1、,Chapter 7Labor Supply:Household Production,the Family,and the Life Cycle,Contents,Household productionLife-cycle aspects of labor supplyLabor supply over the business cycle,Household Production as Non-Market Work,“Leisure”is really a form of workProduce household commodities Child rearingCleaning t
2、he houseCookingCounting both market and nonmarket workMarried men and women work similar hoursUnmarried men and women work similar hoursWomen allocate more hours to the nonmarket sector than men.,Evidence of Time Budget Data,Purpose of Studying Household Production,Explain patterns of household time
3、 allocation.The allocation of time between house work and market workThe allocation of time between house work,market work,and leisureThe division of labor in a householdsFertility behavior?,The Theory of Household Production(Becker),Objective:Maximize goods consumed by the household(Z)Examples:Rais
4、ing children,seeing a movieU=U(Z)The household commodity is produced with two inputs:Household production time(H)purchased goods or services(X)Households are both production and consumption units.,Household Production Function,Z=Z(X,H),properties:Positive marginal productsDiminishing marginal produc
5、t,Diminishing TRSSubstituting the production into utility function yieldsU(Z)=U(Z(X,H)This may be represented by an isoquant.Higher isoquants give higher utility.,Budget Constraint,Purchased commodity is paid for by earnings from market work X=wN where N is working hoursHome and market hours satisfy
6、 time budget constraintH+N=TOr,X+wH=wT,The Optimal Choice,The problem is re-written as:Max U(Z(X,H)s.t.X+wH=wT Optimal choice:|MRTS|=w,The Production of Child Care,Figure 7.1,Comparative Static Analysis,Income effectMarriage instabilityMarket wage goes upWomens educationIncome effects reduce market
7、timeSubstitution effects increase market timeTechnology in home productionEasier to substitute time for purchased goodsUtility isoquant becomes flatterIncrease market time,The Tripartite Choice(Gronau),Market Work,Household Work and Leisure Utility comes from consuming goods(X)and leisure(L):U(X,L)X
8、 is composed of two types of goods:Home produced()Market goods purchased using earnings()Household production function:Budget constraint for market goods:Time constraint:H+N+L=T,Explaining LS of Men and Women,Stylized fact on labor supply:At low female participation,substitution effect tended to dom
9、inate income effect.At high participation,substitution effect fades,andThe relative size of the two effects of men and women has begun to converge.Explanation:Substitution between market and household work is easier at low participation,and harder at high participation.Substitution between market wo
10、rk and leisure is more difficult.,Large vs.Small Substitution Effects Attendant to a Wage Increase,Figure 7.2,Work and Leisure:Past vs.Present(Fogel),1880(weekly)Adult male:Market:66.5 hrs;Household:14 hrs;Personal care:75 hrs;Leisure:12.5 hrsAdult female:Leisure:10.5 hrs1980(weekly)Adult male:Marke
11、t:44 hrs;household:13.8 hrs;Personal care:68.2 hrs;Leisure:41.8 hrsAdult female:Leisure:41.9 hrsLifetime changeEnter market 5 yrs later;after retirement 11 yrs longerDiscretionary time:225,000 to 298,500 hrsLifetime leisure:43,800 to 176,100 hrsLeisures share:20%to 60%,Joint HH Labor Supply Decision
12、s,Single decision modelCross effectsSpecializationBargaining modelCooperative gameIndependent decisionNon-cooperative game,Family Labor Supply,Utility function for the familyBudget constraintOptimal decision in two dimensions:LF participationHours of workBoth are affected by the wage rate of the spo
13、use.,Empirical Evidence on Cross Wage Effect,Supports the notion thatFamily labor supply a joint decisionFemale LS more responsive to changes in spouses wage rate.A 10%increase in the husbands wage lowers the LFPR of women by 5.3 ppts.reduces the hours that working wives allocate to the labor market
14、 by 1.7%.There is little evidence that husbands labor supply is affected by the wifes wage rate.,Specialization in the Household(Blau et al.),Two people:Jack and Jill;two goods:Market goods and home goodsJack is more productive at work than JillJill is more productive at home than JackBoth have a ti
15、me constraint of 10 hours,Deriving production possibility frontiers,Jack:Jill:,Jack and Jills Production Sets,Changes in Market Wages or Home Productivity,Home productivity goes up.,Market wage goes up.,Joint Production Possibility Set if Jack and Jill Marry,Jill specializes in the household sector,
16、Jack divides his time.,Jack specialized in the labor market,Jill divides her time,Division of Labor in the Household,Jack specializes in the market sector,Jill specializes in the household sector.,Division of Labor in the Household,Some Points,Specialization is caused by differences in market wages
