The Basic Neoclassical Model of Labor Supply

1. The Basic Neoclassical Model of Labor Supply The labor-leisure tradeoff

2. Assumptions: • there are only two possible uses of time: labor and leisure, • each individual selects the combination of hours of work and leisure that maximizes his or her level of satisfaction (utility).

3. Opportunity costs • For individuals who are working, the opportunity cost of an additional hour of leisure time is the wage rate. • Individuals choose not to work if the value of leisure time exceeds the market wage.

4. Change in the wage A change in the wage generates: • a substitution effect, and • an income effect

5. Substitution effect • the opportunity cost of leisure time rises as the wage rate increases. • as leisure time becomes more costly, individuals consume less leisure time and spend more time at work. • this is the substitution effect resulting from a higher wage.

6. Income effect • as the wage rate rises, an individual’s real income rises. • this leads to an increase in the consumption of all normal goods. • if leisure is a normal good, the higher wage rate will induce the individual to consume a larger quantity of leisure time (and reduce hours of work). • This is the income effect resulting from a wage increase.

7. Net effect • If leisure is a normal good, an increase in the wage rate will cause the quantity of labor supplied to: • increase if the substitution effect is larger than the income effect, and • decrease if the income effect is larger than the substitution effect.

8. Backward-bending labor supply curve

9. Indifference curves • An indifference curve is a graph of alternative combinations of goods that provide a given level ofsatisfaction (utility).

10. Utility function • It is assumed that the individual’s utility level is a function of two goods: real income (Y), and leisure time (L). • In mathematical terms, this utility function may be expressed as: U=U(Y,L)

11. Indifference curve U=Uo

12. Indifference curve (cont’d.) An indifference curve is downward sloping since an individual is willing to give up some income to receive additional leisure (or vice versa).

13. Indifference curves (cont’d.) A point that lies above an indifference curve provides a higher level of utility than a point on the curve.

14. Indifference curves (cont’d.) An indifference curve passes through each point in the diagram. (U’ > Uo)

15. Constrained maximization • Individuals attempt to attain the highest possible level of utility. • The choice among alternative levels of Y and L, however, is restricted due to two constraints: • a time constraint, and • a goods constraint.

16. Time constraint: • The time constraint is given by: H + L = T where: H = hours of work L = hours of leisure T = total time available

17. Goods constraint • The goods constraint is given by: wH = pY where: w = wage rate H = hours of work p = price index for real income Y = real income

18. Budget constraint • Thus, the following two equations must be satisfied: • 1. H+L = T • 2. pY=wH • Rewriting equation (1) as: H = T-L • and substituting this into equation (2) results in: • pY=wT-wL

19. Full-income constraint With a little algebraic manipulation, this becomes: wT=pY+wL (3) • This equation is called a full-income constraint. • full income = an individual’s maximum earnings potential (= wT in this case). • full income equals the total explicit cost of goods and services (pY) plus the total implicit cost of leisure time (wL).

20. Budget constraint An alternative form of equation (3) is given by: Y = -(w/p)L + (w/p)T (3’) This equation describes the relationship that exists between hours of leisure and real income. Equation (3’) is the individual’s budget constraint.

21. Budget constraint (cont’d.) The intercept of the budget constraint on the horizontal axis equals T (the maximum amount of leisure time that an individual can receive). Notice that H decreases from T to 0 as L rises from 0 to T.

22. Budget constraint (cont’d) The intercept of the budget constraint on the vertical axis equals: wT / p (= real full income). The slope of the budget constraint equals -w/p.

23. Optimal work/leisure mix • Utility is maximized at the point of tangency between an indifference curve and the budget constraint.

24. Corner solution (cont.) • the highest level of utility in this case occurs at zero hours of work. • An individual chooses to remain out of the labor force when a corner solution such as this occurs. U2 U3 Uo U1 Y wT p 0 T L T 0 H

25. Corner solution (cont.) • A corner solution at zero hours of work will occur when: • the opportunity cost of time is relatively high, and/or • the market wage rate is low. U2 U3 Uo U1 Y wT p 0 T L T 0 H

26. Reservation wage • The absolute value of the slope of the indifference curve at the point corresponding to zero hours of work is the individual’s “reservation wage” (expressed in real terms). U2 U3 Uo U1 Y |slope| = reservation wage 0 T L T 0 H

27. Real wage > reservation wage • If the real wage in the labor market exceeds the reservation wage, the individual chooses to work. U2 U3 Uo U1 Y Budget constraint |slope| = real wage |slope| = reservation wage 0 T L T 0 H

28. Real wage < reservation wage • If the real wage is less than the reservation wage, the individual chooses to remain out of the labor force and a corner solution occurs. U2 U3 Uo U1 Y Budget constraint |slope| = real wage wT p |slope| = reservation wage 0 T L T 0 H

29. Nonlabor income • Initially, it was assumed that all income was received in the form of labor income. • Individuals, however, also receive income from nonlabor income. • income from nonlabor sources is referred to as “unearned income.” • nonlabor income may be received in the form of interest payments, rent, dividends, profits, alimony payments, transfer payments, lottery winnings, lawsuit settlements, or any other income that does not vary with hours worked.

