is the amount by which U rises when the consumption of a good increases by one unit, holding all else equal C ($) L (hours) U (utils) 30000 1054.8 3002077.5 3003094.9 30040109.5 30050122.5 Diminishing Marginal Utility

8. 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 Indifference Curves

9. Example: Indifference curve with U 0 = 10 LC 10 402.5 1001 U 0 = 10 Indifference Curves

10. Example: Indifference curve with U 1 = 20 LC 1040 10 1004 U 0 = 10 U 1 = 20 Indifference Curves

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. Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) LC 10800 40500 80100 800 10 40 80 leisure 500 100 Budget line

13. Example: What happens if A increases to 200 ($ per week) LC 10900 40600 80200 800 10 40 80 leisure 500 100 Budget line

14. Example: What happens if w increases to 12 ($ per hour) LC 10940 40580 80100 800 10 40 80 leisure 500 100 Budget line

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. Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) 10 40 80 leisure 500 100 U2U2 U1U1 U0U0 L * = 41 H * = 80 – 41 = 39 C * = 900 – 10(41) = 490 The Hours of Work Decision

17. Change in non-earned income Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) 10 40 80 leisure 500 100 U1U1 L * = 41 H * = 39 C * = 490 What happens if A increases to 200 ($ per week)? L * = 38 H * = 42 C * = 1000 – 10(38) = 620 Leisure is an inferior good since hours of leisure falls

18. Example: The budget constraint with T = 80 (hours per week), A = 100 ($ per week), w = 10 ($ per hour) 10 40 80 leisure 500 100 U1U1 L * = 41 H * = 39 C * = 490 What happens if A increases to 200 ($ per week)? L * = 50 H * = 30 C * = 1000 – 10(50) = 500 Leisure is a normal good since hours of leisure increases Change in non-earned income

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

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

21. When the Income Effect dominates: U1U1 U0U0 A 6040 80 0 44 TE Consumption ($) SE IE Leisure An increase in w decreases H because IE > SE Change in the wage rate

22. When the Substitution Effect dominates: U1U1 U0U0 A 5040 80 0 35 TE Consumption ($) An increase in w increases H because SE > IE SE IE Leisure Change in the wage rate

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. Initially the individual does not work because w is too low U2U2 U0U0 A 704080 0 Consumption ($) Leisure U1U1 L * = 80 H * = 0 If w increases a little, H * = 0 If w increases a lot, L * = 70 H* = 10 The reservation wage

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. Example of backward bending labor supply: Hours of Work 0 Wage Rate ($) 40 2430 10 20 27 SE > IE IE > SE Labor Supply

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. Let A = $500 per month, w = $5 per hour, and BRR = –0.5 Welfare Programs and Work Incentives HwHA Benefit Reduction Actual Transfer Total Income 005000 15 -2.5497.5502.5 210500-5495505 315500-7.5492.5507.5 176880500-44060940 199995500-497.52.5997.5 2001000500-50001000 2011005500-50001005 2021010500-50001010

29. In some states the cash grant is reduced at the “benefit reduction rate”. The BRR acts as a tax on earnings. Consumption ($) 500 Hours of Leisure 0 80 40 U1U1 L * = 40 H * = 40 L * = 55 H * = 25 55 BRR = tax = 50% U0U0 Welfare Programs and Work Incentives

30. If states choose a BRR equal to 100%, workers will not work because earnings are taxed at a rate of 100%. Consumption ($) Hours of Leisure 0 80 40 U0U0 L * = 40 H * = 40 BRR = tax = 100% U1U1 500 L * = 80 H * = 0 Welfare Programs and Work Incentives

31. Choosing a BRR equal to 0%, means the worker will work more than she did when the BRR was equal to 50%. Consumption ($) 500 Hours of Leisure 0 80 40 L * = 40 H * = 40 L * = 55 H * = 35 45 BRR = tax = 0% U1U1 U0U0 Welfare Programs and Work Incentives

32. The EITC phase in a cash grant at 40% for low-income workers is a wage subsidy (negative tax) of 40%. Consumption ($) 500 Hours of Leisure 0 80 40 L * = 40 H * = 40 L * = 35 H * = 45 35 EITC = -tax = -40% U1U1 U0U0 Welfare Programs and Work Incentives

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