Economics 1 - Fall 2003 - Train - Final Answers

Econometrics IChina Center for Economic Research, Peking UniversityMinggao Shen, Fall 2003Office: 621 CCER; Phone: 6275-3109; Email: mshen@.Office Hour: Mondays 11:00-12:00amTA: Fei XU, phoenix-xf@Class Meets: Wednesdays 1:30-4:20 pm; TA Session: TBACourse DescriptionThis is an introductory graduate level course in Econometrics. This course helps students understand and use regression. In addition, the course should give students insight into how to correct some common problems found in estimation. As such, the lectures will tend to emphasize the practical uses of econometric theory, and students will have considerable opportunity to put this to use in computer-based assignments. At the end of the course, it is expected that students will be able to conduct their own empirical investigations, as well as to critically evaluate econometric and other statistical evidence.Required TextbooksEconometric Analysis, by William H. Green (Fifth Edition), FT Prentice Hall, 2003. (WG)Econometric Analysis of Cross Section and Panel Data, by Jeffrey M. Wooldridge, The MIT Press, 2002. (JW1)Recommended TextbookIntroductory Econometrics: A Modern Approach, by Jeffrey M. Wooldridge.South-Western College Publishing, 2000. (JW2)PrerequisitesProbability and Statistics, Calculus, Linear AlgebraHomeworkThere are weekly graded homework assignments. They will involve both theoretical and empirical exercises. Homework assignments are due in a week.Grading PolicyThe course grade will be based on homework assignments and, a midterm exam, and a final exam. Both exams are open book ones. The weights are:Homework 30%Exam 30%Midterm40%ExamFinalCourse Outline1 Econometrics and Data: An Introduction (WG, Ch.1; JW1, Ch. 1)2 The Simple Regression Model (JW2, Ch. 2)3 The Multiple Linear Regression Model (WG, Ch. 2,3)PropertiesSampleSmallHoliday4 Large Sample Theory (WG, Ch. 5)5 Maximum Likelihood Estimation (WG, Ch. 17)6 Data Problems (JM1, Ch. 4,5)MulticollinearityErrorsMeasurementErrorsUnobservable7 Functional Form and Model Selection (WG, Ch. 7,8; JW1, Ch. 6)VariablesOmittedExtraneousVariablesEndogeneityEstimationInstrumentalVariablesMidterm Exam8 The Nonlinear Regression Model (WG, Ch. 9)9/10 Generalized Regression Models (WG, Ch. 10,11,12,19) HeteroskedasticitySerial Correlation11/12 Systems of Regression Equations (WG, Ch. 14,15; JW1, Ch. 7,9) The Seemingly Unrelated Regression ModelThe Simultaneous Equations Model13 The Generalized Method of Moments (WG, Ch. 18)14 The Dynamic Regression Model (WG, Ch. 19)Final Exam。

