中级微观经济学模拟试题(2) -True or false.(2points*10) 1.A consumer's preference is directly related to his income and prices of goods. 2.The relation "strictly preferred to"satisfies completeness,reflexivity and transitivity. 3.A consumer has a von Neumann-Morgenstern utility function of the form U(cA,cB,pA,pB)=pAv(cA)+pBv(cB)where pA and pB are the probabilities of events A and B where cA and cB are consumptions contingent on events A and B respectively. This consumer must be a risk lover if v is an increasing function. 4.Suppose a consumer has strictly convex preferences and her Engel curve for a good is a vertical line for some range of income.In that same income range,her demand curve for the good slopes down. 5.If the supply is perfectly elastic,then an upward shift of the demand curve will lead to a higher price and quantity in equilibrium. 6.If a competitive firm uses two inputs and it has the production function F(x1;x2)=x11/2+x21/2 then its marginal cost curve is horizontal. 7.A general has the two possible pure strategies,sending all of his troops by land or all of his troops by sea.An example of a mixed strategy is where he sends 1/4 of his troops by land and 3/4 of his troops by sea. 8.If two people have identical homothetic preferences and if their indifference curves have diminishing marginal rate of substitution,then in an Edgeworth box, the locus of Pareto optimal allocations between them is a diagonal straight line. 9.When there is production,a competitive equilibrium is not Pareto optimal unless there are increasing returns to scale. 10.A firm produces one input with one output and has decreasing returns to scale. The price that it pays per unit of input and the price it gets per unit of output are independent of the amount that this firm buys or sells.If the government taxes its net profits at some percentage rate and subsidizes its inputs at the same percentage rate,the firm's profit maximizing output will not change
中级微观经济学模拟试题（2） 一、True or false.（2points*10） 1.A consumer’s preference is directly related to his income and prices of goods. 2.The relation “strictly preferred to” satisfies completeness, reflexivity and transitivity. 3.A consumer has a von Neumann-Morgenstern utility function of the form U(cA,cB,pA,pB)=pAv(cA)+pBv(cB) where pA and pB are the probabilities of events A and B where cA and cB are consumptions contingent on events A and B respectively. This consumer must be a risk lover if v is an increasing function. 4.Suppose a consumer has strictly convex preferences and her Engel curve for a good is a vertical line for some range of income. In that same income range, her demand curve for the good slopes down. 5.If the supply is perfectly elastic, then an upward shift of the demand curve will lead to a higher price and quantity in equilibrium. 6.If a competitive firm uses two inputs and it has the production function F(x1;x2) = x11/2+x21/2 , then its marginal cost curve is horizontal. 7.A general has the two possible pure strategies, sending all of his troops by land or all of his troops by sea. An example of a mixed strategy is where he sends 1/4 of his troops by land and 3/4 of his troops by sea. 8.If two people have identical homothetic preferences and if their indifference curves have diminishing marginal rate of substitution, then in an Edgeworth box, the locus of Pareto optimal allocations between them is a diagonal straight line. 9.When there is production, a competitive equilibrium is not Pareto optimal unless there are increasing returns to scale. 10.A firm produces one input with one output and has decreasing returns to scale. The price that it pays per unit of input and the price it gets per unit of output are independent of the amount that this firm buys or sells. If the government taxes its net profits at some percentage rate and subsidizes its inputs at the same percentage rate, the firm's profit maximizing output will not change
Fill in the blanks for the following questions:(2points*10) 11.If good 1 is measured on the horizontal axis and good 2 is measured on the vertical axis,and if the price of good 1 is pl and the price of good 2 is p2;then the slope of the budget line is 12.Manuel consumes only apples and bananas.He prefers more apples to less,but he gets tired of bananas.If he consumes fewer than 17 bananas per week,he thinks that one banana is a perfect substitute for one apple.But you would have to pay him one apple for each banana beyond 17 that he consumes.The indifference curve that passes through the consumption bundle with 25 apples and 26 bananas also passes through the bundle with A apples and 11 bananas,where A equals_ 13.Rabelaisian Restaurants has a monopoly in the town of Upper Glutton.Its production function is where L is the amount of labor it uses and Q is the number of meals produced.Rabelaisian Restaurants finds that in order to hire L units of labor,it must pay a wage of per unit of labor.The demand curve for meals at Rabelaisian Restaurants is given by.The profit maximizing output for Rabelaisian Restaurants is_ 14.An airline has exclusive landing rights at the local airport.The airline flies one flight per day to New York with a plane that has a seating capacity of 100.The cost of flying the plane per day is $(4,000 +10q)where q is the number of passengers.The number of flights to New York demanded is.If the airline maximizes its monopoly profits,the difference between the marginal cost of flying an extra passenger and the amount the marginal passenger is willing to pay to y to New York is 15.Socrates owns just one ship.The ship is worth $200 million dollars.If the ship sinks,Socrates loses $200 million.The probability that it will sink is.02. Socrates'total wealth,including the value of the ship is $225 million.He is an expected utility maximizer with von Neuman Morgenstern utility U(W)equal to the square root of W.What is the maximum amount that Socrates would be willing to pay in order to be fully insured against the risk of losing his ship? 三、Calculation(25 points)
