Labor Supply : Theory and EvidenceLabor 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 Supply1. Some Stylized Facts about Labor Supply

Trends in LFP:Trends in LFP:(1)(1) 女性勞動參與率由女性勞動參與率由 19641964 年的年的 34%34% 逐漸上升 逐漸上升 至至 19871987 年的年的 45%45% ，， 19871987 年至今則維持在年至今則維持在 4545%% 左右。男性勞參率由左右。男性勞參率由 19781978 年的年的 78%78% 逐漸逐漸下降至下降至 20042004 年的年的 68%68% 。。

(2) 15-19(2) 15-19 歲組勞參率由歲組勞參率由 19781978 年的年的 45%45% 顯著下顯著下降至降至 20032003 年的年的 12%12% ，， 20-2420-24 歲組勞參率由歲組勞參率由 11978978 年的年的 65%65% 逐漸下降到逐漸下降到 20032003 年的年的 55%55% ， ， 其他各年齡組均呈現上升或持平之趨勢。其他各年齡組均呈現上升或持平之趨勢。

Trends in Hours of Work:Trends in Hours of Work:

(1)(1) 平均每週工時在平均每週工時在 1990-20001990-2000 年間均為年間均為 4848 小小時左右時左右 , , 但到但到 20052005 年年 11 月時下降為月時下降為 45.4645.46小時，男性平均工時由小時，男性平均工時由 19781978 年的每週年的每週 5050小時下降為小時下降為 20052005 年年 11 月的月的 45.8245.82 小時小時 , , 女女性平均工時則由性平均工時則由 19781978 年的每週年的每週 4646 小時上小時上升為升為 19971997 年的年的 4747 小時，又下降至小時，又下降至 20052005 年年11 月的月的 44.9844.98 小時。小時。

2. A Theory of The Decision to Work2. A Theory of The Decision to Work

The decision to work is ultimately a decision about hThe decision to work is ultimately a decision about how to spend time. ow to spend time.

Spend time in pleasurable leisure activitiesSpend time in pleasurable leisure activities Use time to work (working for pay)Use time to work (working for pay)

The discretionary time we haveThe discretionary time we have (24 hours – time spent eating and sleeping) (24 hours – time spent eating and sleeping) can be allocated to either work or leisure.can be allocated to either work or leisure.

Demand for Leisure Supply of Labor.Demand for Leisure Supply of Labor.

Basically, the demand for a good is a function ofBasically, the demand for a good is a function of

three factors:three factors:

1.1. The opportunity cost of the good.The opportunity cost of the good.

2.2. One’s level of wealth.One’s level of wealth.

3.3. One’s set of preference.One’s set of preference.

The demandThe demand （（ DD ） ） for a normal good can befor a normal good can be

characterized as a function of opportunitycharacterized as a function of opportunity

costcost （（ CC ）） and wealthand wealth （（ VV ）） D = fD = f （（ C, VC, V ））

Where f depends on preferences.Where f depends on preferences. Demand for Leisure:Demand for Leisure:(1) The opportunity cost of an hour of leisure is (1) The opportunity cost of an hour of leisure is

very closely related to one’s wage rate. Fvery closely related to one’s wage rate. For simplicity, we shall say that leisure’s oppoor simplicity, we shall say that leisure’s opportunity cost is the wage rate.rtunity cost is the wage rate.

(2) Economists often use total income as an indic(2) Economists often use total income as an indicator of total wealth, since the two are conceptator of total wealth, since the two are conceptually so closely related.ually so closely related.

Demand for leisure function becomesDemand for leisure function becomes DL = fDL = f （（ W, YW, Y ））

(1)(1) If income increases, holding wages If income increases, holding wages （（ and and ff ）） constant, the demand for leisure goes up.constant, the demand for leisure goes up.

If income increasesIf income increases （（ decreasesdecreases ）） , holding , holding wages constant, hours of work will go downwages constant, hours of work will go down（（ upup ）） ..

Income effect on hours of work is negative.Income effect on hours of work is negative.

