Labor Supply Theory and Evidence Labor supply

Labor Supply : Theory and Evidence Labor supply decisions can be roughly divided into two categories: (1) Decisions about whether to work at all, if so, how long to work. (2) Decisions about the occupation or general class of occupation in which to seek offers and the geographical area in which offers should be sought.

1. Some Stylized Facts about Labor Supply l Trends in LFP: (1) 女性勞動參與率由 1964年的 34%逐漸上升至 1987年的 45%， 1987年至今則維持在 45%左右， 1999年開始逐漸上升，至 2007年已達到 49. 4%。男性勞參率由 1978年的 78%逐漸下降至 2007 年的 67. 24%。 (2) 15 -19歲組勞參率由 1978年的 45%顯著下降至 2003 年的 12%，至 2007年都維持在 10%上下。 20 -24歲組勞參率由 1978年的 65%逐漸下降至 2005年的 53%，自 2005年始到 2007年為止都在 53%上下起伏。

l Trends in Hours of Work: (1) 平均每週時在 1990 -2000年間均為 48小時左右，在 2005年 1月時下降為 45. 46小時，到 2008年 7月時上升為 46. 98小時。男性平均時由 1978年的每週 50小時下降 2005 年 1月的 45. 82小時 , 到 2008年 7月時為每週 45. 98 小時。女性平均時則由 1978年的每週 46小時上升為 1997年的 47小時，又下降至 2005年 1月的 44. 98 小時，到 2008年 7月時又上升至 46. 67小時。

2. A Theory of The Decision to Work l The decision to work is ultimately a decision about how to spend time. Spend time in pleasurable leisure activities Use time to work (working for pay) l The discretionary time we have (24 hours – time spent eating and sleeping) can be allocated to either work or leisure. Demand for Leisure Supply of Labor.

Basically, the demand for a good is a function of three factors: 1. The opportunity cost of the good. 2. One’s level of wealth. 3. One’s set of preference. The demand（D） for a normal good can be characterized as a function of opportunity cost（C）and wealth（V） D = f（C, V）

Where f depends on preferences. Demand for Leisure: (1) The opportunity cost of an hour of leisure is very closely related to one’s wage rate. For simplicity, we shall say that leisure’s opportunity cost is the wage rate. (2) Economists often use total income as an indicator of total wealth, since the two are conceptually so closely related. Demand for leisure function becomes DL = f（W, Y） l

(1) If income increases, holding wages（and f） constant, the demand for leisure goes up. If income increases（decreases）, holding wages constant, hours of work will go down （up）. Income effect on hours of work is negative. Income Effect = w <0

(2) If income is held constant, an increase（ decrease）in the wage rate will reduce（ increase）the demand for leisure, thereby increasing（decreasing）work incentives. Substitution effect on hours of work is positive. Substitution Effect = Y >0

Both Effect Occur When Wages Rise Income effect: For a given level of work effort, he/she now has a greater command over resources than before because more income is received for any given number of hours of work. Substitution effect: The wage increase raises the opportunity costs of leisure, and thereby increases hours of work.

If income effect is dominant, the person will respond to a wage increase by decreasing his/her labor supply. Should the substitution effect dominate, the person’s labor supply curve will be positively sloped. Wage Backward-bending W* Desired hours of work

3. A Graphic Analysis of the Labor-Leisure Choice Two categories of goods: Leisure（L）and Money Income ( M ) Since both leisure and money can be used to generate satisfaction, these two goods are to some extent substitutes for each other. M Indifference Curve: A B C D IC 2 IC 1 L A curve connecting the various combinations of money income and leisure that yield equal utility.

Indifference curves have certain specific characteristics: 1. Any curve that lies to the northeast of another one is preferred to any curve to the southwest because the northeastern curve represents a higher level of utility. 2. Indifference curves do not intersect. 3. Indifference curves are negatively sloped. 4. Indifference curves are convex. When money income is relatively high and leisure hours are relatively few, leisure is more highly valued than when leisure is abundant and income relatively scarce. 5. Different people have different sets of IC’s

M M L Person who place high value on an extra hour of leisure L Person who place low value on an extra hour of leisure

The resources anyone can command are limited. Budget constraint reflects the combinations of leisure and income that are possible for the individual. M The slope of the budget constraint is a graphic representation of the wage rate. E Wage rate = OE/OD 0 D L

Note: Full income = wage rate * T →It represents the maximum attainable income. M At point B: MUL/MUM>W or MUL>W*MUM L should increase E B A* IC* C IC 2 IC 1 D L IC 2：impossible under current condition IC 1：possible, but higher level of utility can be attained IC*：utility-maximized level A* ：utility-maximization point At point C: MUL/MUM<W or MUL<W*MUM L should reduce, or H should increase • An indifference curve that is just tangent to the constraint represents the highest level of utility that the person can obtain given his or her constraint.