二、Fill in the blanks for the following questions:（2points*10） 11.If good 1 is measured on the horizontal axis and good 2 is measured on the vertical axis, and if the price of good 1 is p1 and the price of good 2 is p2; then the slope of the budget line is______________. 12.Manuel consumes only apples and bananas. He prefers more apples to less, but he gets tired of bananas. If he consumes fewer than 17 bananas per week, he thinks that one banana is a perfect substitute for one apple. But you would have to pay him one apple for each banana beyond 17 that he consumes. The indifference curve that passes through the consumption bundle with 25 apples and 26 bananas also passes through the bundle with A apples and 11 bananas, where A equals____________. 13.Rabelaisian Restaurants has a monopoly in the town of Upper Glutton. Its production function is where L is the amount of labor it uses and Q is the number of meals produced. Rabelaisian Restaurants finds that in order to hire L units of labor, it must pay a wage of per unit of labor. The demand curve for meals at Rabelaisian Restaurants is given by . The profit maximizing output for Rabelaisian Restaurants is______________. 14.An airline has exclusive landing rights at the local airport. The airline flies one flight per day to New York with a plane that has a seating capacity of 100. The cost of flying the plane per day is $(4,000 +10q) where q is the number of passengers. The number of flights to New York demanded is . If the airline maximizes its monopoly profits, the difference between the marginal cost of flying an extra passenger and the amount the marginal passenger is willing to pay to y to New York is_____________. 15.Socrates owns just one ship. The ship is worth $200 million dollars. If the ship sinks, Socrates loses $200 million. The probability that it will sink is .02. Socrates' total wealth, including the value of the ship is $225 million. He is an expected utility maximizer with von Neuman Morgenstern utility U(W) equal to the square root of W. What is the maximum amount that Socrates would be willing to pay in order to be fully insured against the risk of losing his ship?_____________ 三、Calculation (25 points)
1.Derive the basic equation for choice of consumption.(10 points) 2.(15 points)D&P,a computer company,monopolizes the domestic market which inverse demand curve is pd 30 000-20 qd.D&P sells computers also to foreign market at constant price pf =20 000.D&P's cost is C=20 020 124+10 000 Q+ 5Q2. 3-1 If D&P is maximizing its profit,how many computers it would sell in each market and at what price?Provide also the corresponding price elasticities of demand. 3-2 Graph to show your price-quantity solutions. 四、Graphing and Analysis(35 points) 1.(10 points)Suppose that airlines fares are reduced by 50%after one flies 25 000 miles a year.Graph to show that a typical flyer-customer with well-behaved preferences will not choose to fly exactly 25 000 miles.Graphing is enough. 2.Draw a typical Edgeworth Box of pure exchange showing also a disequilibrium budget line.Tell which good is too cheap in the case.Then draw another Edgeworth Box to show very clearly in the box how to determine the final equilibrium.(10 points) 3.Draw to show a (8 points)How does a change in the price of a good shift the Income Expansion Path; b (7 points)How does a change in income shift the Price Offer Curve
1. Derive the basic equation for choice of consumption.(10 points) 2. (15 points) D&P, a computer company, monopolizes the domestic market which inverse demand curve is pd = 30 000－20 qd . D&P sells computers also to foreign market at constant price pf = 20 000. D&P’s cost is C = 20 020 124 + 10 000 Q + 5 Q2 . 3-1 If D&P is maximizing its profit, how many computers it would sell in each market and at what price? Provide also the corresponding price elasticities of demand. 3-2 Graph to show your price-quantity solutions. 四、Graphing and Analysis (35 points) 1. (10 points) Suppose that airlines fares are reduced by 50% after one flies 25 000 miles a year. Graph to show that a typical flyer-customer with well-behaved preferences will not choose to fly exactly 25 000 miles. ( Graphing is enough.) 2. Draw a typical Edgeworth Box of pure exchange showing also a disequilibrium budget line. Tell which good is too cheap in the case. Then draw another Edgeworth Box to show very clearly in the box how to determine the final equilibrium. (10 points) 3. Draw to show a (8 points) How does a change in the price of a good shift the Income Expansion Path; b (7 points) How does a change in income shift the Price Offer Curve