Income Effect = Income Effect = ww <0<0

ww

(2)(2) If income is held constant, an increas If income is held constant, an increas （（ decrdecreaseease ）） in the wage rate will reducein the wage rate will reduce （（ increaincreasese ）） the demand for leisure, thereby increathe demand for leisure, thereby increasingsing （（ decreasingdecreasing ）） work incentives.work incentives.

Substitution effect on hours of work is positivSubstitution effect on hours of work is positive.e.

Substitution Effect = Substitution Effect = YY >0 >0WH

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

Desired hours of work

Backward-bendingW*

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

L

IC1

IC2

A

B

CD

Indifference Curve:

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

L

M

L

Person who place high value on an extra hour of leisure

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

L0

E

D

The slope of the budget constraint is a graphic representation of the wage rate.

Wage rate = OE/OD

Note: Full income = wage rate * T →It represents the maximum attainable income.

M

L

IC1

IC*IC2

E

D

A*

B

C

At point B: MUL/MUM>W or MUL>W*MUM L should increase

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.

IC2 ： impossible under current condition IC1 ： possible, but higher level of utility can be attainedIC* ： utility-maximized levelA* ： utility-maximization point

The Decision Not to WorkWhat happens if there is no point of tangency?

M

L

E

D

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.

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

L

IC1

IC2

E

D

AB

Note that the new constraint is parallel to the old one.

→The increase in nonlabor income has not changed the person’s wage rate.

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 IncreaseThe wage increase would cause both an income and a substitution effect; the person would be wealthier and face a higher opportunity cost of leisure.

N1→N3: income effect → L↑, H↓N3→N2: substitution effect →L↓, H↑N1→N2: 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 N1 to N3.

N1→N3: income effect →L↑, H↓N3→N2: substitution effect →L↓, H↑N1→N2: 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 Application4. Policy ApplicationVirtually all government income maintenance programs-from welfare payments to unemployment compensation-have work-incentive 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

L

IC1

IC2

E0

T

When employment ceases, the worker receives benefits equal to E0, 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

L

D

A

BCE0

If the injured worker earned E0 before injury and workers’ compensation replaced all earnings loss up to E0, then workers’ compensated budget constraint would be ABCD line.

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.

L

D

A

BC

M

Grand benefit according to some schedule without regard to the individual’s actual earnings loss.→ Budget constraint BE.

G

Using an impersonal schedule of disability benefits preserves at least some incentive to work because benefits are not reduced if earnings increase.

→ There are greater incentives to work if benefits are scheduled than if benefits are calculated to completely replace earnings losses.

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.

E

5. Child Care, Commuting, and the Fixed Costs of 5. Child Care, Commuting, and the Fixed Costs of WorkingWorking

(1) Fixed Monetary Costs of Working

not work: at point a with utility U1

ab: fixed per-period monetary cost

→ If the individual works, the budget line starts from point b.

a.a. How large does the wage rate need to be to induce tHow large does the wage rate need to be to induce this person to work for pay?his person to work for pay?

→→The slope of the budget line bd represent the wage suThe slope of the budget line bd represent the wage such that any decrease in this wage will cause the indich that any decrease in this wage will cause the individual to drop out of the labor force. This is because vidual to drop out of the labor force. This is because utility Uutility U11 will no longer be attainable if he/she work will no longer be attainable if he/she work

any hour.any hour.

→→The wage represented by the slope of bd is this persoThe wage represented by the slope of bd is this person’s n’s reservation wagereservation wage-the lowest wage for which he-the lowest wage for which he/she will work./she will work.

b.b. What would happen to the reservation wages if the fWhat would happen to the reservation wages if the fixed costs were to increase to ae?ixed costs were to increase to ae?

→→An increase in the fixed costs of work will tend to raiAn increase in the fixed costs of work will tend to raise the reservation wage of potential workers. Consise the reservation wage of potential workers. Consider the change from bg to ef:der the change from bg to ef:

→→Increasing fixed costs of work will tend to increase thIncreasing fixed costs of work will tend to increase the hours of work for some workers but cause others te hours of work for some workers but cause others to drop out of the labor force.o drop out of the labor force.

→→The net effect on labor supply is ambiguous a priori.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 T1.

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.