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经济学(Economics)：研究人和社会对具有不同用途的稀缺资源配置并加以选择的科学；其目标是有效利用稀缺资源来生产商品和劳务，并在现在或将来把它们合理地分配给社会成员或集团以供消费之用。
微观经济学(Microeconomics)：研究微观(Micro)、或“小型”经济单位的经济行为，如单个消费者、生产者和单一市场的经济行为。
宏观经济学(Macroeconomics)：研究社会总体的经济行为及其后果，即对整个社会的消费、投资、生产、收入等进行分析研究。
经济人(Economic man)：作出决策的出发点是个人利益，寻求个人利益最大化。
需求（Demand）：一种商品的需求是指消费者在一定时期内在各种可能的价格下愿意而且能够购买的该种商品的数量。
需求函数（Demand function）：用来表示一种商品的需求数量和影响该需求数量的各种因素之间相关关系的数学表达式。
供给（Supply）：一种商品的供给是指生产者在一定时期内在各种可能的价格下愿意而且能够提供出售的该种商品的数量。
供给函数（Supply function）：用来表示一种商品的供给数量和影响该供给数量的各种因素之间相关关系的数学表达式。
均衡（Equilibrium）：指各个经济决策者（消费者、厂商）所作出的决策正好相容，在外界条件不变的情况下，每个人都不愿意再调整自己的决策，是一种相对静止的状态。
均衡价格（Equilibrium price）：指商品的市场需求量和市场供给量相等时候的价格。
均衡数量（Equilibrium quantity）：在均衡价格水平下相等的供求数量。
均衡点（Equilibrium point）：一种商品的市场需求曲线和市场供给曲线的交点。
需求量的变动（Variation of demand quantity）：仅仅因价格因素的变动而引起的需求数量的变动,是一种线上运动。
需求的变动（Variation od demand）：由于价格以外的因素的变动而引起的需求数量的变动,是一种线的移动。
经济学专业英语术语表专业简介: 经济学主要研究经济学、金融学、投资学、精算学等方面的基本知识和技能，在银行、证券、信托等金融机构进行经济分析、预测、规划、管理以及各类金融服务。
例如：债券、基金的投资前景分析，股票、投资的风险评估，汽车、房子的抵押贷款，企业破产时的资产清算等。
开设课程: 经济学主要课程：政治经济学、《资本论》、西方经济学、统计学、国际经济学、货币银行学、财政学、经济学说史、发展经济学、企业管理、市场营销、国际金融、国际贸易等1. 政治经济学 (Political Economy)术语术语术语术语术语生产力 (Productivity)生产关系 (ProductionRelations)经济制度 (EconomicSystem)社会主义市场经济(Socialist MarketEconomy)资本主义市场经济(Capitalist MarketEconomy)劳动价值论 (Labor Theory of Value)剩余价值 (SurplusValue)利润率 (Profit Rate)资本积累 (CapitalAccumulation)资本有机构成 (OrganicComposition of Capital)经济危机 (EconomicCrisis)货币 (Money)信用 (Credit)利息 (Interest)货币政策 (MonetaryPolicy)财政 (Fiscal)税收 (Taxation)政府支出 (GovernmentExpenditure)财政政策 (Fiscal Policy)公共债务 (Public Debt)国民收入 (NationalIncome)国内生产总值 (GrossDomestic Product,GDP)国民生产总值 (GrossNational Product, GNP)经济增长率 (EconomicGrowth Rate)经济发展水平 (EconomicDevelopment Level)2. 《资本论》(Capital)术语术语术语术语术语商品 (Commodity)使用价值 (Use Value)交换价值 (ExchangeValue)商品拜物教(CommodityFetishism)商品流通形式 (Forms ofCommodity Circulation)简单商品流通 (Simple Commodity Circulation)货币商品流通 (MoneyCommodityCirculation)货币转化为资本(Money Transformedinto Capital)资本循环过程(Circuit of Capital)资本周转时间 (TurnoverTime of Capital)不变资本 (ConstantCapital)变动资本 (VariableCapital)剩余价值率 (Rate ofSurplus Value)剥削率 (Rate ofExploitation)绝对剩余价值生产方式(Absolute Surplus ValueProduction Method)相对剩余价值生产方式(Relative Surplus Value Production Method)简单再生产(SimpleReproduction)扩大再生产(ExpandedReproduction)生产部门(Department ofProduction)消费部门(Department ofConsumption)资本主义生产方式(Capitalist Mode of Production)资本主义生产关系(Capitalist ProductionRelations)资本主义经济规律(Capitalist EconomicLaws)资本主义经济危机(Capitalist EconomicCrisis)资本主义的历史趋势(Historical Trend ofCapitalism)3. 西方经济学 (Western Economics)术语术语术语术语术语微观经济学(Microeconomics)宏观经济学(Macroeconomics)经济学方法论(EconomicMethodology)经济学思想史 (Historyof Economic Thought)经济学流派 (Schools ofEconomics)边际分析 (MarginalAnalysis)需求 (Demand)供给 (Supply)市场均衡 (MarketEquilibrium)弹性 (Elasticity)消费者行为(Consumer Behavior)效用 (Utility)预算约束 (BudgetConstraint)消费者选择(Consumer Choice)消费者剩余 (ConsumerSurplus)生产者行为 (ProducerBehavior)生产函数 (ProductionFunction)成本函数 (CostFunction)收益函数 (RevenueFunction)利润最大化 (ProfitMaximization)市场结构 (Market Structure)完全竞争市场 (PerfectCompetition Market)垄断市场 (MonopolyMarket)寡头垄断市场(Oligopoly Market)竞争性垄断市场(Monopolistic CompetitionMarket)4. 