The Basic Neoclassical Model of Labor Supply The

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

Assumptions: n n 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).

Opportunity costs n n 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.

Change in the wage A change in the wage generates: n a substitution effect, and n an income effect

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

Income effect n n 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.

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

Backward-bending labor supply curve

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

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

Indifference curve U=Uo

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).

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

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

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

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

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

Budget constraint Thus, the following two equations must be satisfied: 1. H+L = T 2. p. Y=w. H Rewriting equation (1) as: H = T-L and substituting this into equation (2) results in: p. Y=w. T-w. L

Full-income constraint With a little algebraic manipulation, this becomes: w. T=p. Y+w. L n n n (3) This equation is called a full-income constraint. full income = an individual’s maximum earnings potential (= w. T in this case). full income equals the total explicit cost of goods and services (p. Y) plus the total implicit cost of leisure time (w. L).

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

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.

Budget constraint (cont’d) The intercept of the budget constraint on the vertical axis equals: w. T / p (= real full income). The slope of the budget constraint equals -w/p.

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

Corner solution (cont. ) Uo Y U 1 U 2 U 3 n w. T p n 0 T T 0 L H 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.

Corner solution (cont. ) Uo Y U 1 U 2 U 3 n w. T p A corner solution at zero hours of work will occur when: n n 0 T T 0 L H the opportunity cost of time is relatively high, and/or the market wage rate is low.

Reservation wage Uo Y U 1 U 2 U 3 n |slope| = reservation wage 0 T T 0 L H 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).

Real wage > reservation wage Uo Y U 1 U 2 U 3 n Budget constraint |slope| = real wage |slope| = reservation wage 0 T T 0 L H If the real wage in the labor market exceeds the reservation wage, the individual chooses to work.

Real wage < reservation wage Uo Y w. T p 0 T If the real wage is less than the reservation Budget constraint wage, the |slope| = real wage individual chooses to |slope| = reservation remain out of wage the labor force and a corner solution occurs. T L 0 H U 1 U 2 U 3 n

Nonlabor income n n Initially, it was assumed that all income was received in the form of labor income. Individuals, however, also receive 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.

Nonlabor income (cont. ) n Using the definition: n n A = total amount of nonlabor income The time and goods constraints become: n n Time constraint: H+L=T Goods constraint: w. H + A = p. Y (1) (2)

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

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

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

Leisure and nonlabor income Y w. T+A 1 p w. T+Ao p w. T p n U 2 U 1 Uo If leisure is a normal good, an increase in nonlabor income results in: n n 0 T T 0 L H An increase in leisure time A reduction in work hours

Leisure and nonlabor income (cont. ) Y w. T+A 1 p w. T+Ao p w. T p n U 2 U 1 Uo 0 T T 0 L H The change in hours worked that results from a change in real income, holding relative prices constant, is called a “pure income effect. ”

Income and substitution effects Y n w 1 T p wo. T p C n A U 1 Uo 0 T T 0 L H A wage increase from wo to w 1 results in a movement from point A to C. In this case, leisure rises, so the income effect exceeds the substitution effect

Substitution effect Y n w 1 T p wo. T p C B A Uo 0 T T 0 U 1 L H Substitution effect = change in the mix of L and Y resulting from a change in relative prices, holding utility constant.

Income effect Y n w 1 T p wo. T p C B A Uo 0 T T 0 U 1 L H Budget constraint at point B is constructed so that it is parallel to the final budget constraint.

Income effect (cont. ) Y n w 1 T p wo. T p n C B A Uo 0 T T 0 U 1 L H Movement from point B to C is a pure income effect. Leisure rises as real income rises in response to the higher wage.

Net effect Y n w 1 T p C wo. T p B A U 1 Uo 0 T T 0 L H When the income effect is smaller than the substitution effect, hours worked increases and leisure decreases when the wage rate increases.

Net effect (cont. ) Y n w 1 T p C wo. T p B n U 1 A Uo 0 T T 0 L H 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.

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

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

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

Unemployment comp. (cont. ) n n 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.

Disability insurance n 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).

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

Partial disability n n n 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).

U. S. welfare system n n 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 1960 s as part of the War on Poverty during the Johnson administration.

Poverty level n n 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. )

Benefits under basic welfare system n n n The government provides welfare benefits to those households in which the level of income falls below the target level (Yt). Welfare benefits may take the form of either monetary payments or subsidies for food, housing, medical care, or other basic commodities. The goal is to provide a level of welfare benefits that brings the level of household income up to the target level.

Basic welfare system – budget constraint n n If the individual does not work at all, the level of welfare benefits equals Yt. If the individual is working, but receives a level of income that falls below Yt, the government provides enough welfare benefits to provide a total income of Yt.

Budget constraint (cont. ) n n The budget constraint is horizontal at an income level of Yt. In this portion of the budget constraint, the marginal wage (the additional income resulting from an additional hour of work) equals zero. If a welfare recipient works an additional hour and receives a wage of $6, welfare benefits are reduced by $6, leaving total income unchanged.

Welfare and labor supply n an individual who, in the absence of a welfare system, has a level of income that lies below the target level of income would always prefer to leave the labor force when such a welfare system is available (since the level of income and leisure both increase in this case).

Welfare and labor supply (cont. ) n Some individuals who, in the absence of this welfare system, would have received a level of income that exceeds Yt, would also choose to leave the labor force.

Welfare and labor supply (cont. ) n Note that the substitution effect of lowering the marginal wage to zero reduces the quantity of labor supply, as does the income effect resulting from the provision of welfare benefits.

Revised welfare system – 1967 -1981 n To reduce the labor supply disincentive effects resulting from this type of welfare system, this system was replaced in 1967 with a welfare system in which individuals were able to keep a small amount of monthly earned income without giving up any welfare benefits. Beyond this point, welfare benefits were reduced by $2 for every $3 earned (as compared to a $1 reduction for every $1 earned under the earlier system).

Welfare revision: 1981 n n During the Reagan administration, the welfare system was restored to a form that was essentially equivalent to that of the early 1960 s. The reason for the change was a desire to reduce welfare benefits for higher income welfare recipients while preserving benefits for the “truly needy. ” With the restoration of a system that provides a marginal wage of zero, the number of “working poor” declined and a larger share of welfare recipients remained out of the labor force.

Workfare n n n Beginning in 1997, a “workfare” system has been adopted. Welfare recipients are required to work a minimum number of hours to qualify for welfare benefits. (welfare benefits are zero unless welfare recipients work the required minimum number of hours or are engaged in approved job training or educational programs). Individuals are restricted to receiving welfare benefits for a maximum of five years under this system.

Workfare budget constraint n n Individuals receive no benefits if they work fewer than the minimum number of hours (Hm, in this example). If they work Hm or more hours, they receive the same level of benefits as under the earlier system.

Workfare and labor supply n n it is expected that welfare recipients would choose to work Hm hours. If they work more than this, the marginal wage is zero (until they work enough hours so that all benefits are eliminated).

Earned-income tax credit n n The earned-income tax credit provides additional income to low-income households with a smaller labor supply disincentive effect than the current welfare system. Under this system, a tax credit is provided that rises with income up to a point and then gradually declines.

Earned-income tax credit (cont. ) n The diagram on the left illustrates the effect of an earned income tax credit.