大二下专业课宏观经济学颜色lecture

1、0Lecture 13Neoclassical Model (part 2)1A Standard Neoclassical Growth ModelGeneral equilibriumInfinite horizonRepresentative agentsA variation: A-K modelSee my notesA Neo-classical Growth Model with Leisure-Labor ChoiceOne consumer, one firmConsumer and firm trade in marketsMarkets for consumption C

2、 and labor N2Market PricesPrices:Price of consumption normalized to onePrice for N is real wage w3The Households Problem in the Market EconomyUtility function U(C,l)C: Consumption (coconuts)l: LeisureBudget constraintConsumption expenditure equals e from capital and labor p is given, capital eN is g

3、iven by time constraint: N=h-l4The Consumers PreferencesUtility function U(C,l)Assumptions:More is better than less: , Diversity is good: Falling MRSConsumption and leisure are normal goods5Indifference Curves6Properties of Indifference CurvesDownward sloping: Follows from positive marginal utilitie

4、sConvex: Follows from falling marginal rate of substitution7Indifference Curves8Marginal Rate of SubstitutionMRS: the minimum # of Coconuts consumer is willing to give up for another unit of leisureEqual to minus slope of indifference curveMathematically:9The Budget Constraint10The Optimization Prob

5、lemMaximize utility subject to the budget constraint by choosing l and C s.t.11Graphical RepresentationDraw indifference curves as beforeDraw budget constraint as a function of leisureOptimal choice is point in the budget set that lies on the highest indifference curve12Graphical Optimization13 e14S

6、lope of indifference curve equals slope of budget constraintSlope of budget constraint: wage wResult: wage = MRSThis is a very general result: the MRS between any two goods is given by the relative price!Mathematical OptimizationSubstitute constraints into U(C,l)First-order condition with respect to

7、 l:Result (once again): wage = MRS15Example wage equals 10 coconuts per hourTime: 24 hoursProfit and tax: p=30 and T=30 16ExampleMaximization problem:Solution: , 17Predicting the Reaction to Changes in the EconomySeparate e and substitution effectsPure e effect: consume more of every (normal) goodPu

8、re substitution effect: consume more of the good that gets cheaperIn practice, often both effects are present18A Pure e Effect19An Increase in the Wage20The Firms Problem in the Market EconomyProduction function Number of coconuts produced with capital and labor input Assumptions: : both inputs requ

9、ired : positive marginal products : decreasing marginal products21Graph of 22The Marginal Product of Labor23Effect of an Increase in Productivity24Effect of an Increase in Productivity25The FirmThe firm maximizes profits subject to the production functionProfit : output minus cost26Graphical Profit

10、Maximization27Optimization ResultSlope of production function equals slope of cost curve This is a very general result: the MP of any factor of production is given by its price!28Mathematical Profit OptimizationThe maximization problem:First-order condition:Wage equals marginal product of labor29Equ

11、ilibriumRequirements for equilibrium:Consumer maximizes utilityFirm maximizes profitsDemand equals supply in every marketCombining firm and household optimization, we get30What is the Simple Model Good for?The ultimate task of any economic model is to shed light on the real worldThe only thing the m

12、odel could be good for is explaining labor-leisure choiceDoes the model explain U.S. data?31Average Workweek in U.S.32Average Workweek in U.S.33How is the Model Evaluated?Model abstracts from many potential factorsWant to know whether model is sufficient to explain decline in time workedNeed to spec

13、ify model more precisely34Making the Model More PreciseNo capital for simplicityVariables:C: consumptionl: leisureN: laborw: wagez: total factor productivityg: growth rate of zProductivity grows over timeWant to determine N as a function of z35Choosing Functional FormsProduction function:Utility fun

14、ction:Budget and time constraints:36Profit Maximization First order condition: 37Utility MaximizationThe maximization problem:First-order condition:Labor constant, independent of wage!38What does It Mean?Model appears to be a complete failure!Reason: with log utility, e and substitution effects on l

15、abor supply cancel (i.e., they have equal size and opposite sign)Is this realistic in the cross-section?39Using the Model for Cross-Country ComparisionEuropean countries (France, Germany, Sweden etc.) have higher taxes and higher transfersIs like a negative substitution effect: e tax lowers the perceived wageModel predicts less work and more leisure in Europe40What Else Could Explain the Facts?There are alternative explanations:Labor-force participationTaxationRelative productivity of “leisure” sectorTry new models in case of failure41Combining Intertemporal Choices and Leisur