统计学 (Statistics)术语术语术语术语术语统计数据 (Statistical Data)数据来源 (DataSources)数据类型 (DataTypes)数据收集方法(DataCollection Methods)数据整理方法(DataProcessing Methods)频数分布表(Frequency Distribution Table)直方图(Histogram)频率多边形(Frequency Polygon)分位数(Quantile)箱线图(Boxplot)中心趋势度量(Measures of Central Tendency)平均数(Mean)中位数(Median)众数(Mode)几何平均数(GeometricMean)离散趋势度量(Measures ofDispersion)极差(Range)方差(Variance)标准差(StandardDeviation)变异系数(Coefficient ofVariation)相关分析(CorrelationAnalysis)散点图(ScatterPlot)相关系数(CorrelationCoefficient)回归分析(RegressionAnalysis)回归方程(RegressionEquation)5. 国际经济学(International Economics)术语术语术语术语术语国际贸易(InternationalTrade)国际收支(Balance ofPayments)汇率(Exchange Rate)国际金融(InternationalFinance)国际货币体系(International MonetarySystem)比较优势(Comparative Advantage)贸易政策(TradePolicy)关税(Tariff)非关税壁垒(Non-TariffBarrier)自由贸易区(Free TradeArea)关税同盟(CustomsUnion)共同市场(CommonMarket)经济一体化(EconomicIntegration)区域贸易协定(RegionalTrade Agreement)世界贸易组织(WorldTrade Organization)汇率制度(Exchange Rate Regime)固定汇率(FixedExchange Rate)浮动汇率(FloatingExchange Rate)管理浮动汇率(ManagedFloating Exchange Rate)汇率决定理论(ExchangeRate DeterminationTheory)汇率风险(Exchange Rate Risk)避险(Hedging)套利(Arbitrage)规模经济(Economies ofScale)产品差异化(ProductDifferentiation)贸易多样化(Trade Diversification)贸易创造(TradeCreation)贸易转移(TradeDiversion)贸易保护主义(TradeProtectionism)贸易自由化(TradeLiberalization)国际金融市场(International FinancialMarket)国际债券市场(International BondMarket)国际股票市场(International StockMarket)国际外汇市场(International ForeignExchange Market)国际金融危机(International FinancialCrisis)金本位制(Gold Standard System)布雷顿森林体系(Bretton WoodsSystem)特别提款权(SpecialDrawing Rights,SDRs)欧洲货币体系(EuropeanMonetary System, EMS)欧元(Euro)6. 货币银行学 (Money and Banking)货币的本质(Nature ofMoney)货币的功能(Functionof Money)货币的种类(Types ofMoney)货币供给(MoneySupply)货币需求(Money Demand)货币创造(Money Creation)存款准备金率(ReserveRequirement Ratio)存款货币乘数(DepositMoney Multiplier)银行的资产负债表(Bank's Balance Sheet)银行的盈亏表(Bank'sIncome Statement)银行的风险管理(Risk Management of Bank)银行的监管(Regulation of Bank)银行的稳健性(Soundnessof Bank)银行的效率(Efficiencyof Bank)银行的竞争力(Competitiveness of Bank)中央银行(CentralBank)中央银行的职能(Function of CentralBank)中央银行的独立性(Independence of CentralBank)中央银行的货币政策(Monetary Policy ofCentral Bank)中央银行的政策工具(PolicyTools of Central Bank)存款利率(Deposit Interest Rate)贷款利率(LoanInterest Rate)基准利率(BenchmarkInterest Rate)政策利率(PolicyInterest Rate)市场利率(Market InterestRate)7. 财政学 (Public Finance)术语术语术语术语术语公共部门(PublicSector)公共财政(Public Finance)公共财政的功能(Function of PublicFinance)公共财政的目标(Objective of PublicFinance)公共财政的原则(Principleof Public Finance)公共支出(Public Expenditure)公共支出的结构(Structure of PublicExpenditure)公共支出的效果(Effect ofPublic Expenditure)公共支出的决策(Decisionof Public Expenditure)公共支出的评价(Evaluation of PublicExpenditure)公共收入(Public Revenue)税收(Tax)税收的分类(Classification of Tax)税收的效果(Effect of Tax)税收的原则(Principle ofTax)税制(Tax System)税率(Tax Rate)税基(Tax Base)税负(Tax Burden)税收弹性(Tax Elasticity)财政赤字(FiscalDeficit)财政平衡(Fiscal Balance)财政盈余(Fiscal Surplus)财政政策(Fiscal Policy)财政乘数(FiscalMultiplier)8. 