30. Nonlabor income (cont.) • Using the definition: • A = total amount of nonlabor income • The time and goods constraints become: • Time constraint: H + L = T (1) • Goods constraint: wH + A = pY (2)

31. Nonlabor income (contd.) Solving equation (1) for H: H = T - L Substituting this into equation (2) results in: w(T - L) + A = pY Solving this for Y results in the following budget constraint: Y = -(w/p)L + (wT+A)/p An inspection of this budget constraint indicates that the slope equals -w/p (as in the simpler model) and the intercept equals: (wT+A)/p.

32. Changes in nonlabor income • As the level of nonlabor income rises, the budget constraint shifts vertically upward Y A > A > 0 wT+A 1 o 1 p wT+A o A = A p 1 wT A = A p o A = 0 0 T L T 0 H

33. Non-labor income (cont.) • The slope of the budget constraint stays the same when nonlabor income changes. • The budget constraint still terminates at T hours of leisure. Y A > A > 0 wT+A 1 p wT+A o A = A p 1 1 0 wT A = A p o A = 0 0 T L T 0 H

34. Leisure and nonlabor income • If leisure is a normal good, an increase in nonlabor income results in: • An increase in leisure time • A reduction in work hours Y wT+A 1 p wT+A o p wT p U2 U1 Uo 0 T L T 0 H

35. Leisure and nonlabor income (cont.) • The change in hours worked that results from a change in real income, holding relative prices constant, is called a “pure income effect.” Y wT+A 1 p wT+A o p wT p U2 U1 Uo 0 T L T 0 H

36. Income and substitution effects Y • A wage increase from wo to w1 results in a movement from point A to C. • In this case, leisure rises, so the income effect exceeds the substitution effect w1 T p woT p C A U1 Uo 0 T L T 0 H

37. Substitution effect Y • Substitution effect = change in the mix of L and Y resulting from a change in relative prices, holding utility constant. w1 T p woT p C B A U1 Uo 0 T L T 0 H

38. Income effect Y • Budget constraint at point B is constructed so that it is parallel to the final budget constraint. w1 T p woT p C B A U1 Uo 0 T L T 0 H

39. Income effect (cont.) Y • Movement from point B to C is a pure income effect. • Leisure rises as real income rises in response to the higher wage. w1 T p woT p C B A U1 Uo 0 T L T 0 H

40. Net effect Y • When the income effect is smaller than the substitution effect, hours worked increases and leisure decreases when the wage rate increases. w1 T p C woT p B U1 A Uo 0 T L T 0 H

41. Net effect (cont.) Y • When the wage changes, individual substitution and income effects are not observed. • A backward-bending labor supply curve may be explained using income and substitution effects. w1 T p C woT p B U1 A Uo 0 T L T 0 H

42. Income replacement programs • At a wage rate of w, this individual will work Ho hours and consume Lo hours of leisure. Income = Yo

43. Unemployment compensation • If all lost income is replaced when the individual becomes unemployed, the individual moves from point A to point B if unemployed.

44. Unemployment comp. (cont.) • utility rises when an individual becomes unemployed under complete income replacement. • unemployment compensation plans do not provide full income replacement.

45. Unemployment comp. (cont.) • The original level of utility is attained at an income level of Y’ when unemployed. • In the U.S., unemployment compensation is roughly equal to ½ of full-time earnings.

46. Disability insurance • If disabled workers receive the same level of income after an injury as before and receive more leisure time, their level of utility would increase (assuming that “pain and suffering” and medical expenses are fully compensated).

47. Disability insurance (cont.) • Disability insurance programs require medical examinations by approved physicians to reduce the possibility that workers will file fraudulent disability claims.

48. Partial disability • A work-related injury that results in a partial disability reduces the wage that the affected worker will receive. • This reduction in the wage generates both substitution and income effects on the quantity of labor supplied. • If the goal is to adequately compensate the worker, however, an appropriate income replacement scheme would be to provide a payment that is just large enough to offset the income effect resulting from the reduction in the wage (since it is only the income effect that involves a loss in utility).

49. U.S. welfare system • The first major national attempt at providing aid to low-income households in the U.S. occurred during the Great Depression. Most of the relief programs developed during this period, however, were temporary programs designed to deal with the problems resulting from the depression. • The modern U.S. welfare system was introduced in the early 1960s as part of the War on Poverty during the Johnson administration.

50. Poverty level • A poverty level was established based upon studies that attempted to determine the amount of income required to provide households with an adequate level of nutrition and basic necessities. • It is assumed that a household of a given size in a particular geographical area must receive a particular level of income (Yt) to ensure that these basic needs could be satisfied. (This level of income is higher for larger households and for residents in geographical regions where the cost of living is higher.)