1、Raising 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.Addison Wesley Longman,Inc.2000Household Production FunctionZ=Z(X,H),properties:Positive marginal pr
2、oductsDiminishing marginal product,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.Addison Wesley Longman,Inc.2000Household timePurchased goods or servicesZ0Z1Addison Wesley Longman,Inc.20
3、00Budget ConstraintPurchased commodity is paid for by earnings from market work X=wN where N is working hoursHome and market hours satisfy time budget constraintH+N=TOr,X+wH=wTAddison Wesley Longman,Inc.2000The Optimal ChoiceThe problem is re-written as:Max U(Z(X,H)s.t.X+wH=wT Optimal choice:|MRTS|=
4、wAddison Wesley Longman,Inc.2000The Production of Child CareFigure 7.1Addison Wesley Longman,Inc.2000Comparative Static AnalysisIncome effectMarriage instabilityMarket wage goes upWomens educationIncome effects reduce market timeSubstitution effects increase market timeTechnology in home productionE
5、asier to substitute time for purchased goodsUtility isoquant becomes flatterIncrease market timeAddison Wesley Longman,Inc.2000The Tripartite Choice(Gronau)Market Work,Household Work and Leisure Utility comes from consuming goods(X)and leisure(L):U(X,L)X is composed of two types of goods:Home produc
6、ed()Market goods purchased using earnings()Household production function:Budget constraint for market goods:Time constraint:H+N+L=TAddison Wesley Longman,Inc.2000Explaining LS of Men and WomenStylized fact on labor supply:At low female participation,substitution effect tended to dominate income effe
7、ct.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 work and leisure is
8、 more difficult.Addison Wesley Longman,Inc.2000Large vs.Small Substitution Effects Attendant to a Wage IncreaseFigure 7.2Addison Wesley Longman,Inc.2000Work 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:10.
9、5 hrs1980(weekly)Adult male:44 hrs;household:13.8 hrs;68.2 hrs;41.8 hrsAdult female: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%Addison Wesley Longman,Inc.2000Join
10、t HH Labor Supply DecisionsSingle decision modelCross effectsSpecializationBargaining modelCooperative gameIndependent decisionNon-cooperative gameAddison Wesley Longman,Inc.2000Family Labor SupplyUtility function for the familyBudget constraintOptimal decision in two dimensions:LF participationHour
11、s of workBoth are affected by the wage rate of the spouse.Addison Wesley Longman,Inc.2000Empirical Evidence on Cross Wage EffectSupports 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
12、women by 5.3 ppts.reduces the hours that working wives allocate to the labor market by 1.7%.There is little evidence that husbands labor supply is affected by the wifes wage rate.Addison Wesley Longman,Inc.2000Specialization 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 time constraint of 10 hoursAddison Wesley Longman,Inc.2000Deriving production possibility frontiersJack:Jill:Addison Wesley Longman,Inc.2000Jack and Jills Production SetsAd
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