Economics2010a Fall2003Edward L.Glaeser Lecture22.Choice and Utility Functionsa.Choice in Consumer Demand Theory and Walrasian Demandb.Properties of demand from continuity and properties from WARPc.Representing Preferences with a Utility Functiond.Demand as Derived from Utility Maximizatione.Application:Fertilityx i denotes commodities,continuous numbersx x 1,x 2,....x Lvector of discretecommodities p p 1,p 2,....p L vector of prices w wealth available to be spentThe budget constraint p x i 1Lp i x iwMWG Definition2.D.1The Walrasian Budget SetB p,w x L:p x wis the set of all feasible consumption bundles for the consumer faces market prices p and has wealth w.Note:We will be treating all prices and consumption levels as being weakly positive.Prices are treated as exogenous–as they will be in the production case.While neither consumer nor producer chooses prices(generally)prices are the extra parameter in each side’s problem that ensures that demand and supply are equal.Non-linear prices are certainly possible(example2.D.4).The Walrasian Demand Function is the set C B p,w which is defined for all p,w ,or at least for a full dimensional subsetp,w L 1We generally assume that C B p,w has a single element(for convenience)but it doesn’t need to.We writeC B p,w x p,w x1 p,w ,...x L p,wWe will also generally assume that demand is continuous and differentiable. MWG Definition2.E.1:The Walrasian Demand Function ishomogeneous of degree zero ifx p, w x p,w for any p,w and 0.This property follows from the fact that choice is only a function of the budget set and B p,w x L:p x w is the same set asB p, w x L: p x wThis fairly obvious claim is in many ways the underlying intellectual basis for the economic bias that the price level doesn’t matter.Differentiating x p, w x p,w totally with respect to gives us the following equation:i 1L x k p ,w p i p i x k p ,w ww 0 i 1L x k p ,w p i p i x k x k p ,w w w x k i 1L pi k w k 0This tells you that for any commodity,the sum of own and cross price elasticities equals -1times the income elasticity.MWG Definition2.E.2Walras’Law:The Walrasian Demand correspondence x p,w satisfies Walras’law if for every p 0and w 0,we have p x w for all x x p,w .This just says that the consumer spends all of his wealth.Looking ahead,Walras’law will come about as long as consumers are not “satiated”in at least one of the goods.Walras’Law and differentiability give us two convenient equalities.Differentiating p x w with respect to w yields:i 1Lp i x i p ,w w 1or manipulating this slightly yields:i 1L x i p ,w w w x i p i x i w i 1Lw i i0,where i p i x i w ,the budget share of good i .This means that income elasticities (when weighted by budget shares)sum to one.All goods can’t be luxuries,etc.Sometimes this is known as Engel aggregation (income effects are after all drawn with Engel curves).Differentiating p x w with respect to p k yields:i 1Lp i x i p ,wp k x k 0or multiplying the whole expression by p k w : i 1L x i p ,w p k p k x i p i x i w p k x k w i 1Lp k ii k0,where again i p i x i wThis means that cross price elasticities sum to-1times the budget share of the relevant good.Overall,these elasticities have to sum to a negative number.MWG Definition2.F.1The Walrasian Demand function satisfies the weak axiom of revealed preference if the following property holds for any two price-wealth situations p,w and p ,w : If p x p ,w w and x p ,w x p,wthen p x p,w w .In words–if the goods that are chosen with budget set(a)are affordable at budget set (b),and not the same as the goods that are chosen at budget set(b),then the goods that are chosen at budget set(b) are not affordable at budget set(a).Just like in the last lecture,WARP meansthat if bundle(b)is preferred to bundle(a) in one setting,it will be preferred in all other settings.A property that follows from WARP:price changes that are fully income compensated make consumers weakly better off.Take any p,w and let p p p Compensate the consumer with an income change so that the old bundle is exactly affordable at the new prices,i.e.:w w w x p,w pThe consumer’s new consumption level atp ,w satisfies the WARP condition:p x p,w w ,which then implies thatp x p ,w w,and this holds with strict equality whenx p ,w x p,wGiven that the consumer