经济学说史 (History of Economic Thought)术语术语术语术语术语经济思想(EconomicThought)经济思想家(EconomicThinker)经济思潮(EconomicTrend)经济范式(EconomicParadigm)经济方法论(EconomicMethodology)古典经济学(Classical Economics)亚当·斯密(Adam Smith)大卫·李嘉图(DavidRicardo)托马斯·罗伯特·马尔萨斯(Thomas Robert Malthus)约翰·斯图亚特·穆勒(John Stuart Mill)新古典经济学(Neoclassical Economics)威廉·斯坦利·杰文斯(William StanleyJevons)卡尔·门格尔(CarlMenger)列昂·瓦尔拉斯(LeonWalras)阿尔弗雷德·马歇尔(Alfred Marshall)凯恩斯主义(Keynesianism)约翰·梅纳德·凯恩斯(John Maynard Keynes)总需求(TotalDemand)总供给(Total Supply)有效需求(EffectiveDemand)马克思主义(Marxism)卡尔·马克思(Karl Marx)弗里德里希·恩格斯(Friedrich Engels)剩余价值(Surplus Value)剩余价值理论(Theory ofSurplus Value)9. 发展经济学 (Development Economics)术语术语术语术语术语发展(Development)经济发展(EconomicDevelopment)社会发展(SocialDevelopment)人类发展(HumanDevelopment)可持续发展(SustainableDevelopment)发展中国家(Developing Countries)发达国家(DevelopedCountries)最不发达国家(LeastDeveloped Countries)新兴市场国家(Emerging MarketCountries)发展中欧洲和中亚国家(Europeand Central Asia DevelopingCountries)发展指标(Development Indicator)经济增长率(EconomicGrowth Rate)人均国民收入(PerCapita NationalIncome)贫困率(Poverty Rate)不平等系数(InequalityCoefficient)发展理论(Development Theory)进化论(Evolutionism)扩散论(Diffusionism)追赶论(Catch-upTheory)结构主义(Structuralism)发展战略(Development Strategy)进口替代战略(ImportSubstitution Strategy)出口导向战略(Export-oriented Strategy)自力更生战略(Self-reliance Strategy)开放型战略(Open Strategy)10. 企业管理 (Business Management)术语术语术语术语术语企业(Business)企业的目标(Objective ofBusiness)企业的环境(Environment ofBusiness)企业的组织(Organization ofBusiness)企业的管理(Management ofBusiness)管理的定义(Definition of Management)管理的功能(Function ofManagement)管理的原则(Principle ofManagement)管理的过程(Process ofManagement)管理的效果(Effect ofManagement)计划(Planning)计划的类型(Type ofPlanning)计划的步骤(Step ofPlanning)计划的工具(Tool ofPlanning)计划的评价(Evaluationof Planning)组织(Organizing)组织的类型(Type ofOrganizing)组织的结构(Structure ofOrganizing)组织的设计(Design ofOrganizing)组织的变革(Change ofOrganizing)领导(Leading)领导的类型(Type ofLeading)领导的风格(Style ofLeading)领导的技能(Skill ofLeading)领导的效果(Effect ofLeading)11. 市场营销 (Marketing)术语术语术语术语术语市场(Market)市场营销(Marketing)市场营销的概念(Conceptof Marketing)市场营销的目标(Objective ofMarketing)市场营销的原则(Principle ofMarketing)市场营销环境(Marketing Environment)微观环境(Microenvironment)宏观环境(Macroenvironment)竞争环境(CompetitiveEnvironment)法律环境(LegalEnvironment)市场营销信息系统(Marketing InformationSystem)市场调查(MarketResearch)市场分析(Market Analysis)市场预测(MarketForecast)市场控制(MarketControl)市场细分(Market Segmentation)目标市场(TargetMarket)市场定位(MarketPositioning)市场选择(MarketSelection)市场组合(Market Mix)产品(Product)产品生命周期(ProductLife Cycle)产品策略(ProductStrategy)产品创新(ProductInnovation)产品品牌(ProductBrand)12. 国际金融 (International Finance)术语术语术语术语术语国际金融(InternationalFinance)国际金融市场(International FinancialMarket)国际金融机构(International FinancialInstitution)国际金融体系(International FinancialSystem)国际金融秩序(International FinancialOrder)国际收支(Balance of Payments)经常账户(CurrentAccount)资本账户(Capital Account)官方储备账户(OfficialReserve Account)国际收支平衡(Balanceof Payment Equilibrium)汇率(Exchange Rate)汇率制度(ExchangeRate Regime)汇率决定理论(ExchangeRate DeterminationTheory)汇率风险(ExchangeRate Risk)汇率政策(ExchangeRate Policy)国际债务(InternationalDebt)外债(Foreign Debt)内债(Domestic Debt)多边债务(MultilateralDebt)双边债务(Bilateral Debt)国际金融危机(International FinancialCrisis)金融全球化(FinancialGlobalization)金融自由化(FinancialLiberalization)金融监管(FinancialRegulation)金融稳定(FinancialStability)13. 国际贸易国际贸易是指不同国家或地区之间进行的商品和服务的交换活动。