The Decision Not to Work What happens if there is no point of tangency? M The person’s IC are at every point more steeply than the budget constraint. Pt. D is not a tangency point. There can be no tangency if the IC has no points at which the slope equals the slope of the budget constraint. E D L At this point（D）the person chooses not to be in the labor force.

The Income Effect Nonlabor income: Even if this person worked zero hour per day, he/she will have this nonlabor income. M Note that the new constraint is parallel to the old one. E B A IC 2 →The increase in nonlabor income has not changed the person’s wage rate. IC 1 D L Pure income effect: The income effect is negative; as income goes up, holding wages constant, hours of work goes down.

Income and Substitution Effects with a Wage Increase The wage increase would cause both an income and a substitution effect; the person would be wealthier and face a higher opportunity cost of leisure. N 1→N 3: income effect → L↑, H↓ N 3→N 2: substitution effect →L↓, H↑ N 1→N 2: observed effect Substitution effect dominates. L↓, H↑ Income effect: Had the person received nonlabor income, with no change in the wage, sufficient to reach the new level of utility, he/she would have reduces work hours from N 1 to N 3.

N 1→N 3: income effect →L↑, H↓ N 3→N 2: substitution effect →L↓, H↑ N 1→N 2: observed effect Income effect dominates. L↑, H↓ Note: The differences in the observed effects of a wage increase are due to differences in the shape of the indifference curve. i. e. , different preference.

• Empirical Findings on the Labor/Leisure Choice (1)The time-series study can be used to look at trends in labor force participation rates and hours of work over time. (2)The cross-section study can be used to analyze the patterns of labor supply across individuals at a given point in time.

4. Policy Application Virtually all government income maintenance programs-from welfare payments to unemployment compensation-have workincentive effect. (1) Income Replacement Programs Unemployment insurance, worker’s compensation, and disability insurance might be called income replacement programs. →All these programs are intended to compensate workers for earnings lost owing to their inability to work. Note: All these programs in the U. S. typically replace roughly just half of before-tax lost earning. The reason for incomplete earnings replacement has to do with work incentives.

Replacing all of lost income could result in overcompensation by generating a higher level of utility than before the loss of income, and would motivate the recipients of benefits to remain out of work as long as possible. M E 0 T IC 2 IC 1 L When employment ceases, the worker receives benefits equal to E 0, he/she will be at pt. T on a higher IC.

（2）Actual Income Loss vs. “Scheduled” Benefits Actual Income Loss: Workers who are either totally or partially disabled receive benefits that replace their actual lost earnings. M If the injured worker earned E 0 before injury and workers’ D compensation replaced all earnings loss up to C E 0, then workers’ B E 0 compensated budget constraint would be ABCD line. A L Note: Throughout the horizontal segment BC, the individual’s net wage is zero. When people cannot increase their income by working, there is usually no incentive to work.

M Using an impersonal schedule of disability benefits preserves at least some incentive to work because benefits are not reduced if earnings increase. E D G C → There are greater incentives to work if benefits are scheduled than if benefits are calculated to completely replace earnings losses. B A Grand benefit according to some schedule without regard to the individual’s actual earnings loss. → Budget constraint BE. L Scheduled benefits cause only an income effect. However, if actual earnings loss were to become the benefit, there would be an income effect and substitution effect, and both would work in the same direction. The benefits would simultaneously increase income while reducing the wage rate to zero.

5. Child Care, Commuting, and the Fixed Costs of Working (1) Fixed Monetary Costs of Working not work: at point a with utility U 1 ab: fixed per-period monetary cost → If the individual works, the budget line starts from point b.

a. How large does the wage rate need to be to induce this person to work for pay? →The slope of the budget line bd represent the wage such that any decrease in this wage will cause the individual to drop out of the labor force. This is because utility U 1 will no longer be attainable if he/she work any hour. →The wage represented by the slope of bd is this person’s reservation wage-the lowest wage for which he/she will work.

b. What would happen to the reservation wages if the fixed costs were to increase to ae? →An increase in the fixed costs of work will tend to raise the reservation wage of potential workers. Consider the change from bg to ef: →Increasing fixed costs of work will tend to increase the hours of work for some workers but cause others to drop out of the labor force. →The net effect on labor supply is ambiguous a priori.

(2) Fixed Time Costs of Working If the individual does work he/she incurs fixed time costs ab. →The maximum number of hours a day available for work or leisure is T 1. At wage represented by bh, he/she would be indifferent between working (pt D) and not working (pt a). reservation wage

Suppose that the fixed time costs of work increase from ab to ad, then as long as leisure and income are both assumed to be normal goods, hours of both work and leisure time will be reduced. The increase in fixed time costs of work has an income effect that reduces the worker’s demand for both leisure and the goods income will buy. Given a constant wage rate, a fall in income implies that hours of work have been reduced. Note: The increase in time cost has two important consequences: （a）It reduces full income from og to ok. （b）It reduces total time available for either leisure or work so long as the individual continues to work.