could have chosen the old bundle,the consumer must have weakly preferred the new bundle.MWG Proposition2.F.1:WARP implies the law of compensated demand.If the Walrasian demand function x p,w satisfies Walras’Law and is homogeneous of degree zero,then x p,w satisfies the weak axiom if and only if the following property holds.For any compensated price change from an initial situation p,w to a new price wealth pair p ,w p ,p x p,x ,then p p x p ,w x p,x 0,and this equality holds strictly whenx p ,w x p,x .We are now interested only in the weakaxiom- law of demand part of the proposition.First,note that if x p ,w x p,w we’re done,so consideronly the case where x p ,w x p,w . In that case,Walras’law gives us:p x p ,w w ,and we havedefined w so that w p x p,w Together,this gives us thatp x p ,w x p,w 0But we also know that as p ,w satisfies theWARP condition:p x p,w w andx p ,w x p,wit follows that p x p ,w w.Using p x p,w w(again by Walras’Law),this gives us that:p x p ,w x p,w 0Subtraction then yields:p p x p ,w x p,w 0 Change in prices times change in quantities is negative.Since p x 0for all compensated price changes,this also holds in the limit for very small price changes and dp dx 0.We can use matrix notation and write:dx D p x p ,w dp D w x p ,w dwwhich just means:dxi 1L x 1 p i dp i x 1 w dw ,.., i 1L x L p i dp i x L w ordx D p x p ,w dp D w x p ,w x p ,w dp ordxD p x p ,w D w x p ,w x p ,wT dpThe D p x p ,w D w x p ,w x p ,wTterm is a matrix where the element in row i ,column j of the matrix isx ip k x i w xkx 1 p 1 x 1 w x 1....x 1 p L x 1w x L.............x L p 1 x L w x 1.... x L p L x Lw xLand thendpD p x p ,w D w x p ,w x p ,wT dp 0The term in brackets is the Slutsky matrix.MWG Proposition2.F.2:If a differentiable Walrasian demand function x p,w satisfies Walras’law, homogeneity of degree zero and WARP, then at any p,w the Slutsky matrix is negative semi-definite,i.e.v Sv 0for any v L.MWG Proposition2.F.3:Suppose that the Walrasian demand function x p,w is differentiably homogeneous of degree zero,and satisfies Walras’Law.Then p S p,w 0 and S p,w p 0for any p,wUtility Functions–Finally getting to the basic tool of99%ofeconomics.Back to preferences.We want fourattributes:(1)completeness and(2)transitivityThese were defined in lecture1and we refer to preferences with these attributes as being rational.Definition3.B.2.:The preference relation on X is monotone if x,y X,and y x impliesy x.It is strongly monotone if y x and y x implies y x.In many cases,we won’t naturally have monotonicity,but then a little redefinition of variables does the trick(turn a bad into a good by multiplying by-1).A slight twist(I mentioned this earlier):Definition3.B.3:The preference relation on Xis locally nonsatiated if for every x,y X,and every0,there exists a ysuch that y x and y x.This means that there exists a y vector that is arbitrarily close to x that is strictly preferred to x.One last property:Definition 3.C.1.:The preference relation on X is continuous if it is preserved under limits.That is,for any sequence of pairs x n ,y n n 1 with x n y n for all n ,x lim n x n and y lim n y n we have x y .The famous counterexample islexicographic preferences,where more of good 2is preferred to less,but unless the bundles have thesame amount good 1,then the bundle with more good 1is always preferred.Consider sequence 1,with no units of good 2and 1/n units of good 1,and sequence 2with no units of good 1,and1 1/n units of good2.For all finite n,sequence1is preferred to sequence1,but in the limit sequence1 yields zero unit of either good and sequence2yields1unit of good2and is therefore preferred.Lexicographic preferences are a famous example,but hardly amainstay of either theory or empirical work.MWG Definition1.B.2:A functionu:X is a utility function representing preference relation if for all x,y X, x y if and only if u x u y Proposition3.C.1:If the rational preference relation on L is continuous, then there is a continuous utility functionu x that represents .The proof in MWG requires monotonicity–a slight variant is toto take a probability measure on L that has positive density everywhere,and then letu x 1 prob y y x .By construction,if x y then u x u y and if u x u y then x y.Now we’ve gotten to a utility