+ + kLecture 4The Utility Maximization ProblemGiven prices p » 0 and wealth w >0, a consumer’s utility maximization problem (UMP) is:Max x ≥0u (x ) ,s.t. p ⋅ x ≤ w .Budget setB p ,w = {x ∈ R L: p ⋅ x ≤w } is bounded and closed. If p » 0 and u (.) iscontinuous, then the UMP always has a solution.The solution, denoted by x(p,w), is the Walrasian demand correspondence . It is called Walrasian demand function when it is single-valued.For each (p, w ) » 0, the utility value of the UMP is denoted v ( p , w ) ∈ R , called indirect utilityfunction . It is equal to u (x * ) with x * ∈ x ( p , w ) .Proposition D2 Suppose that u (.) is a continuous utility function representing a locallynon-satiated preference relation > defined on consumption setdemand correspondence x(p,w) possesses the following properties:X = R L . Then the Walrasian(i) Homogeneity of degree zero in (p,w): x(ap, aw)=x(p,w) for any p, w and scalar a >0; (ii) Walras’ law : p.x=w for all x in x(p,w);(iii) Convexity/uniqueness : if > is convex, so that u (.) is quasi-concave, then x(p,w) is a convex set. Moreover, if > is strictly convex, so that u (.) is strictly quasi-concave, then x(p,w) consists of a single element.If utility function u (.) is continuously differentiable , the Kuhn-Tucker conditions imply ifx * ∈ x ( p , w ) , there exists a multiplier λ ≥ 0 such that for l = 1,..., L ,∂u (x * )≤ λ∂x lp l , with equality if * > 0 ,or equivalently∇u (x * ) ≤ λ p and x * ⋅[∇u (x * ) - λ p ] = 0 .∂u (x * ) / ∂xp Hence if x * > 0 and x *> 0 , we have l = l . l k ∂u (x *) / ∂x p x l kL (x , ) ⋅ * j i 1 2 ∑ 2[Kuhn-Tucker Conditions: The optimal point x * of problemMax xsatisfies the following conditions:f (x ) s.t.g i (x ) ≤ 0 , ( i = 1,..., m ),x ≥ 0 ，(1) ∂L (x *, λ* ) f - λ g i ≤ 0 , ∂ * λ* x = 0 , and x * ≥ 0 , for j = 1,..., n . ∂x * j i j i =1∂x * j j(2) g i (x * ) ≤ 0 , andλ* ≥ 0 ; g i (x * ) ⋅ λ*= 0 . ]Example 1 (Cobb-Douglas utility function): Suppose L =2 and u (x , x ) = x α x 1-α with α ∈ (0,1)and k >0. This utility function can be transformed to strictly concave function. The UMP is121 2u (x 1 , x 2 ) = α ln x 1 + (1 - α ) ln x 2 , which is aMax x 1 , x 2u (x 1 , x 2 ) = α ln x 1 + (1 - α ) ln x 2 , s.t.,p 1 x 1 + p 2 x 2 = w .The first order conditions are:= λ p 11and 1 - αx 2= λ p 2 .From the budget constraint, we have λ = 1. It is the “shadow price of wealth”, which meanswthat∂v ( p , w ) = 1. It is easy to obtain the Walrasian demand functions ∂w wx ( p , w ) = α w and x ( p , w ) = (1 - α )w. 1p 2The indirect utility function is: v ( p , w ) = ln w + ln αα (1- α )1-α + ln p -α p α -1.Example 2 (Quasi-linear utility function): Suppose a consumer has differentiable and monotoneutility function of u (x ) = x 1 + ϕ (x 2 ,..., x L ) . The UMP isMax x 1 ,..., x Lu (x ) = x 1 + ϕ (x 2 ,..., x L ) , s.t.,p 1 x 1 + ... + p L x L ≤ w .Suppose there are interior solutions. The first order conditions areλ p = 1and∂ϕ = λ p ,l = 2,..., L ,i.e., 1λ = 1/ p ∂x land l∂ϕ =p l ,l = 2,..., L . 