中级微观经济学模拟试题(8) 一、True or false(2 points*10), 1.The marginal cost curve passes through the minimum point of the average fixed cost curve 2.The area under the marginal cost curve measures total fixed costs. 3.In the Cournot model,each firm chooses its actions on the assumption that its rivals will react by changing their quantities in such a way as to maximize their own profits. 4.In a Nash equilibrium,everyone must be playing a dominant strategy. 5.In the prisoners'dilemma game,if each prisoner believed that the other prisoner would deny the crime,then both would deny the crime. 6.Hicks and Slutsky decomposition differs in the definition of "real income unchanged”. 7.Mark strictly prefers consumption bundle A to consumption bundle B and weakly prefers bundle B to bundle A.These preferences can be represented by a utility function. 8.If the interest rate at which you can borrow is higher than the interest rate at which you can lend,your budget for current and future consumption is still a convex set. 9.If a consumer does not have convex preferences,then a point of tangency between her indifference curve and her budget line must be an optimal consumption point. 10.A profit-maximizing monopolist practices third degree price discrimination. If he charges pl in market 1 and p2 in market 2,where pl>p2;then if the law forced him to charge the same price in both markets,more would be demanded in market 1 than in market 2. .Fill in the blanks for the following questions (2points*10): (1)The utility function U(X,x2)=2Inx+3lnx2 represents (Please fill the typical type of preference which is proper in the blank)
中级微观经济学模拟试题（8） 一、True or false（2points*10）. 1.The marginal cost curve passes through the minimum point of the average fixed cost curve. 2.The area under the marginal cost curve measures total fixed costs. 3.In the Cournot model, each firm chooses its actions on the assumption that its rivals will react by changing their quantities in such a way as to maximize their own profits. 4.In a Nash equilibrium, everyone must be playing a dominant strategy. 5.In the prisoners' dilemma game, if each prisoner believed that the other prisoner would deny the crime, then both would deny the crime. 6.Hicks and Slutsky decomposition differs in the definition of “real income unchanged”. 7.Mark strictly prefers consumption bundle A to consumption bundle B and weakly prefers bundle B to bundle A. These preferences can be represented by a utility function. 8.If the interest rate at which you can borrow is higher than the interest rate at which you can lend, your budget for current and future consumption is still a convex set. 9.If a consumer does not have convex preferences, then a point of tangency between her indifference curve and her budget line must be an optimal consumption point. 10.A profit-maximizing monopolist practices third degree price discrimination. If he charges p1 in market 1 and p2 in market 2, where p1> p2; then if the law forced him to charge the same price in both markets, more would be demanded in market 1 than in market 2. 二、Fill in the blanks for the following questions（2points*10）: (1)The utility function 1 2 1 2 U(x , x ) = 2ln x + 3ln x represents _______________ (Please fill the typical type of preference which is proper in the blank)
preferences. (2)Daisy received a tape recorder as a birthday gift and is not able to return it.Her utility function is U(x,y,z)=x+z2f(y)where z is the number of tapes she buys,y is the number of tape recorders she has and x is the amount of money she has left to spend.f(y)=0 If y 1 and f(y)=8 if y is 1 or greater.The price of tapes is 2 and she can easily afford to buy dozens of tapes.How many tapes will she buy? 23 (3)A firm has the production function f(x,y)=40x5y5.The slope of the firm's isoquant at the point (x,y)=(70,50)is (4)The Chrysler Belvedere Truck Plant is attempting to minimize production costs. Over one month,1,600 fenders are needed on the production line,which runs continuously.If it costs $200 to set up the stamping press to produce fenders,and $1 per month to store produced fenders,how many times should the stamping press be run per month? (5)In equilibrium,each player is making an optimal choice for herself,given the choices of the other players. 三、Calculation(25 points) 1.For a typical Cobb-Douglas production function with two inputs,x1 and x2, derive using calculus the conditional factor demand function of x1.(10 points) 2.N people play a game as follows:each of them contribute an arbitrary amount of money up to $100 to a machine,and then the machine triple the total collection and then distribute them equally to each player. a.Guess and verify a Nash equilibrium.(10 points) b.Is your finding the only Nash equilibrium or not?Is it Pareto efficient or not?(5 points) 四、Graphing and Analysis(35 points) 1.Graph to show the Hecscher-Ohlin model of international trade.Briefly explain the assumption lying in the model,and the change of relative price, production,and social welfare.(10 points)
preferences. (2)Daisy received a tape recorder as a birthday gift and is not able to return it. Her utility function is ( , , ) ( ) 2 1 U x y z = x + z f y where z is the number of tapes she buys, y is the number of tape recorders she has and x is the amount of money she has left to spend. f ( y) = 0 If y < 1 and f ( y) = 8 if y is 1 or greater. The price of tapes is 2 and she can easily afford to buy dozens of tapes. How many tapes will she buy? _____________ (3)A firm has the production function 5 3 5 2 f (x, y) = 40x y . The slope of the firm's isoquant at the point (x, y) = (70, 50) is ______________________. (4)The Chrysler Belvedere Truck Plant is attempting to minimize production costs. Over one month, 1,600 fenders are needed on the production line, which runs continuously. If it costs $200 to set up the stamping press to produce fenders, and $1 per month to store produced fenders, how many times should the stamping press be run per month?____________________ (5)In ___________ equilibrium, each player is making an optimal choice for herself, given the choices of the other players. 三、Calculation (25 points) 1.For a typical Cobb-Douglas production function with two inputs, x1 and x2, derive using calculus the conditional factor demand function of x1. (10 points) 2. N people play a game as follows: each of them contribute an arbitrary amount of money up to $100 to a machine, and then the machine triple the total collection and then distribute them equally to each player. a. Guess and verify a Nash equilibrium. (10 points) b. Is your finding the only Nash equilibrium or not? Is it Pareto efficient or not? (5 points) 四、Graphing and Analysis (35 points) 1. Graph to show the Hecscher-Ohlin model of international trade. Briefly explain the assumption lying in the model, and the change of relative price, production, and social welfare.(10 points)
2.Graph to show the income offer curve of a inferior good.Note that your graph should reflect the fact that no good is always inferior.(10 points) 3.Each year Sam grows 200 units of wheat and 100 units of sunflower seeds for his own consumption and for sale. a.If the price of wheat is $2 per unit and sunflower seeds sell for $10 per unit,Sam chooses to sell 20 units of the sunflower seeds.Graph to show Sam's utility-maximizing situation and indicate also his initial production levels.(5 points) b.Suppose somehow sunflower seeds price falls to also $2.Will Sam be made better-off or worse-off by this price decline?Or is the situation ambiguous?Show that if Sam is to be made better-off,he must become a seller of wheat and a buyer of sunflower seeds.(10 points)
2. Graph to show the income offer curve of a inferior good. Note that your graph should reflect the fact that no good is always inferior.(10 points) 3. Each year Sam grows 200 units of wheat and 100 units of sunflower seeds for his own consumption and for sale. a. If the price of wheat is $2 per unit and sunflower seeds sell for $10 per unit, Sam chooses to sell 20 units of the sunflower seeds. Graph to show Sam’s utility-maximizing situation and indicate also his initial production levels. (5 points) b. Suppose somehow sunflower seeds price falls to also $2. Will Sam be made better-off or worse-off by this price decline? Or is the situation ambiguous? Show that if Sam is to be made better-off, he must become a seller of wheat and a buyer of sunflower seeds. (10 points)