function and we know that it is continuous.MWG Definition3.B.4:The preference relation is convex if for every x X the upper contour sety Y:y x is convex,that is if y x and z x then y 1 z x for every 0,1 .MWG Definition3.B.5:The preference relation is strictly convex if for every x X if y x and z x andy z implies that y 1 z x for every 0,1 .Convex preferences imply that u . is quasi-concave,i.e.the sety L:u y u xis concave(equivalentlyu y 1 x Min u x ,u y for any x,y and all 0,1 .Strict convexity implies strictquasi-concavity.The utility maximization problem is to maximize u x subject to theconstraint p x 0.MWG Proposition3.D.1:If p 0and u . is continuous then the utility maximization problem has a solution. The proof relies on the fact that a continuous function always has a maximum on a compact set,so you just need to show that the budget set is closed and bounded,pact.Proposition3.D.2:Suppose that u . is a continuous utility functionrepresenting a locally non-satiated preference relation defined on the consumption set X L.Then the Walrasian demand correspondence has the following properties:(1)x p,w is homogeneous of degree zero in prices and wealth,i.e.x p,w x p, w for every 0(2)Walras’law p x p,w w(3)If is convex so that u . isquasi-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.In practice,we write down a Langrangianmax x, U x1,x2,...x Lwi 1Lp i xiwhich yields us a system of first order conditions:U x1,x2,...x Lx ip iThese are L equations and we have L 1 unknowns,so we need to use the budget set as well to solve the problem.An application:fertility decisions.Many empirical puzzles:(1)Why does fertility drop with income so substantially across countries?(2)Why is fertility below replacement in all of Europe,but not in the U.S.?How would we capture this:Begin with U C,N –utility over consumption and kids.Assume that kids have both a cash cost(k),and a time cost(t)Assume that you have a time budget that can either be used producing kids or making money.Write down the total budget constraintWT Y C k tW NSolving C from the budget set the agent’s maximization problem reduces toU WT Y k tW N,NmaxNWhich in turn produces a F.O.C.k tW U1 WT Y k tW N,NU2 WT Y k tW N,N 0 where U1is the partial w.r.t.the1st argumentof U and similarly for U2.The marginal utility of another kid is weighed off against the marginal cost in terms of time and money.Comparative statics can be derived by (1)Using the implicit function theorem to define N Z ,where Z is a vectorrepresenting all of the parameters in this equation(i.e.,Z t,T,Y,W,k )and(2)Totally differentiating the F.O.C.to findNZ.LetF N,Z k tW U1 WT Y k tW N,NU2 WT Y k tW N,Nso that the F.O.C is F N Z ,Z 0.Differentiation w.r.t parameter Z then gives us:F1 N Z ,Z NZF2 N Z ,Z 0 from whichN Z F2 NZ ,ZF1 N Z ,Z.In this caseF1 N ,Z k tW 2U11 C ,N U22 C ,NU22 C ,N 2 k tW U12 C ,N and C WT Y k tW N .We generally assume that terms likeF1 N Z ,Z are negative(Why?)so thesign of Ndepends entirely on the sign ofZF2 N ,Z F N ,Z.ZIn the case of Z Y for example:Y k tW U1 WT Y k tW N ,N U2 WT Y k tW N ,Nk tW U11 WT Y k tW N ,N U12 WT Y k tW N ,NWhat can we say about this?Does this give us any intuition about anything?In the case of W:W k tW U1 WT Y k tW N ,N U2 WT Y k tW N ,Nk tW T tN U11 WT Y k tW N ,N T tN U12 WT Y k tW N ,NtU1 WT Y k tW N ,NIt’s the same as the unearned incomeeffect expect for the third term.What doesthat third term represent?Now let’s get a little more fancy and assume that parents care about both quantity and quantity,i.e.U C,Q,N .For simplicity assume utility is a separableand quasi-linear in consumption,soU C,Q,N C V Q,Z Q W N,Z N . Assume children cost WtQN.Then the first order conditions are:V Q,Z QWtNQandW N,Z NWtQNIf a parameter increases the marginal return to quality–this will have the following effect2V Q,Z QQ2 QZ Q2V Q,Z QQ Z QWt NZ Qand2W N,Z NN2 NZ QWt QZ Qor QZ Q2V Q,Z QQ Z Q2V Q,ZQQ2Wt 22W N,Z NN2and NZ Q2V Q,Z QQ Z Q2V Q,ZQQ22W N,Z NN2Wt 2How can we sign these two things?Each equation also tells you that the price per child rises as the quality of each child increases,and the price of quality rises as the number of children rises.Through the budget set there is an inherent substitutability between quantity and quality of children.。

