中级微观经济学模拟试题(5) 一、True or false(2 points*10), 1.There are two goods.You know how much of good 1 consumers can afford if she spends all of her income on good 1.If you know the ratio of the prices of the two goods,then you could draw the consumer's budget line without any more information. 2.Wanda Lott has the utility function U(x,y)=max{x,y),Wanda's preferences are convex. 3.In a two-good model,if two goods are bad and neutral respectively,a consumer may choose not to use all his money. 4.Angela's utility function is x yl/2.It is possible that if her income is very high,an increase in income will not make her spend more on y. 5.If a rational consumer must consume either zero or one unit of a good,then an increase in the price of that good with no change in income or in other prices can never lead to an increase in the consumer's demand for it. 6.The marginal product of a factor is just the derivative of the production function with respect to the amount of this factor,holding the amounts of other factor inputs constant. 7.The cost function C(y)=100+3y2has marginal cost less than average cost for all positive levels of output. 8.A competitive firm has a continuous marginal cost curve.It finds that as output increases,its marginal cost curve first rises,then falls,then rises again. If it wants to maximize profits,the firm should never produce at a positive output where price equals marginal cost and marginal cost decreases as output increases. 9.The possibility of more firms entering an industry in the long run tends to make long run industry supply more price elastic than short run industry supply. 10.If a game does not have an equilibrium in pure strategies,then it will not have an equilibrium in mixed strategies either. Fill in the blanks for the following questions (2points*10): (1)A person with the utility function U(x,y)=10+y+x has
中级微观经济学模拟试题（5） 一、True or false（2points*10）. 1.There are two goods. You know how much of good 1 consumers can afford if she spends all of her income on good 1. If you know the ratio of the prices of the two goods, then you could draw the consumer's budget line without any more information. 2.Wanda Lott has the utility function U(x, y) = max{x, y}, Wanda's preferences are convex. 3.In a two-good model, if two goods are bad and neutral respectively, a consumer may choose not to use all his money. 4.Angela's utility function is x + y1/2. It is possible that if her income is very high, an increase in income will not make her spend more on y. 5.If a rational consumer must consume either zero or one unit of a good, then an increase in the price of that good with no change in income or in other prices can never lead to an increase in the consumer's demand for it. 6.The marginal product of a factor is just the derivative of the production function with respect to the amount of this factor, holding the amounts of other factor inputs constant. 7.The cost function C(y)= 100 + 3y2has marginal cost less than average cost for all positive levels of output. 8.A competitive firm has a continuous marginal cost curve. It finds that as output increases, its marginal cost curve first rises, then falls, then rises again. If it wants to maximize profits, the firm should never produce at a positive output where price equals marginal cost and marginal cost decreases as output increases. 9.The possibility of more firms entering an industry in the long run tends to make long run industry supply more price elastic than short run industry supply. 10.If a game does not have an equilibrium in pure strategies, then it will not have an equilibrium in mixed strategies either. 二、Fill in the blanks for the following questions（2points*10）: (1)A person with the utility function U x y = + y + x 2 ( , ) 10 has ____________
(convex or concave)preferences. (2)Charlie's utility function is.The price of apples used to be $1,the price of bananas used to be $2,and his income used to be $40.If the price of apples increased to 5 and the price of bananas stayed constant,the substitution effect on Charlie's apple consumption reduces his consumption by (3)If someone has strictly convex preferences between all contingent commodity bundles,then he or she must be risk (averse or loving). (4)A firm has the production function =In the short run it must use exactly 20 units of factor 2.The price of factor 1 is $60 per unit and the price of factor 2 is $2 per unit.The firm's short run marginal cost function is (5)Suppose that in New Crankshaft,Pa the quality distribution of the 7,000 used cars on the market is such that the number of used cars of value less than V is Original owners must sell their used cars.Original owners know what their cars are worth,but buyers can't determine a car's quality until they it.An owner can either take his car to an appraiser or pay the appraiser $100 to appraise the car (accurately and credibly)or he can sell the car unapprised.In equilibrium,car owners will have their cars appraised if and only if their value is at least 三、Calculation(25 points) 1.Suppose in the market of some commodity,the supply curve is Q=P+20,the (inverse)demand is P =40-Q/3.Roughly graph and (accurately)calculate to a Determine the equilibrium.(5 points) b Determine the new equilibrium if an export demand P=60-Q is added.(7 points) c Determine the new equilibrium if instead a sale subsidy of 20 per unit is put into effect.(8 points) d Discuss the effects of a ceiling of 25 upon the price paid by the consumers for the cases A,B,and C.(5 points) 四、Graphing and Analysis(35 points)
