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I True or false.（2points*10）
1. 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. 2. Henrietta's utility function is U(x1, x2) = x1x2. She has diminishing marginal rate of substitution between goods 1 and 2.
3. 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.
4. 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.
5. 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.
6. Just as in the theory of utility maximizing consumers, the theory of profit maximizing firms allows the possibility of \e leads to a fall in demand.
7. If there are increasing returns to scale, then average costs are a decreasing function of output.
8. 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.
9. A Stackelberg leader will necessarily make at least as much profit as he would if he acted as a Cournot oligopolist.
10. Dominant strategy equilibrium is a set of choices such that each player's choices are optimal regardless of what the other players choose.
II Fill in the blanks for the following questions:（2points*10）
(1) 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? ___________
(2) 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? __________
(3) 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? ______________
(4) The marginal cost curve of a firm is MC = 6y. Total variable costs to produce 8 units of outputs are____________
(5) 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? ___________
III 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)
I 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) = x
11/2+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.
II 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?_____________
III Calculation (25 points)