武汉大学2003攻读硕士学位研究生入学考试试题考试科目:现代经济理论(含宏、微观经济学) 科目代码：４６１1. (25’) Consider an economic model in which the production function can be written as 10 1≤+=−ββa g L K Y a a p , here g is the government spending per capita, K, L, Y are aggregate capital, population and output respectively. The government spending is financed by an income tax, i.e., Y Lg G τ==. Capital accumulation equation is K sY K δ−=. Suppose the saving rate s ,income tax rate τ,depreciation rate δand population growth rate n are given exogenously, S+τ＜1.(1)Show that if 1p βα+, then the capital stock per capita will convergesto a steady-state value k * which is positively correlated with income tax rate τ.(2)Show that if 1=+βα, then the capital stock per capital will increase with a constant growth rate if δτ+n s f .2. (25’) Consider an economy with identical long-lived individuals whose utility functions can be written as 10 0, ,]lnk lnc [t t 0p p f βγγβdt e t +∫−∞, her c t ,k t are consumption and capital stock per capita in time t. Suppose the population growth rate is zero. The capital accumulation equation is 1a 0 ,p p k c Ak k a δ−−=.Solve the steady state values of consumption, capital stock and output per capita.3. (25’) Consider an OLG model in which each individual can live two period. Individuals’ utility function can be written as 12t 1t lnc lnc ++=βt U , here c 1t and c 2t+1 are the consumptions in period t of young and old individuals respectively. Individual’s wealth constraints are,1t t t w s c =+ )1(112+++=t t t r s cHere w t , s t and r t+1 are wage, saving and interest rate respectively. Production function can be written as at t Ak y =. Suppose that the depreciation rate δ＝1 and population growth rate are zero. Assumption the government levies an output tax with a constant tax rate τ.(1) Solve the steady state values of capital stock and output per capita.(2) Show that the relationship between the tax income of the government and tax rate can be described as a Laffer Curve, i.e., as the tax rate increase, the tax income increases when the tax rate is small and decreases when it is large enough. Solve the tax rate with the maximum tax income.4. (25’) If preferences are locally nonsatiated, and if (x *,y *,p )is anequilibrium with transfers, then the allocation(x *,y *)is Pareto optimal.5. (25’) If preference i ≥ is homothetic, assume that x i (p,w i ) is differentiable, then x i (p,w i ) satisfies the uncompensated law of demand property.6. (25’) Suppose that production set Y is convex. Then every efficient production Y y ∈is a profit-maximizing production for some nonzero price vector 0≥p .答案部分武汉大学2003攻读硕士学位研究生入学考试试题考试科目:现代经济理论(含宏、微观经济学) 科目代码：４６１1. Consider an economic model in which the production function can be written as 10 1≤+=−ββa g L K Y a a p , here g is the government spending per capita, K, L, Y are aggregate capital, population and output respectively. The government spending is financed by an income tax, i.e., Y Lg G τ==. Capital accumulation equation is K sY K δ−=. Suppose the saving rate s ,income tax rate τ,depreciation rate δand population growth rate n are given exogenously, S+τ＜1.(1) Show that if 1p βα+, then the capital stock per capita will convergesto a steady-state value k * which is positively correlated with income tax rate τ.(2)Show that if 1=+βα,then the capital stock per capital will increase with a constant growth rate if δτ+n s f .2. Consider an economy with identical long-lived individuals whose utility functions can be written as 10 0, ,]lnk lnc [t t 0p p f βγγβdt e t +∫−∞, her c t , k t areconsumption and capital stock per capita in time t. Suppose the population growth rate is zero. The capital accumulation equation is 1a 0 ,p p k c Ak k a δ−−=.Solve the steady state values of consumption, capital stock and output per capita.3. Consider an OLG model in which each individual can live two period. Individuals’ utility function can be written as 12t 1t lnc lnc ++=βt U , here c 1t and c 2t+1 are the consumptions in period t of young and old individuals respectively. Individual’s wealth constraints are,1t t t w s c =+ )1(112+++=t t t r s cHere w t , s t and r t+1 are wage, saving and interest rate respectively. Production function can be written as a t t Ak y =. Suppose that the depreciation rate δ＝1 and population growth rate are zero. Assumption the government levies an output tax with a constant tax rate τ.(1) Solve the steady state values of capital stock and output per capita.(2) Show that the relationship between the tax income of the government and tax rate can be described as a Laffer Curve, i.e., as the tax rate increase, the tax income increases when the tax rate is small and decreases when it is large enough. Solve the tax rate with the maximum tax income.4. If preferences are locally nonsatiated, and if (x *,y *,p )isan equilibrium with transfers, then the allocation(x *,y *)is Pareto optimal.5. If preference i ≥ is homothetic, assume that x i (p,w i ) is differentiable, then x i (p,w i ) satisfies the uncompensated law of demand property.6. Suppose that production set Y is convex. Then every efficient production Y y ∈is a profit-maximizing production for some nonzero price vector 0≥p .。