1 ∂x pl 1m j = αx 1 p+ We see from the first order conditions that the demand for commodityl = 2,..., L only dependson the relative prices but not the wealth.Proposition D3 Suppose that u (.) is a continuous utility function representing a locallynon-satiated preference > defined onX = R L . The indirect utility function v ( p , w ) is(i)Homogeneous of degree zero in (p, w );(ii)Strictly increasing in w and non-increasing inp l for any l ;(iii)Quasiconvex, that is, the set {( p , w ) : v ( p , w ) ≤ v } is convex for any v ;(iv) Continuous in p and w .Proof: (iii) ∀v ∈ R , for any (p,w) and (p’,w’) such that v ( p , w ) ≤ v and v ( p ', w ') ≤ v , denote( p ", w ") = α ( p , w ) + (1 - α )( p ', w ') = (α p + (1 - α ) p ',α w + (1 - α )w ') .We need to show that v ( p ", w ") ≤ v (which means set {( p , w ) : v ( p , w ) ≤ v } is convex).Since p "⋅ x ( p ", w ") ≤ w " , i.e.,α p ⋅ x ( p ", w ") + (1- α ) p '⋅ x ( p ", w ") ≤ α w + (1- α )w ' ,we shall have eitherp ⋅ x ( p ", w ") ≤ w or p '⋅ x ( p ", w ") ≤ w ' , which means eitheru (x ( p ", w ")) ≤ v ( p , w ) or u (x ( p ", w ")) ≤ v ( p ', w ') . Hence we have v ( p ", w ") ≤ v .x 2x 1+ + The Expenditure Minimization ProblemAn expenditure minimization problem (EMP ) is for p » 0andu > u (0) :Min x ≥0p.x , s.t. u (x ) ≥ u .The EMP is the “dual” problem to the UMP. It captures the same aim of efficient use of the consumer’s purchasing power while reversing the roles of objective function and constraint. The solution of the problem is denoted as h ( p , u ) , and e ( p , u ) ≡ p ⋅ h ( p , u ) .Proposition E1 Suppose that u (.) is a continuous utility function representing a locallynon-satiated preference > defined on consumption setX = R L and that the price vector isp » 0 . We have(i) Give wealth w >0, ifx * = x ( p , w ) , then x * = h ( p , u (x * )) and e ( p , u (x * )) = w . Inwords, if x * is optimal in the UMP with wealth w >0, thenx * is optimal in the EMP withutility level u ( x * ), and the minimized expenditure level in this EMP is exactly w .(ii) Give utility level u > u 0 , if x * = h ( p , u ) , then x * = x ( p , p ⋅ x * ) and v ( p , p ⋅ x * ) = u .In words, if x * is optimal in the EMP with utility levelu > u 0 , then x * is optimal in theUMP with wealth p ⋅ x * , and the maximized utility level in this UMP is exactly u .Proposition E1 says that e(p,u)=w if and only if v(p,w)=u.For any p » 0 , w > 0 , and u > u 0 , we havee ( p , v ( p , w )) = w and v ( p , e ( p , u )) = u .The set of optimal commodity vectors in the EMP,h ( p , u ) ⊂ R L , is known as the Hicksian(or compensated) demand correspondence . Using Proposition E1, we can relate the Hicksian and Walrasian demand correspondences as:h(p, u)=x(p, e(p, u))andx(p, w)=h(p, v(p, w)).