(convex or concave) preferences. (2)Charlie's utility function is . The price of apples used to be $1, the price of bananas used to be $2, and his income used to be $40. If the price of apples increased to 5 and the price of bananas stayed constant, the substitution effect on Charlie's apple consumption reduces his consumption by ___________________. (3)If someone has strictly convex preferences between all contingent commodity bundles, then he or she must be risk _________(averse or loving). (4)A firm has the production function 2 1 2 Q = X1 X . In the short run it must use exactly 20 units of factor 2. The price of factor 1 is $60 per unit and the price of factor 2 is $2 per unit. The firm's short run marginal cost function is __________________. (5)Suppose that in New Crankshaft, Pa the quality distribution of the 7,000 used cars on the market is such that the number of used cars of value less than V is . Original owners must sell their used cars. Original owners know what their cars are worth, but buyers can't determine a car's quality until they it. An owner can either take his car to an appraiser or pay the appraiser $100 to appraise the car (accurately and credibly) or he can sell the car unapprised. In equilibrium, car owners will have their cars appraised if and only if their value is at least __________________. 三、Calculation (25 points) 1. Suppose in the market of some commodity, the supply curve is Q = P + 20, the (inverse) demand is P = 40 - Q / 3. Roughly graph and (accurately) calculate to a Determine the equilibrium.(5 points) b Determine the new equilibrium if an export demand P = 60 - Q is added. (7 points) c Determine the new equilibrium if instead a sale subsidy of 20 per unit is put into effect. (8 points) d Discuss the effects of a ceiling of 25 upon the price paid by the consumers for the cases A, B, and C. (5 points) 四、Graphing and Analysis (35 points)
1.Draw to show an inferior good in Fig.1.(10points) an ultra superior good Fig.1 an inferior good 2.In the two commodity case,derive the price offer curve and demand curve of a perfect complement.(10 points) 3.This is a puzzle-just for fun.Lewis Carroll (1832-1898),author of Alice in Wonderland.Through the Looking Glass,were a mathematician,logician,and political scientist?Carroll loved careful reasoning about puzzling things.Here Carroll's Alice presents a nice bit of economic analysis.At first glance,it may seem that Alice is talking nonsense,but,indeed,her reasoning is impeccable. "I should like to buy an egg,please.she said timidly."How do you sell them?” "Five pence farthing for one-two pence for two,the Sheep replied. "Then two are cheaper than one?"Alice said,taking out her purse. "Only you must eat them both if you buy two,said the Sheep. "Then I'1l have one please,"said Alice,as she put the money (a)Let us try to draw a budget set and indifference curves that are consistent with this story.Suppose that Alice has a total of 8 pence to spend and that she can buy 0,1,or 2 eggs from the Sheep,but no fractional eggs.Then her budget set consists of just three points.The point where she buys no eggs is (0,8).Plot this point and label it A.On your graph,the point where she buys 1 egg is (1,2,3). (A farthing is 1/4 of a penny.)Plot this point and label it B.(7 points) (b)The point where she buys 2 eggs is (2,6).Plot this point and label it C.If Alice chooses to buy 1 egg,she must like the bundle B better than either the
1. Draw to show an inferior good in Fig. 1.(10points) an ultra superior good 2. In the two commodity case, derive the price offer curve and demand curve of a perfect complement. (10 points) 3. This is a puzzle—just for fun. Lewis Carroll (1832-1898), author of Alice in Wonderland. Through the Looking Glass, were a mathematician, logician, and political scientist? Carroll loved careful reasoning about puzzling things. Here Carroll’s Alice presents a nice bit of economic analysis. At first glance, it may seem that Alice is talking nonsense, but, indeed, her reasoning is impeccable. “I should like to buy an egg, please.” she said timidly. “How do you sell them?” “Five pence farthing for one—two pence for two,” the Sheep replied. “Then two are cheaper than one?” Alice said, taking out her purse. “Only you must eat them both if you buy two,” said the Sheep. “Then I’ll have one please,” said Alice, as she put the money (a) Let us try to draw a budget set and indifference curves that are consistent with this story. Suppose that Alice has a total of 8 pence to spend and that she can buy 0, 1, or 2 eggs from the Sheep, but no fractional eggs. Then her budget set consists of just three points. The point where she buys no eggs is (0, 8). Plot this point and label it A. On your graph, the point where she buys 1 egg is (1, 2, 3). (A farthing is 1/4 of a penny.) Plot this point and label it B. (7 points) (b) The point where she buys 2 eggs is (2, 6). Plot this point and label it C. If Alice chooses to buy 1 egg, she must like the bundle B better than either the
bundle A or the bundle C.Draw indifference curves (8 points)
bundle A or the bundle C. Draw indifference curves (8 points)