Department of Economics Professor Kenneth Train University of California, Berkeley Spring 2003ECONOMICS 1FINAL EXAMINATIONMay 16, 5-8pmINSTRUCTIONS1. Please fill in the information below:Your Name:Your SID#:GSI’s Name:Section Days/Time:2. There are a total of 180 points, 8 questions, and 11 pages (including this cover sheet). The suggested times to spend oneach question are in parentheses.3. Answer the questions in the space provided. (NO BLUE BOOKS.) If you need extra room to answer questions, use thebacks of the pages.4. Calculators are not permitted.5. You may leave early if you finish prior to 7:45. So that the end of the exam is orderly, please do not leave between 7:45and 8pm.6. When time is called, stop writing immediately and pass your exam to your right.HAVE A GOOD SUMMER! J>>> D O NOT TURN THE PAGE UNTIL YOU ARE TOLD TO BEGIN THE EXAM. <<<QUUESTION 1: 40 Total Points (40 Minutes)True, False, or Uncertain For each of the following decide whether the statement is true, false, or uncertain and explain why. Your explanation determines the grade; you will be given no credit for an answer without an explanation. Use diagrams where they are appropriate to complement your answer.a) [8 points] A competitive market maximizes social welfare because in a competitive market profits are zero.b) [8 points] The socially optimal level of pollution is zero.c) [8 points] An additional dollar of tax reduction has the same effect on the economy as an additional dollar of governmentexpenditure.QUESTION 1 (Continued)d) [8 points] When OPEC triples the price of oil used by American producers, it causes aggregate output and prices to rise.e) [8 points] The aggregate demand curve for the economy is derived by aggregating market demand curves across allmarkets.Consider an island economy with only two persons, Alex and Ben, and only two goods, fish and coconuts. Alex could catch 6 fish per hour or collect 12 coconuts per hour, and Ben could catch 4 fish per hour or collect 2 coconuts per hour. These rates are the same no matter how much time they spend in each activity. Each person works 10 hours each day.a) [3 points] What is the opportunity cost of fish for Alex?b) [7 points] Draw the production possibility frontier for this island economy. Be sure to label the axes, and show the unitson the axes.c) [10 points] Now suppose that a third person, Maria, enters the island economy. She could catch 5 fish per hour or 5coconuts per hour. She also works 10 hours each day. Draw the new PPF for this three-person economy1010 20 MC ACD $20Q MR 2 4 6 812 14 18 16 12 86 4214 16 18Berkeley Waste Management (BWM) has a monopoly on the garbage pickup market in Berkeley. BWM’s costs are shown below.a) [6 points] Given the costs of BWM and the demand curve as in the graph above, explain the most likely reason that BWM has a monopoly.b) [5 points] What are the profit maximizing level of output and price? Calculate profits and deadweight loss. Show yourwork.c) [6 points] The government decides to regulate BWM by inquiring them to produce at the socially optimal level of output.What are the firm’s output, price, and profits and inefficiency (i.e., deadweight loss) under this regulation? Show your work.d) [8 points] Suppose instead of forcing BWM to produce at the socially optimal level, the government decided to regulatethe monopoly by placing a business tax of $200 on the land owned by BWM. When entry/exit is not allowed, will trash pickup consumers prefer this policy over the policy proposed in part c)? Use consumer surplus and efficiency (deadweight loss) as criteria for making your judgment.Consider an oligopoly consisting of two firms. The table below depicts each firm’s profits, depending on what price both firms charge. Firm B chooses: Firm A chooses:a) [5 points] Find (if any) each firm’s dominant strategy.b) [5 points] Which strategy does each firm choose in equilibrium when no collusion is allowed?c) [5 points] Suppose that collusion is allowed between the two firms. Could these firms benefit from collusion? Why orwhy not?QUESTION 5: 15 Total Points (15 Minutes) The demand and supply schedule for coffee are:Price ($ per cup)Qd Qs 1.50 90 30 1.75 70 40 2.00 50 50 2.25 30 60 2.751070a) [3 points] If there is no tax on coffee, what is the price and how much coffee is consumed?b) [6 points] If a tax of 75 cents a cup is imposed, what is the price and how much coffee is consumed?c) [6 points] How much of the tax is paid by consumers? How much of the tax is paid by sellers? Low High Low Firm A earns $18 Mill. Firm B earns $18 Mill. Firm A earns $20 Mill. Firm B earns $23 Mill. High Firm A earns $23 Mill. Firm B earns $4 Mill. Firm A earns $16 Mill. Firm B earns $16 Mill.The Korean economy, a small and open economy, is in quite a slump these days. Its president, Moo Hyun Roh, has decided to use either monetary or fiscal policy to revive economic activity. Suppose the following model provides a good description of this economy:C = 0.9 (Y – T)T = 100I = 100G = 100EX = 20IM = 20 + 0.1Ywhere C is consumption, Y is aggregate output, T is tax, G is government expenditure, I is planned investment, EX is exports, and IM is imports. Suppose that prices, interest rates and exchange rates are fixed. (Since these variables are fixed, you can ignore the “feedback effects” to answer the following questions.)a) [4 points] Find the equilibrium values of output, consumption, imports, and the trade deficit (or surplus). Show yourwork.b) [4 points] Increase G by 100 to observe the effects of fiscal policy. What is the G multiplier? What is the newequilibrium output? Show your work.c) [4 points] What is the G multiplier if there were no exports and imports? Is it greater or smaller than the multiplier youfound in part b)? Explain.Now assume that prices, interest rate, and exchange rates are no longer fixed. In reality, the Korean economy is little bit more complicated than the equations given above. For the following questions, consider the usual relationships among different variables that we discussed in class.d) [7 points] As a result of the fiscal policy in part b),• Does Korean Won appreciate or depreciate?• Does the balance of trade improve or worsen?• Does the price level increase or decrease?Answer using graphs and explain in words.e) [7 points] Now suppose that the money supply increases by 40, without a change in G. Answer the following questionsusing graphs and explain in words.• Does the equilibrium output increase or decrease?• Does Korean Won appreciate or depreciate?• Does the balance of trade improve or worsen?• Does the price level increase or decrease?f) [4 points] Suppose that Mr. Roh wants to choose a policy that can enhance the long term growth of the Korean economy.If you were an economist making a recommendation to Mr. Roh, which policy would you recom mend? Explain.QUESTION 7: 20 Total Points (20 Minutes)Consider two countries, Japan and U.S., producing two goods, cell phones and computers. Suppose that there are 10 workers in each country. The table below depicts how many goods can be produced by a worker per day in each country.Output per workerJapan U.S.Cell phones 1 2Computers 6 6a) [2 points] Which country (if any) has the absolute advantage in producing cell phones?b) [2 points] Which country (if any) has the absolute advantage in producing computers?c) [3 points] Which country (if any) has the comparative advantage in producing cell phones?d) [3 points] Which country (if any) has the comparative advantage in producing computers?e) [5 points] If the terms of trade are one cell phone for one computer, can trade benefit both countries? Why or why not?f) [5 points] Describe the range of terms of trade (i.e., relative prices) at which both countries would want to specialize (i.e.,produce only one good) and trade. Explain your answer.Page 11 of 11 QUESTION 8: 15 Total Points (15 Minutes)Using AS-AD curves to illustrate your point, discuss the impact of the following events on the equilibrium price level and output:a) [5 points] In an effort to fight inflation, the fed decides to implement contractionary monetary policy.b) [5 points] After some period of time inflation is finally under control but the country is still in recession. The Congresspasses a tax cut with no corresponding change in government spending.c) [5 points] Due to the outbreak of Severe Acute Respiratory Syndrome (SARS) in Asia, shipments of input products fromAsia to the U.S. have decreased significantly.。

