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# Chapter 6

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1. Chapter 6 Supply of Labor to the Economy: The Decision to Work

2. Recall the trends in labor force participation that we discussed in Chapter 2: • a dramatic increase in the number of women in the labor force • a decline in labor force participation by men (especially older men) • the average workweek has fallen from 54.3 hours in 1901 to 37.0 hours in 1989.

3. What affects an individual's decision to work? • the supply of labor can be thought of as the opposite of the demand for leisure • in this class, every hour that you are not working for pay is considered “leisure” • we’re going to assume that people need 8 hours for sleeping, eating, etc. so they have 16 hours per day available for either work or leisure

4. Why do people work? • income is used to buy goods and services

5. People wish to maximize utility • U = U(C , l) + + Or: • U = U(C , h) + - • utility maximization is subject to a consumer’s budget constraint

6. Marginal utility • the additional utility from consuming an additional unit of a good • MUx is positive, but diminishing

7. Utility is maximized where MUx/Px = MUy/Py We can then say that if a person is choosing between leisure (l) and consumption (C), utility is maximized when: MUl / Pl = MUC / PC This is another version of the equi-marginal principle

8. What if MUl/Pl MUC/PC? Suppose that MUl/Pl< MUC/PC : • need to increase the left-hand side or decrease the right hand side • therefore, we need to either decrease l or increase C • this should make sense because the MU of the last \$1 spent on C is larger than the MU of the last \$1 spent on l • thus, we should buy less l and more C

9. What if MUl/Pl MUC/PC? Suppose that MUl/Pl >MUC/PC : • need to decrease the left-hand side or increase the right hand side • therefore, we need to either increase l or decrease C • this should make sense because the MU of the last \$1 spent on C is smaller than the MU of the last \$1 spent on l • thus, we should buy more l and less C

10. Review of Income and Substitution Effects

11. Income Effect • when income increases, the consumer can continue to buy the original combination and still have money left over • we assume that consumers spend their budgets • therefore he buys more normal goods and fewer inferior goods

12. Substitution Effect • when relative prices change, a consumer will buy more of the relatively cheaper good • substitute the relatively cheaper good for the relatively more expensive good

13. What happens if income increases? • any increase in nonlabor income (so the wage has not changed) will lead to a drop in hours worked • assume that h = hours of work and Y = income:

14. What happens if the wage increases? • any increase in wage (when total income has not changed) will lead to an increase in hours worked

15. Both of these effects occur when wages rise • as w increases, the worker has an increase in real income since at current hours he is now earning more money; the income effect implies a reduction in hours of work • as w increases, the price of leisure rises relative to the price of consumption; thus, there is a substitution effect, where the worker substitutes consumption (the relatively cheaper good)for leisure (the relatively more expensive good) by working more hours

16. The income and substitution effects offset each other. • if the income effect is dominant, the worker will respond by reducing his hours of work (increasing leisure) • if the substitution effect is dominant, the worker will respond by increasing his hours of work (decreasing leisure)

17. Individual labor supply curves may be backward bending • the substitution effect usually dominates at low wages and the income effect usually dominates at high wages • because of these offsetting effects, tax incentives may either increase or decrease hours of work

18. Backward-bending Labor Supply Curve w Hours of work

19. w When the wage rises from W1 to W2, Ls rises W2 W1 Hours of work L1 L2

20. w W2 W1 When the wage rises from W1 to W2, Ls falls L2 L1 Hours of work

21. Graphic analysis of the hours of work decision- - Maximizing utility subject to a budget constraint.

22. Indifference curves • reflect the combination of consumption (C) and leisure (l) that result in the same level of utility

23. C(\$) Leisure

24. C(\$) C1 l1 Leisure

25. C(\$) C1 C2 l2 l1 Leisure

26. Rules for indifference curves: • a whole set of indifference curves can be drawn through any point on the plane • indifference curves cannot intersect • indifference curves have negative slopes • indifference curves are convex • indifference curves differ across people

27. Indifference curves have negative slopes • a person must give up leisure to get additional consumption • the slope of the indifference curve is equal to the marginal rate of substitution (MRS) • MRS shows the rate that the individual is willing to give up an additional unit of C for an additional unit of l along an indifference curve

28. C(\$) slope = - MUl / MUC C1 C2 Leisure l1 l2

29. Indifference curves are convex • when consumption is relatively high (and leisure is relatively low), an additional hour of leisure is highly valued • consumers are willing to give up more consumption for an additional hour of leisure at this point than they are when consumption is low and leisure is relatively high. • this is due to diminishing marginal utility

30. C(\$) slope = - MUl / MUC C1 C2 C3 C4 l1 l2 Leisure l3 l4

31. Different people have different indifference curves • a person who places a high value on leisure will have a relatively steeper indifference curve than someone who places a low value on leisure • likewise, a person who places a high value on consumption will have a relatively flatter indifference curve than someone who places a low value on consumption

32. C(\$) Tom places a higher value on leisure (and a lower value on consumption) than Joe does C1 UJoe UTom l1 Leisure

33. C(\$) Tom requires more additional consumption to give up another hour of leisure than Joe does C1 UJoe UTom l1 Leisure l1-1

34. Indifference curves cannot intersect • preferences are assumed to be transitive This means that: If A is preferred to B, and B is preferred to C, then A is preferred to C • more is assumed to be preferred to less

35. C(\$) D has more C and l than B does. Therefore, a person could not be indifferent between combinations A and B and A and D A D U0 B U1 Leisure

36. C(\$) Which indifference curve represents a higher level of utility? U1 U0 Leisure

37. Since more is preferred to less, we would like to consume everything possible, but we are constrained by our income.

38. Budget Constraint • reflects all possible combinations of consumption and leisure that can be purchased given the worker’s wage and the prices of consumption goods

39. Total time available is T • T can be divided up into hours of work (h) and hours of leisure (l) • the Y-intercept is equal to nonlabor income (v) plus labor earnings (w*h) Y = v + w*h • let’s start with no nonlabor income (v=0)

40. C(\$) slope = -w Leisure Hours of work

41. C(\$) w*T slope = -w Leisure T

42. C(\$) What if nonlabor income is not equal to 0? w*T v } v Leisure T

43. C(\$) If nonlabor income is equal to v, the budget constraint shifts up by that amount w*T+v w*T slope = -w v } v Leisure T

44. Let’s assume: • a person has 16 hours in a day to use to either work or consume leisure (the other 8 are used to sleep, eat, etc.) • the hourly wage is \$5 • the individual has no nonlabor income • the price of consumption goods is \$1 (we measure consumption in \$ worth of goods)

45. C(\$) slope = - 5 \$80 Leisure 16

46. C(\$) If the hourly wage increases to \$10, what will happen to the budget constraint? slope = - 5 \$80 Leisure 16

47. C(\$) \$160 slope = - 10 \$80 slope = - 5 Leisure 16