+ x 21Proposition E2 Suppose that u (.) is a continuous utility function representing a locallynon-satiated preference relation > defined on the consumption setX = R L . The expenditurefunction e ( p , u ) is(i) Homogeneous of degree one in p ;(ii) Strictly increasing in u and non-decreasing in(iii) Concave in p ; (iv) Continuous in p and u .p l for any l ;Proof: (i) When e(p,u)=w , we have v(p,w)=u. Then e(ap,u)=e(ap,v(p,w))=e(ap,v(ap,aw))=aw .(ii) For any u”>u’, let w”=e(p,u”) and w’=e(p,u’). Since v(p,w”)>v(p,w’), we have w”>w’ , because v(p,w) is strictly increasing in w .Consider price vector p” and p’, with p " > p ' and p " = p ' for j ≠ l . Let w”=e(p”, u)lljjand w’=e(p’, u). Then u=v(p”, w”)=v(p’, w’). Since v(p, w) is non-increasing in p andstrictly increasing in w , we have w” ≥ w’. Hence e(p, w) is non-decreasing in p l for any l .(iii) For any utility level u and price p and p’, denote p”=ap+(1-a)p’. Let w”=e(p”, u),w=e(p, u) and w’=e(p’, u). We need to show that w " ≥ aw + (1 - a )w ' .Indeed, we have u=v(p”, w”)=v(p, w)=v(p’, w’). From the quasi-convexity of v (.,.), wehave v ( p ", aw + (1 - a )w ') ≤ u = v(p”, w”). Hence we must havew " ≥ aw + (1 - a )w 'from the monotonicity of v (.,.).+ * lpp 2Proposition E3 Suppose that u(.) is a continuous utility function representing a locallynon-satiated preference relation > defined on the consumption setX = R L . Then for anyp » 0 , the Hicksian demand correspondence h ( p ,u ) possesses the following properties:(i) Homogeneity of degree zero in p : h (α p , u ) = h ( p , u ) for any p, u and α > 0 .(ii) No excess utility: for any x ∈ h ( p , u ) , u(x)=u .(iii) Convexity/uniqueness: if > is convex, thenh ( p , u ) is a convex set; and if > is strictlyconvex, so that u (.) is strictly quasi-concave, then there is a unique element in h ( p , u ) .Proposition E4 Suppose that u (.) is a continuous utility function and that h(p,u) consists of asingle element for allp >> 0 . Then the Hicksian demand function h(p,u) satisfies thecompensated law of demand: For all p’ and p”, ( p "- p ')[h ( p ", u ) - h ( p ', u )] ≤ 0 .With an interior solution of the EMP, we shall have the first-order conditions:p = λ ∂u (x ) , for ∂x ll = 1,..., L ,where λ is the Lagrangean multiplier. Hence for any l , k ∈{1,..., L }, we havepu (x * ) l = l .Note that the first-order conditions are virtually the same as those of UMP.* p k u k (x )1 2 12αExample 3: (EMP with Cobb-Douglas utility function ) Consider following EMP:Min x 1 , x 2p 1 x 1 + p 1 x 2 , st. α ln x 1 + (1 - α ) ln x 2 ≥ ln uThe first order conditions are p = αλ x 1and p = (1 - α )λ. Solving for x 2p α p 1-αux 1 ,x 2and substitutingthem into the budget constraint, we have λ= 1 2 . Substituting it back to the first-orderαα (1 - α )1-αconditions, we obtain the Hicksian demand functions:h ( p , u ) = ϒ α p 2 /1-αu ,andh ( p , u ) = ϒ (1 - α ) p 1 / u . 1 ' (1- α ) p ∞ 2 ' α p ∞≤ The expenditure function is: 1 ƒ≤ 2 ƒe (p ,u )= u α -α (1 - α )α -1 p α p1-α .Homework : Page 97, 3.D.4, 3.E.5.。