2003年首都经济贸易大学经济学考研真题及详解一、名词解释1．边际产品价值（VMP）答：边际产品价值（VMP）指在完全竞争条件下，厂商在生产中增加某种生产要素一个单位的投入所增加的产品的价值，等于边际物质产品（MP）与价格（P）的乘积，即：VMP＝MP·P。

因为存在边际收益递减规律，随着这种可变要素投入量的增多，其边际产品递减，从而边际产品价值也逐渐下降，所以边际产品价值曲线为一条自左上方向右下方倾斜的曲线。

在完全竞争条件下，边际产品价值曲线（VMP）与边际收益产品曲线（MRP）互相重合，该生产要素的边际收益产品曲线，同时就是其边际产品价值曲线，从而也就是完全竞争条件下厂商对该生产要素的需求曲线。

在不完全竞争市场上，MR、AR、P 三者不全相等，厂商必须降低商品价格才能出售更多的产品，因此边际收益产品必然小于边际产品价值。

VMP、MRP 两条曲线不再重合，此时仅有厂商的边际收益产品曲线代表了对该种生产要素的需求曲线。

2．帕累托标准答：帕累托标准也称为帕累托最优状态，是指在一个经济体中，资源的任何一种重新配置，已经不可能在其他人的效用水平不下降或福利不减少的情况下使任何一个人的效用水平或福利水平提高的状态。

换言之，社会已达到这样一种情况，即任何变革都不可能使任何人的福利有所增加，而不使其他人的福利减少。

3．投资乘数答：投资乘数指收入的变化与带来这种变化的投资变化量的比率。

投资乘数的大小与居民边际消费倾向有关：居民边际消费倾向越高，投资乘数则越大；居民边际储蓄倾向越高，投资乘数则越小。

即k i＝ΔY/ΔI＝1/（1－b）或k i＝1/（1－MPC）＝1/MPS。

式中，ΔY 是增加的收入，ΔI 是增加的投资，MPC 或b 是边际消费倾向，MPS 是边际储蓄倾向。

投资增加会引起收入多倍增加，投资减少会引起收入成比例减少。

由于这是凯恩斯最早提出来的，所以又称之为“凯恩斯乘数”。

投资乘数发挥作用的前提假设是：①社会中存在闲置资源；②投资和储蓄的决定相互独立；③货币供应量的增加适应支出增加的需要。

对外经济贸易大学2003年攻读硕士学位研究生入学考试（金融学院）金融学：专业基础课（试题代码：471）所有答题（包括英语的判断题和选择题）均做在答卷纸上，并在每题答案前标明各级题号。

答在本试题卷上无效。

本试卷共4页。

一、True-False Questions (1×15=15 points. Please write “T” for true statements or “F” forfales statements following every question number on your answer sheet)1.International investment position is a concept of stocks.n currency market does not belong to European currency market.3.Tariff is of expenditure shifting policies, but monetary policy is just one of expenditure switching policies.4.Yankee bond is a kind of Eurobonds.5.Foreign exchange control is mainly aimed at residents.6.The theoretical foundation of commodity arbitrage is the Law of One Price, so is that of interest arbitrage.7.The meaning of foreign exchange at premium or discount in direct quotation system is just the opposite of that in indirect quotation system.8.Monetary Approach to exchange rate determination is actually another version of Purchasing Power Parity Theory.9.Interest Parity Theory is about determination of short-run exchange rate.10.Buying in the international gold market will increase international reserves.11.Free floating of exchange rate leads to a huge drain on foreign exchange reserves.12.Devaluating native currency may improve on trade account balance.13.In buyer’s credit, payment at sight is required.14.Bretton Woods System can be regarded as an exchange rate system of gold exchange standard.15.Reverse position in IMF is included in general drawing rights.答案：1T 2F 3F 4F 5F 6t 7F 8F 9 T 10F 11F 12F 13F 14F 15F二、Single or Multiple-Choice Questions(2×10=20 points. In each question, at least oneanswer in true. If your choices are right but fewer than the standard, you will still get fewer points. Please write the letters of your choice following every question number on your answer sheet)1.Meade’s conflict will take place in conditions ofa. unemployment and deficit in the balance of paymentsb. unemployment and surplus in the balance of paymentsc. inflation and deficit in the balance of paymentsd. inflation and surplus in the balance of payments2.Which of the following organizations are included in the world bank group?a. International Bank for Reconstruction and Developmentb. International Development Associationc. International Finance Companyd. Bank for International settlements3.Assume that annual interest rate of Great British pound is 21% and that of US dollar is 9%, then according to Interest Parity Theory Great British pound relative to US dollar in 3 monthsforward exchange market will be devaluated bya. 30%b. 12%c. 10%d. 7.5%e. 4%f. 3%4.Bretton Woods System is the result ofa. White Planb. Keynes Planc. Brady Pland. Marshall Plan5.Currencies determining value of SDRs after 1999 includea. Swiss Francb.United State Dollarc. French Francd. Deutsche Marke. Italian Liraf. Great British Poundg. Japanese Yenh. Euro6.According to Balance of Payment Theory of Exchange Rate , which of the following factors will lead to devaluation of native of native currency?a. domestic interest rate level upb. foreign GNP increasedc. native GNP increasedd. domestic price level up7.Eurodollat meansa. US dollar in Europeb. US dollar outside USAc. a general term of US dollars in the whole worldd. US dollar reserve8.In general, a letter of credit isa. irrevocableb. confirmedc. unconfirmedd. transferablee. nontransferable9.In Absorption Approach to the balance of payments , the direct influence of devaluation on absorption includesa. cash balances effectb. terms-of-trade effectc. income redistribution effectd. monetary illusion effecte. idle resources effect10. When economy is in conditions of inflation and deficit in the balance of payments, which of policy mixes should be practiced by Mundell Assignment Rule?a. decreasing fiscal expenditure and raising interest rateb. increasing fiscal expenditure and reducing interest ratec. increasing fiscal expenditure and raising interest rated. decreasing fiscal expenditure and reducing interest rate答案：1ad 2abc 3f 4ab 5cde 6cd 7b 8 9acd 10ac三、简答题（每小题4分，共36分）1.什么是边际效用递减规律？答：（1）基数效用论者的两个基本概念就是总效用和边际效用。

