中级微观经济学模拟试题(3) 一、True or false.(2 points*:10) 1.Richard has utility function U(x,y)=x +2y.If the price of x is 1 and the price of y is 1/2;then Richard must consume equal amounts of both goods in order to maximize his utility. 2.A consumer's utility function is U(x1,x2)=min{x1,2x2}.If Good 2 has a price of zero,the consumer will always prefer more of Good 2 to less. 3.A consumer's utility function is U(x,y)=min{x,2y }If the price of good x is zero and the price of good y is p,then the consumer's demand function for good y is m/2p. 4.If a person is a net supplier of a normal good and its price increases while all other prices stay the same,then his demand for the good must decrease. 5.Market demand curve is simply the horizontal summation of individual demand curves. 6.The economist's distinction between long and short run captures the idea that quantities of some factor inputs can be varied in the short run but not in the long run. 7.A firm uses a single variable input x to produce outputs according to the production function f (x)=300x-5x2.This firm has fixed costs of $300.This firm's short run marginal cost curve lies below its short run average variable cost curve for all positive values of x. 8.Third degree price discrimination occurs when a monopolist sells output to different people at different prices,but every unit that an individual buys costs the same amount. 9.In the Bertrand model of duopoly,each firm sets its price,believing that the other's price will not change.When both firms have identical production functions and produce with constant returns to scale,the Bertrand equilibrium price is equal to marginal cost. 10.While game theory predicts non-cooperative behavior for a single play of
中级微观经济学模拟试题（3） 一、True or false.（2points*10） 1.Richard has utility function U(x,y) = x +2y. If the price of x is 1 and the price of y is 1/2; then Richard must consume equal amounts of both goods in order to maximize his utility. 2.A consumer’s utility function is U(x1, x2) = min{x1, 2x2}. If Good 2 has a price of zero, the consumer will always prefer more of Good 2 to less. 3.A consumer’s utility function is U(x ,y)=min{x ,2y }. If the price of good x is zero and the price of good y is p, then the consumer's demand function for good y is m/2p. 4.If a person is a net supplier of a normal good and its price increases while all other prices stay the same, then his demand for the good must decrease. 5.Market demand curve is simply the horizontal summation of individual demand curves. 6.The economist's distinction between long and short run captures the idea that quantities of some factor inputs can be varied in the short run but not in the long run. 7.A firm uses a single variable input x to produce outputs according to the production function f (x) = 300x-5x2.This firm has fixed costs of $300. This firm's short run marginal cost curve lies below its short run average variable cost curve for all positive values of x. 8.Third degree price discrimination occurs when a monopolist sells output to different people at different prices, but every unit that an individual buys costs the same amount. 9.In the Bertrand model of duopoly, each firm sets its price, believing that the other's price will not change. When both firms have identical production functions and produce with constant returns to scale, the Bertrand equilibrium price is equal to marginal cost. 10.While game theory predicts non-cooperative behavior for a single play of
prisoners'dilemma,it would predict cooperative tit-for-tat behavior if the same people play prisoners'dilemma together for,say,20 rounds. .Fill in the blanks for the following questions (2points*10): 11.Charlie's utility function is.If Charlie's income were 40,the price of apples were 3 and the price of bananas were 7,how many apples would there be in the best bundle that Charlie could afford? 12.In Problem 12.9,Billy has a von Neumann-Morgenstern utility function.If Billy is not injured this season,he will receive an income of 4 million dollars. If he is injured,his income will be only $10,000.The probability that he will be injured is 0.1 and the probability that he will not be injured is 0.9.His expected utility is_ 13.Suppose that Dent Carr's long run total cost of repairing s cars per week is.If the price he receives for repairing a car is 16,then in the long run,how many cars will he fix per week if he maximizes profits?_ 14.A situation where everyone is playing a dominant strategy must be a equilibrium. 15.A firm has the long run cost function.In the long run,it will supply a positive amount of output,so long as the price is greater than 三、Calculation(25 points) 1.A monopolist can sell outputs Q1 and Q2 in two markets that are effectively isolated from one another.His cost function is C=1988 29Q +Q2/40,where Q Q1 +Q2.The demand in the two markets are given by Q1 =480 -4 P1 and Q2 200 -2 P2 respectively. a.How much does he sell in each market?Compare the prices and the price elasticities of demand in the two markets;(10 points) b.If the markets are not separated any more and he must charge the same price in the two markets,what price does he charge?How much does he sell in each market? (10 points) c.Calculate the profit change from Case a)to Case b).(5 points) 四、Graphing and Analysis(35 points)