17、and/or home productivities,i.e.,comparative advantage.If relative market/home productivity is the same,then we do not expect to see specialization.The model predicts that the spouse with the lower wage or with a greater home productivity tends to specialize in home production.The theory does not say
18、 that custom etc.are unimportant.,Fertility,Principle of Population by Malthus(1798)As income rises above the subsistence,people have more children.Because the resource is limited,competition for the scarce resources leads to wars,etc.Incomes fall back to the subsistence level.Fertility is contained
19、.The essence:income effects.What about the price of children?,Modern Economic Analysis of Fertility,Two commodities:Goods(X)and the number of children(N)Preferences:both are normal.Budget constraint:Income IPrice of children Pn:direct costs(diaper,education)foregone earnings for the caregiverPrice o
20、f goods PxGraph.,As Income Changes,As the Price of Children Changes,Empirical Findings on Fertility,Correlating measures of fertility to measures of household income and of the price of having children.There is a very strong relationship between a womans wage rate and the number of children.A 10%inc
21、rease in wage reduces the number of children by about 3%.The relationship between income and the number of children is much weaker.A 10%increase in income increases the number of children by less than 0.4%.,Fertility Changes in the World,Life-Cycle Labor Supply,Labor supply is part of a life-cycle d
22、ecision-making process.attend school early in lifeaccumulate wealth while in labor forcemake retirement decisions late in lifeSavings from labor earnings are often required to sustain living when out of the LF.Variations in health,family composition and wages provide incentives for people to vary th
23、e timing of their labor earnings.,Stylized Facts,The typical age-earnings profile has a predictable pathlow when youngrise as worker ages,peak at about 50remain stable or decline slightly after 50Hours of work and the wage rate move together over time.Explanation?,Life-Cycle Allocation of Time,Figur
24、e 7.5,A Basic Framework,Assume the life-time utility function is additive over timeThe life-time budget constraint is,Prediction on Hours,Exogenous to work decisionConcave age-earning profileWage low at young and oldWage high in 30s and 40sPrediction(given reservation wage):Concentrate on work activ
25、ities when the wage is high.Concentrate on leisure activities when the wage is low.,Prediction on Participation,Compare market wage and reservation wageGiven reservation wageParticipate when market wage is high.Leave when market wage is low.Life-cycle pattern of reservation wageThe presence of small
26、 children increases the reservation wage of married women.,Evidence:Participation by Age,Evidence:Hours by Age,Empirical Studies on Hours,A typical study uses a sample of workers to estimate how a given worker adjusts hours of work to wage changes that occur as the worker ages.Many studies conclude
27、that the response of hours of work to evolutionary wage changes is small:a 10%increase in the wage leads to only a 1%increase in hours of work,Empirical Studies on LFP for Married Women,Cross sectional data:participation rates decline in the 20s and rise from ages 30 to 50.Synthetic cohort analysis:
28、Participation rises in each decade of life,with the increases after age 30 typically being much greater than those from 20 to 30.,Labor Supply Over the Business Cycle,Added worker effect:As the main breadwinner becomes unemployed,family income falls and the secondary workers get jobs to make up the
29、loss.Labor force participation rate of secondary workers has a counter-cyclical trend.Discouraged worker effect:Many unemployed workers find it almost impossible to find jobs during a recession,and simply give up.The labor force participation rate has a pro-cyclical effect.,Implications for Unemploy
30、ment Rate,The added worker effect increases the unemployment rate.The discouraged worker effect depresses the unemployment rate.Empirical evidence:The discourage worker effect is dominant.Official unemployment rate data may understate the unemployment problem during severe recession.,The Hidden Unem
31、ployed,Official unemployment rate in the US:5.4%in 1990 and 7.3%in 1992.If discouraged workers were to be included,the numbers would have been:6.1%in 1990 and 8.2%in 1992.Definition:One who wants work but does seek it because he/she feels that jobs are unavailable.Should the discouraged worker be included?As the price of leisure is low during recession,a worker can make an intertemporal substitution.,