北京市考研经济学复习资料发展经济学重要模型解析北京市考研经济学复习资料——发展经济学重要模型解析经济学作为一门重要的社会科学，研究的是如何有效分配有限资源满足人类无限的需求。

发展经济学作为经济学中的一支重要分支，主要关注的是如何实现经济的增长、减少贫困、提高社会福利等方面的问题。

在北京市考研经济学复习资料中，发展经济学的重要模型是学习的重点之一。

本文将对几个重要的发展经济学模型进行解析。

一、哈罗德-多马模型哈罗德-多马(Harrod-Domar)模型是描述投资和经济增长关系的经济模型，也被称为投资等于储蓄模型。

该模型基于一个简化的国民收入模型，认为经济增长主要依赖于实际投资和储蓄之间的关系。

哈罗德-多马模型的核心思想是，投资决定了经济增长速度，而储蓄决定了投资水平。

二、索洛模型索洛(Solow)模型是描述经济增长过程的模型，也被称为新古典增长模型。

该模型基于一系列假设，包括技术进步、人口增长和储蓄率等因素对经济增长的影响。

索洛模型的核心思想是，人口增长和技术进步是经济增长的主要驱动力，而储蓄投资是经济增长的基础。

三、劳伦斯曲线模型劳伦斯(Laffer)曲线模型是描述税收与经济增长之间关系的模型，也被称为税收弯曲理论。

该模型基于税收对经济活动的影响，认为税收率对税收收入的影响存在一个临界点，即超过临界点后，增加税收率反而会降低税收收入。

劳伦斯曲线模型的核心思想是，合理的税收政策可以激励经济发展，但过高的税收率可能导致经济活动的减少。

四、大卫-罗默模型大卫-罗默(David Romer)模型是描述技术进步与经济增长之间关系的模型，也被称为新增长理论。

该模型基于技术进步对经济增长的重要性，强调技术创新和知识的积累对经济发展的影响。

大卫-罗默模型的核心思想是，通过增加知识和创新投资，可以促进经济增长和社会福利的提高。

以上是北京市考研经济学复习资料中的发展经济学重要模型解析。

通过对这些模型的学习和理解，可以帮助我们更好地把握和分析经济发展的规律，为解决现实经济问题提供理论指导。

贸易对产业内重新配置和产业总生产率的影响（The Impact of Trade On Intra-industry Reallocations and Aggregate Industry Productivity）Melitz, Marc(2003)，Econometrica; Nov 2003; 71, 6浙江财经大学经济与国际贸易学院茹玉骢翻译\推导并注释摘要：本文发展了一个异质性产业动态模型，分析国际贸易的产业内作用。

模型显示如何开展贸易，会导致更有生产率的企业进入出口市场（同时，一些生产率比较低的企业只在国内市场进行生产），并同时迫使最没有生产率的企业退出市场。

它还表明产业的贸易开放会导致向更有生产率企业的公司之间额外的重新配置。

文章也表明，通过重新配置所导致的产业总生产率的提高带来了福利的改进，从而揭示了以前从未探讨的贸易益处。

本文把Hopenhayn（1992）的动态产业模型结合垄断竞争，在一般均衡中加以讨论。

因此，文章结合生产率的差异，拓展了Krugman1980的贸易模型。

不同生产率的企业共存于一个产业是因为，每个企业在做不可逆转投资进入该产业之前，面临不确的初始生产率。

进入出口市场也是颇费成本，但企业仅在获得其生产率知识后做出出口决定。

1、引言最近的经验研究表明企业之间的生产率存在持续性的差异，另外一些研究也表明生产率高的企业通常会倾向于出口。

文章发展了一个异质性动态产业模型，用来分析国际贸易所祈祷了产业内企业之间配置催化剂作用。

模型重复了许多与贸易相关的微观研究，它显示贸易如何导致那些生产率更高的企业出口，而同时迫使生产率最低的企业退出。

效率最低企业的退出和更有效率企业获得额外出口销售，使得市场份额更趋向于生产率更高的企业，并导致总生产率的提高。

利润也分配给更有生产率的企业。

模型和许多经验研究相吻合，如Bernard and Jensen(1999a)(对美国), Aw, Chung and Roberts(2000)(对台湾),Clerides, Lack and Tybout(1998)（对哥伦比亚、墨西哥和摩洛哥）都, 发现了更有效率企业选择出口市场的证据。