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1、0Lecture 13Neoclassical Model1Economic ModelsReal economy is too complicated to understandBuilt your own, simple economyIngredientslPeoplelGoods and technologieslInstitutionsMicrofoundationsUse models that explicitly incorporate household and firm decision problemsAllows to capture how decisions adj
2、ust when economic environment of policies change2Using ModelsTools to predict outcomes:lOptimizationlMarket ClearingCheck whether model matches data:lYes: Likely that model world captures key features of the real worldlNo: Build new model3A Simple Market EconomyOne consumer, one firmConsumer and fir
3、m trade in marketsMarkets for consumption C and labor N4Market PricesPrices:lPrice of consumption normalized to onelPrice for N is real wage w5The Households Problem in the Market EconomyUtility function U(C,l)lC: Consumption (coconuts)ll: LeisureBudget constraintlConsumption expenditure equals inco
4、me from capital and laborl l p is given, capital incomelN is given by time constraint: N=h-l6The Consumers PreferencesUtility function U(C,l)Assumptions:lMore is better than less: , lDiversity is good: Falling MRSlConsumption and leisure are normal goods7Indifference Curves8Properties of Indifferenc
5、e CurvesDownward sloping: Follows from positive marginal utilitiesConvex: Follows from falling marginal rate of substitution9Indifference Curves10Marginal Rate of SubstitutionMRS: the minimum # of Coconuts consumer is willing to give up for another unit of leisureEqual to minus slope of indifference
6、 curveMathematically:11The Budget Constraint12The Optimization ProblemMaximize utility subject to the budget constraint by choosing l and C s.t.13Graphical RepresentationDraw indifference curves as beforeDraw budget constraint as a function of leisureOptimal choice is point in the budget set that li
7、es on the highest indifference curve14Graphical Optimization15Outcome16Slope 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 Optimizatio
8、nSubstitute constraints into U(C,l)First-order condition with respect to l:Result (once again): wage = MRS17Example wage equals 10 coconuts per hourTime: 24 hoursProfit and tax: p=30 and T=30 18ExampleMaximization problem:Solution: , 19Predicting the Reaction to Changes in the EconomySeparate income
9、 and substitution effectsPure income effect: consume more of every (normal) goodPure substitution effect: consume more of the good that gets cheaperIn practice, often both effects are present20A Pure Income Effect21An Increase in the Wage22The Firms Problem in the Market EconomyProduction function N
10、umber of coconuts produced with capital and labor input Assumptions:l : both inputs requiredl : positive marginal productsl : decreasing marginal products23Graph of 24The Marginal Product of Labor25Effect of an Increase in Productivity26Effect of an Increase in Productivity27The FirmThe firm maximiz
11、es profits subject to the production functionProfit : output minus cost28Graphical Profit Maximization29Optimization 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!30Mathematical Profit Optimizatio
12、nThe maximization problem:First-order condition:Wage equals marginal product of labor31EquilibriumRequirements for equilibrium:lConsumer maximizes utilitylFirm maximizes profitslDemand equals supply in every marketCombining firm and household optimization, we get32What is the Simple Model Good for?T
13、he ultimate task of any economic model is to shed light on the real worldThe only thing the model could be good for is explaining labor-leisure choiceDoes the model explain U.S. data?33Average Workweek in U.S.34Average Workweek in U.S.35How is the Model Evaluated?Model abstracts from many potential
14、factorsWant to know whether model is sufficient to explain decline in time workedNeed to specify model more precisely36Making the Model More PreciseNo capital for simplicityVariables:lC: consumptionll: leisurelN: laborlw: wagelz: total factor productivitylg: growth rate of zProductivity grows over t
15、imeWant to determine N as a function of z37Choosing Functional FormsProduction function:Utility function:Budget and time constraints:38Profit Maximization First order condition: 39Utility MaximizationThe maximization problem:First-order condition:Labor constant, independent of wage!40What does It Me
16、an?Model appears to be a complete failure!Reason: with log utility, income and substitution effects on labor supply cancel (i.e., they have equal size and opposite sign)Is this realistic in the cross-section?41Using the Model for Cross-Country ComparisionEuropean countries (France, Germany, Sweden e
17、tc.) have higher taxes and higher transfersIs like a negative substitution effect: income tax lowers the perceived wageModel predicts less work and more leisure in Europe42What Else Could Explain the Facts?There are alternative explanations:lLabor-force participationlTaxationlRelative productivity o
18、f “leisure” sectorTry new models in case of failure43Intertemporal ChoiceMost of macroeconomics is about changes over timeSo far, have jus considered the decision of work versus leisureNeed to add choice of today versus tomorrow44ExamplesSome intertemporal choices:lBorrowing and saving by consumersl