prisoners' dilemma, it would predict cooperative tit-for-tat behavior if the same people play prisoners' dilemma together for, say, 20 rounds. 二、Fill in the blanks for the following questions（2points*10）: 11.Charlie's utility function is . If Charlie's income were 40, the price of apples were 3 and the price of bananas were 7, how many apples would there be in the best bundle that Charlie could afford? _____________ 12.In Problem 12.9, Billy has a von Neumann-Morgenstern utility function . If Billy is not injured this season, he will receive an income of 4 million dollars. If he is injured, his income will be only $10,000. The probability that he will be injured is 0.1 and the probability that he will not be injured is 0.9. His expected utility is____________. 13.Suppose that Dent Carr's long run total cost of repairing s cars per week is .If the price he receives for repairing a car is 16, then in the long run, how many cars will he fix per week if he maximizes profits?________________ 14.A situation where everyone is playing a dominant strategy must be a ______________equilibrium. 15.A firm has the long run cost function . In the long run, it will supply a positive amount of output, so long as the price is greater than_____________. 三、Calculation (25 points) 1. A monopolist can sell outputs Q1 and Q2 in two markets that are effectively isolated from one another. His cost function is C = 1988 + 29Q + Q2 / 40, where Q = Q1 + Q2 . The demand in the two markets are given by Q1 = 480 - 4 P1 and Q2 = 200 - 2 P2 respectively. a. How much does he sell in each market? Compare the prices and the price elasticities of demand in the two markets; (10 points) b. If the markets are not separated any more and he must charge the same price in the two markets, what price does he charge? How much does he sell in each market? ( 10 points) c. Calculate the profit change from Case a) to Case b). (5 points) 四、Graphing and Analysis (35 points)
1.Following the analysis of the former question,graph to show: (1)Graph to show roughly your solution to Case a)if instead C=1988 +Q2/ 10;(10 points) (2)By the inner market we call the market with AR i curve south-west to the other market in (1).Suppose now the inner market imposes a crazy sales tax of 50% on purchases. Show graphically in the same diagram how the prices and the quantities would change.(5 points) (Hint:Graph the change of the corresponding demand curve first.) 2.The price of bread is strictly controlled.Loaves of bread cost $1 each at the government store.However,a consumer can purchase only 5 loaves at the government store,and any additional loaves cost $5 on the black market.The consumer has an income of $30 and purchases bread and one other good,X.The price of X is $1. A Draw the consumer's budget constraint.(5 points) B Suppose the market for bread is decontrolled,and the price is $2 a loaf. Draw the new budget constraint on the same diagram.(5 points) C On the diagram,show a consumer who prefers the new policy.(5 points) D On a new graph with both the old and the new budget constraints,show a consumer who is indifferent between the two policies.(5 points)
1. Following the analysis of the former question, graph to show: (1) Graph to show roughly your solution to Case a) if instead C = 1988 + Q2 / 10; (10 points) (2) By the inner market we call the market with AR i curve south-west to the other market in (1). Suppose now the inner market imposes a crazy sales tax of 50% on purchases. Show graphically in the same diagram how the prices and the quantities would change. (5 points) (Hint: Graph the change of the corresponding demand curve first.) 2. The price of bread is strictly controlled. Loaves of bread cost $1 each at the government store. However, a consumer can purchase only 5 loaves at the government store, and any additional loaves cost $5 on the black market. The consumer has an income of $30 and purchases bread and one other good, X. The price of X is $1. A Draw the consumer's budget constraint. (5 points) B Suppose the market for bread is decontrolled, and the price is $2 a loaf. Draw the new budget constraint on the same diagram. (5 points) C On the diagram, show a consumer who prefers the new policy. (5 points) D On a new graph with both the old and the new budget constraints, show a consumer who is indifferent between the two policies. (5 points)