中级微观经济学模拟试题(4) 一、True or false(2 points*10), 1.In a model with two consumers,two goods,and no production,the contract curve must be a line going from one consumer's origin to the other consumer's origin. 2.If some firm in an industry has the production function F (x ;y)= x3/4y3/4,,where x and y are the only two inputs in producing the good,then that industry can not be competitive in the long run. 3.Price equals marginal cost is a sufficient condition for profit maximization. 4.If the supply is perfectly elastic,then an upward shift of the demand curve will lead to a higher price and quantity in equilibrium. 5.If a consumer can borrow and lend at the same interest rate,then he can exactly afford a consumption plan if the present value of his consumption equals the present value of his income. 6.The Hicks version of the substitution effect of a price change measures the change in a consumer's demand if the consumer's income were changed just enough so the consumer would remain on the same indifference curve as before the price change. 7.The Hicks version of the substitution effect of a price change measures the change in a consumer's demand if the consumer's income were changed just enough so the consumer would remain on the same indifference curve as before the price change. 8.A natural monopoly occurs when a firm gains ownership of the entire stock of some natural resource and thus is able to exclude other producers. 9.Partial equilibrium analysis concerns only supply or only demand while general equilibrium analysis deals with supply and demand at the same time. 10.A game has two players and each has two strategies.The strategies are Be Nice and Be Mean.If both players play Be Nice,both get a payo of 5.If both players play Be Mean,both get a payoff of-3.If one player plays Be Nice and the other plays Be Mean,the player who played Be Nice gets 0 and the player who played Be Mean gets 10.Playing Be Mean is a dominant strategy for both players. Fill in the blanks for the following questions (2points*10):
中级微观经济学模拟试题（4） 一、True or false（2points*10）. 1.In a model with two consumers, two goods, and no production, the contract curve must be a line going from one consumer's origin to the other consumer's origin. 2.If some firm in an industry has the production function F (x ;y) = x3/4y3/4, ,where x and y are the only two inputs in producing the good, then that industry can not be competitive in the long run. 3.Price equals marginal cost is a sufficient condition for profit maximization. 4.If the supply is perfectly elastic, then an upward shift of the demand curve will lead to a higher price and quantity in equilibrium. 5.If a consumer can borrow and lend at the same interest rate, then he can exactly afford a consumption plan if the present value of his consumption equals the present value of his income. 6.The Hicks version of the substitution effect of a price change measures the change in a consumer's demand if the consumer's income were changed just enough so the consumer would remain on the same indifference curve as before the price change. 7.The Hicks version of the substitution effect of a price change measures the change in a consumer's demand if the consumer's income were changed just enough so the consumer would remain on the same indifference curve as before the price change. 8.A natural monopoly occurs when a firm gains ownership of the entire stock of some natural resource and thus is able to exclude other producers. 9.Partial equilibrium analysis concerns only supply or only demand while general equilibrium analysis deals with supply and demand at the same time. 10.A game has two players and each has two strategies. The strategies are Be Nice and Be Mean. If both players play Be Nice, both get a payo of 5. If both players play Be Mean, both get a payoff of -3. If one player plays Be Nice and the other plays Be Mean, the player who played Be Nice gets 0 and the player who played Be Mean gets 10. Playing Be Mean is a dominant strategy for both players. 二、Fill in the blanks for the following questions（2points*10）:
11.Tim has preferences represented by the utility function:.If x is on the horizontal axis and y is on the vertical axis,what is the slope of his indifference curve at the point (8;9)? 12.If the demand function for tickets to a play is at what price will total revenue be maximized? 13.A firm has the production function.The slope of the firm's isoquant at the point (x,y)=(80,10)is 14.Wobble's Weebles is the only producer of weebles.It makes weebles at constant marginal cost c (where c >0)and sells them at a price of per weeble in Market 1 and at a price of per weeble in Market 2.The demand curve for weebles in Market 1 has a constant price elasticity of demand equal to-2.The demand curve for weebles in Market 2 has constant price elasticity equal to The ratio of the profit maximizing price in Market 1 to the profit maximizing price in Market 2 is 15.On a certain island there are only two goods,wheat and milk.The only scarce resource is land.There are 1000 acres of land.An acre of land will produce either 16 units of milk or 31 units of wheat.Some citizens have lots of land;some have just a little bit.The citizens of the island all have utility functions of the form. At every Pareto optimal allocation,every consumer's marginal rate of substitution between milk and wheat is 三、Calculation(25 points) 1.Show by calculus at what point is a optimal choice of consumption.(10 points) 2.In the case of intertemporal choice when interest rate of lending (bank deposits)exceeds that of borrowing (bank loan),show that a well-behaved consumer will never choose to consume exactly all his/her income in every period.(10 points) 四、Graphing and Analysis(35 points) 1.Given TM=f (Q)in Fig.1,draw corresponding AM and MM in Fig.2.(10 points)
11.Tim has preferences represented by the utility function: .If x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point (8; 9)? _______________ 12.If the demand function for tickets to a play is ; at what price will total revenue be maximized?____________________ 13.A firm has the production function . The slope of the firm's isoquant at the point (x, y) = (80,10) is ____________________. 14.Wobble's Weebles is the only producer of weebles. It makes weebles at constant marginal cost c (where c > 0) and sells them at a price of per weeble in Market 1 and at a price of per weeble in Market 2. The demand curve for weebles in Market 1 has a constant price elasticity of demand equal to -2. The demand curve for weebles in Market 2 has constant price elasticity equal to . The ratio of the profit maximizing price in Market 1 to the profit maximizing price in Market 2 is _______________________. 15.On a certain island there are only two goods, wheat and milk. The only scarce resource is land. There are 1000 acres of land. An acre of land will produce either 16 units of milk or 31 units of wheat. Some citizens have lots of land; some have just a little bit. The citizens of the island all have utility functions of the form . At every Pareto optimal allocation, every consumer's marginal rate of substitution between milk and wheat is __________ 三、Calculation (25 points) 1. Show by calculus at what point is a optimal choice of consumption. (10 points) 2. In the case of intertemporal choice when interest rate of lending (bank deposits) exceeds that of borrowing (bank loan), show that a well-behaved consumer will never choose to consume exactly all his/her income in every period. (10 points) 四、Graphing and Analysis (35 points) 1.Given TM = f (Q) in Fig. 1, draw corresponding AM and MM in Fig. 2. (10 points)
TMe Fig.1 Q 2.Draw to show very clearly that if leisure is an inferior good,the slope of the individual labor supply curve must be positive.(10 points) 3.Harsanyi and Selten have identical utility functions U(x,y)=x2 y2,where x and y stand for the numbers of good 1 and good 2 respectively.There are totally 10 units of good 1 and 10 units of good 2 to be distributed among them. a.To start,draw an Edgeworth box with a pair of their indifference curves and mark all the Pareto efficient allocations in the box.(Hint:Notice that the indifference curves are concave in this case.)(10 points) b.Mark all allocations you think not only Pareto efficient but also fair in the box.(5 points)
2. Draw to show very clearly that if leisure is an inferior good, the slope of the individual labor supply curve must be positive. (10 points) 3. Harsanyi and Selten have identical utility functions U (x, y) = x2 + y2, where x and y stand for the numbers of good 1 and good 2 respectively. There are totally 10 units of good 1 and 10 units of good 2 to be distributed among them. a. To start, draw an Edgeworth box with a pair of their indifference curves and mark all the Pareto efficient allocations in the box. (Hint: Notice that the indifference curves are concave in this case.) (10 points) b. Mark all allocations you think not only Pareto efficient but also fair in the box. (5 points)