中级微观经济学模拟试题（1) 一、True or false.(2 points*10) If Good 1 is on the horizontal axis and Good 2 is on the vertical axis,then an increase in the price of Good 1 will not change the horizontal intercept of the budget line. Henrietta's utility function is U(x1,x2)=x1x2.She has diminishing marginal rate of substitution between goods 1 and 2. Other things being equal,a lump sum tax is at least as good for a consumer as a sales tax that collects the same revenue from him. Sharon spends all of her income on peaches and strawberries.Peaches are a normal good for her.Her income increased by 20 percent and prices did not change.Her consumption of strawberries could not have increased by more than 20 percent. Beatrice has the utility function U(x,y)=min{x,y}.The price of x used to be 3,but rose to 4.The price of y remained at 1.Her income is 12.The price increase was as bad for her as a loss of $3 in income. Just as in the theory of utility maximizing consumers,the theory of profit maximizing firms allows the possibility of "Giffen factors".These are factors for which a fall in price leads to a fall in demand. If there are increasing returns to scale,then average costs are a decreasing function of output. Since a monopoly makes excess profits beyond the normal rate of return on investment,an investor is likely to get a higher rate of return in the stock market by investing in monopolistic rather than competitive industries. A Stackelberg leader will necessarily make at least as much profit as he would if he acted as a Cournot oligopolist. Dominant strategy equilibrium is a set of choices such that each player's choices are optimal regardless of what the other players choose. Fill in the blanks for the following questions:(2points*10) Your budget constraint for the two goods A and B is 12A+4B =I where I is your
中级微观经济学模拟试题（1） 一、True or false.（2points*10） If Good 1 is on the horizontal axis and Good 2 is on the vertical axis, then an increase in the price of Good 1 will not change the horizontal intercept of the budget line. Henrietta's utility function is U(x1, x2) = x1x2. She has diminishing marginal rate of substitution between goods 1 and 2. Other things being equal, a lump sum tax is at least as good for a consumer as a sales tax that collects the same revenue from him. Sharon spends all of her income on peaches and strawberries. Peaches are a normal good for her. Her income increased by 20 percent and prices did not change. Her consumption of strawberries could not have increased by more than 20 percent. Beatrice has the utility function U(x ,y)= min{x ,y}. The price of x used to be 3, but rose to 4. The price of y remained at 1. Her income is 12. The price increase was as bad for her as a loss of $3 in income. Just as in the theory of utility maximizing consumers, the theory of profit maximizing firms allows the possibility of "Giffen factors". These are factors for which a fall in price leads to a fall in demand. If there are increasing returns to scale, then average costs are a decreasing function of output. Since a monopoly makes excess profits beyond the normal rate of return on investment, an investor is likely to get a higher rate of return in the stock market by investing in monopolistic rather than competitive industries. A Stackelberg leader will necessarily make at least as much profit as he would if he acted as a Cournot oligopolist. Dominant strategy equilibrium is a set of choices such that each player's choices are optimal regardless of what the other players choose. 二、Fill in the blanks for the following questions:（2points*10） Your budget constraint for the two goods A and B is 12A+ 4B = I where I is your
income.You are currently consuming more than 45 units of B.In order to get 5 more units of A,how many units of B would you have to give up? Matt's utility function is.The price of x is 1,the price of y is 4,and the price of z is 7.Matt's income is 8.How many units of x does Matt demand? Daily demand for gasoline at Billy-Bob's Mobile Station is described by where Q are gallons of gasoline sold and p is the price in dollars.Billy-Bob's supply is.Suppose the state government places a tax of 20 cents on every gallon of gasoline sold.What is the deadweight loss resulting from this tax?_ The marginal cost curve of a firm is MC=6y.Total variable costs to produce 8 units of outputs are There are two major producers of corncob pipes in the world,both located in Herman, Missouri.Suppose that the inverse demand function for corncob pipes is described by where q is total industry output and suppose that marginal costs are zero.What is the Cournot reaction function of firm 1 to the output q2 of firm 2? 三、Calculation(25 points) (1)(10points)Spence and Akerlof are the only two owner of mineral water spring of equal quality in an isolated economy.It costs Spence $2 per gallon to get his water bottled and costs Akerlof $6 per gallon.The inverse demand curve for mineral water is P=100-Q/6,where P is the price per gallon and Q is the number of gallon sold.Determine the Cournot duopoly equilibrium. (2)John Henry,an avid gardener,has found that the number of happy plants, h,depends on the amount of light,1,and water,w.The production function is as follows:h min (1,2w). a.Suppose John wants to produce 4 happy plants,what are the minimum amounts of light and water required?(10points) b.If each unit of light costs wl,and each unit of water costs w 2,derive John's cost function c (wl,w2,h).(15points) IV Graphing and Analysis (35 points)
income. You are currently consuming more than 45 units of B. In order to get 5 more units of A, how many units of B would you have to give up? ___________ Matt's utility function is . The price of x is 1, the price of y is 4, and the price of z is 7. Matt's income is 8. How many units of x does Matt demand? __________ Daily demand for gasoline at Billy-Bob's Mobile Station is described by where Q are gallons of gasoline sold and p is the price in dollars. Billy-Bob's supply is . Suppose the state government places a tax of 20 cents on every gallon of gasoline sold. What is the deadweight loss resulting from this tax? ______________ The marginal cost curve of a firm is MC = 6y. Total variable costs to produce 8 units of outputs are____________ There are two major producers of corncob pipes in the world, both located in Herman, Missouri. Suppose that the inverse demand function for corncob pipes is described by where q is total industry output and suppose that marginal costs are zero. What is the Cournot reaction function of firm 1 to the output q2 of firm 2? ___________ 三、Calculation (25 points) (1) (10points) Spence and Akerlof are the only two owner of mineral water spring of equal quality in an isolated economy. It costs Spence $2 per gallon to get his water bottled and costs Akerlof $6 per gallon. The inverse demand curve for mineral water is P = 100 - Q / 6 , where P is the price per gallon and Q is the number of gallon sold. Determine the Cournot duopoly equilibrium. (2) John Henry, an avid gardener, has found that the number of happy plants, h, depends on the amount of light, l, and water, w. The production function is as follows: h = min {l, 2w}. a. Suppose John wants to produce 4 happy plants, what are the minimum amounts of light and water required? (10points) b. If each unit of light costs w1, and each unit of water costs w 2, derive John’s cost function c (w1, w2, h). (15points) IV Graphing and Analysis (35 points)
(1)In the two-commodity case,derive the price offer curve if the two goods are perfect complements for the consumer.(10points) (2)Graph to present roughly the Heckscher-Ohlin theory on international trade, showing how trade leads to production specialization and to welfare improvements.(10 points) (3)Suppose individuals derive utility from two goods,housing and all other consumption. a.Graph to show that if the government requires individuals to buy more housing than they would freely choose (say,by setting minimum housing standards),such a policy may reduce utility.(10 points) b.Could you imagine such a situation?(2 points) c.Which group would you expect to suffer the greatest losses of utility from such a policy?(3 points)
(1) In the two-commodity case, derive the price offer curve if the two goods are perfect complements for the consumer. (10points) (2) Graph to present roughly the Heckscher-Ohlin theory on international trade, showing how trade leads to production specialization and to welfare improvements.(10 points) (3)Suppose individuals derive utility from two goods, housing and all other consumption. a. Graph to show that if the government requires individuals to buy more housing than they would freely choose (say, by setting minimum housing standards), such a policy may reduce utility. (10 points) b. Could you imagine such a situation? (2 points) c. Which group would you expect to suffer the greatest losses of utility from such a policy? (3 points)