19、Investment by firmslHuman capital investment by studentslFamily decisions45Important Factors for Intertemporal Choice:Preferences over time (patience)Expected return on investmentExpected future economic conditions46Modeling Intertemporal ChoiceFor simplicity:lLook at one consumer in isolationlTwo p
20、eriods onlyVariables:l : consumption today and tomorrow l : discount factor (measures patience)l : income today and tomorrowl : savingl : interest rate (return on saving)47The SetupUtility function:Budget constraints:Want to know how and depend onl (intertemporal preferences)l (economic conditions)l
21、 (return on investment)48Mathematical SolutionSubstitute constraints into utility function:Setting derivative wrt. s to zero:49OutcomeMRS = Interest rateSame as before Simple Model:lChoice between leisure and laborlMRS(l,C) = Relative price (l, C)Intertemporal model:lChoice between today and tomorro
22、wl MRS = Relative price 50The Present-Value Budget ConstraintPresent value of x dollars tomorrow:lAmount needed to be saved today to have x dollars tomorrowl Solving period-2 constraint for s: 51The Present-Value Budget ConstraintPlugging the result into the period-1 constraint: PV(total consumption
23、)=PV(total income)52Graphical AnalysisLifetime wealth: we = PV(total income)Rewriting the budget constraint:Can now represent choice in standard diagram 53The Diagram54OutcomeMRS = Relative pricePure income effect (increase in either or ) will increase both and lImplies that s increases when riseslI
24、mplies that s falls when risesOnly present value of income matters, distribution irrelevant for consumption55Example: Log UtilityFOC for and 56Computing ConsumptionExample I:Example II: 57ConclusionsModel predicts strong consumption smoothing: timing of income does not matterResult relies on perfect
25、 capital marketEven so, evidence for consumption smoothing is strong58Consumption Smoothing in PracticeLife-cycle consumption: borrow early in life, then save for retirement59Informal Capital MarketsDefault risk prevents some people from borrowingSociety often finds ways around that problem:lTransfe
26、rs from parents and relativeslGift giving and neighborhood helplSocial insurance60A Neoclassical Growth ModelOverlapping generations:lEach consumer lives for two periodslEach year, one old and one young consumer are aliveThe young work one unit of timeThe old are retired and supply capital61Generati
27、onal Structure62The Decision Problem of a Consumer Born at Time tUtility function:Budget constraints:Notice that:lThere is no income in the old periodlSavings are capital in the old period63Solving the Consumers ProblemChoose to solve:First-order condition:Solution: 64The Profit-Maximization Problem
28、 of the FirmFirm maximizes production minus cost:First-order conditions are:65Closing the ModelMarket clearing for capital and labor:Assume constant productivity (for now):66Working out the Predictions of the ModelUsing market-clearing conditions in equations for w and r:Using wage equation in savin
29、g equation of household:67Using the Law of Motion for CapitalHave derived a law of motion for capital (capital tomorrow depending on capital today)Starting at any initial capital, can determine how capital will develop in the futureCan compute production and growth rates over time68ExampleParameter
30、choices:l l l The law of motion is:69Graph of the Law of Motion70Convergence71Capital Over Time72ResultModel predicts convergence across countries with different initial capitalIntuition:lReturns to capital are decreasinglWage increases less than proportionally with capitallSavings increase less tha
31、n proportionally with capital73Long-run PredictionsCapital convergence to steady stateSolving for capital in steady state:74What Happens if there is Productivity Growth?Steady-state level of capital depends on productivity zSteady state shifts upwards if productivity increasesAssume constant product
32、ivity growth g:75The Law of Motion after a Change in Productivity76Implications In the long run, capital k grows at the same rate as productivity:What happens to output and the return to capital?77Implication for GrowthOutput grows at the same rate as capitalTherefore capital/output ratio is constan
33、t 78Remaining Growth FactsLabor and capital shares are constant because of Cobb-Douglas technologyReturn to capital:Constant because K and z both grow at rate g79Convergence from Different Initial Conditions80Catching-up after a destruction of Capital81Two Countries with Different Discount Factors82
34、Summary The model explains all the growth factsDriving force is exogenous, constant productivity growth combined with decreasing returns to capitalExplains catch-up of Germany of Japan after the war83Revisiting the Asian Miracle84Unraveling the PuzzleAsian Tigers started with low capital stock after
35、 World War IIRapid growth through capital accumulation is exactly what model predictsThere is no Asian miracle!85Log of GDP per capita in the Asian Tigers86Limits of the Neoclassical Growth ModelTechnological progress is just assumed, not explainedModel does not offer a perspective on stagnation throughout history and in poor countries87
