|Solved Review Questions From Past Exams For Exec. MBAs
(a) (5 points) Suppose that a person is faced with two alternatives. The first alternative gives him $10,000. The second alternative gives him $0 with probability 2/3 and $30,000 with probability 1/3. Suppose he decides to choose the first alternative. How would you characterize his attitude towards risk? Do you expect such a person to buy insurance?
The consumer here faces two alternatives that have the same expected dollar value of $10,000. This is obvious for the first alternative. The second alternative has expected dollar value of 0*(2/3) + 30,000*(1/3) = 10,000. Since the consumer prefers the first alternative, he is risk averse. Since the consumer is risk averse, he is willing to receive even less than $10,000 rather than the second alternative. Therefore the consumer is willing to buy insurance to avoid the risky alternative.
(b) (5 points) A firm in a competitive market faces a price of $4 and has marginal costs MC(q) = q. It is observed that in the long run the firm is not in operation. Assuming that the manager made the right decision, how high is his fixed cost?
If the firm is in operation, it will choose the quantity that solves p = MC(q), i.e., 4 = q. The variable costs at q = 4 is the area under the MC curve, i.e., 4*4/2 = 8. R = 4*4 = 16. Therefore R - V = 8. For the firm to shut down in the long run, we need an F 8 since it has to make profits zero or negative, and Π = R - V - F.
2. (25 points) A firm has fixed costs F = 4, variable costs V(q) = q2 + 2q, and marginal costs MC(q) = 2 + 2q.
(a) (10 points) Find and graph the average variable cost and the average total cost functions. In the same diagram, also graph the marginal cost function given above.
Total cost is T(q) = 4 + q2 + 2q. ATC(q) = 4/q + q + 2. AVC(q) = (q2 + 2q)/q = q + 2. AFC = 4/q. MC = d(TC)/dq = 2q + 2. ATC reaches its minimum where MC = ATC, 2q + 2 = 4/q + q + 2. Dropping the 2 in both sides, and multiplying by q, 2q2 = 4 + q2 q2 = 4 q = 2, MC = ATC = 6.
(b) (5 points) At price p = 10 find and graph the profit maximizing output q*.
To maximize profits, firm set production at the point where MC(q) = P 2q + 2 = 10 q* = 4.
(c) (5 points) Find and graph the profits for p = 10.
At p = 10, TC(q) = 4 + 42 + 2*4 = 28. Revenues = 4*10 = 40. Thus, profits = 40 - 28 = 12. Alternatively, profits per unit = 10 - ATC = 10 - (AFC + AVC) = 10 - (4 + 2 + 4/4) = 3. So total profits = q*(average profit) = 4 * 3 = 12.
(d) (5 points) Find and graph the supply curve in the long run and in the short run.
The long run supply is q = 0 for p < min(ATC) = 6. For p 6 the supply curve is MC. Thus, for p 6, the supply curve is p = 2q + 2, or equivalently, q = (p - 2)/2. The short run supply curve is p = 2q + 2 for q 0, or equivalently, q = (p - 2)/2 for all p 2.
3. Consultants Inc. has a total cost function C(Q) = 50Q2.
(a) (5 points) Find and graph its marginal cost, average variable cost and average total cost functions.
AVC(Q) = 50Q , ATC(Q) = 50Q, MC(Q) = 100Q.
(b) (5 points) If the price of its output is $200.00, what will be its production level and profits?
Since the firm is perfectly competitive, p = MC 200 = 100Q. Therefore, Q* = 2. Profits = [p - ATC(Q*)]Q* = (200 - 50*2)*2 = $200.
(c) (10 points) An urgent call from the accounting department of Consultants Inc. informs you that by error they omitted to report a set-up cost of $100. Redraw the affected curves in your diagram. Given the now correct cost curves, what are the long run and short run supply functions of Consultants Inc.?
F = 100, C(Q) = 100 + 50Q2. AVC(Q) = 50Q, ATC(Q) = (50Q2 + 100)/Q = 50Q + 100/Q, MC = 100Q.
4. Suppose that the demand function for Japanese cars in the United States is such that annual sales of cars (in thousands of cars) will be 250 - 2P, where P is the price of Japanese cars in thousands of dollars.
(a) If the supply schedule is horizontal at a price of $5,000 what will be the equilibrium number of Japanese cars sold in the United States? How much money will Americans spend in total on Japanese cars?
If the supply schedule is horizontal at $5,000, then the equilibrium price = $5,000. Since D(p) = 250 - 2p, D(p) = 250 - 2*5 = 240,000 cars. Americans will spend 240,000*5,000 = $1,200,000,000.
Suppose that in response to pressure from American car manufacturers, the United States imposes an import duty on Japanese cars in such a way that for every car exported to the United States the Japanese manufacturers must pay a tax to the U.S. government of $2,000. How many Japanese automobiles will now be sold in the United States? At what price will they be sold? Draw a supply/demand diagram.
The supply schedule shifts upward $2,000, and is horizontal at $7,000. The market price is now $7,000. Hence, D(p) = 250 - 2*7 = 236,000 cars.
(c) How much revenue will the U.S. government collect with this tariff?
Revenues to the US government = (tax/car)*no. cars sold = $2,000*236,000 = $472,000,000.
(d) Suppose that instead of imposing an import duty, the U.S. government persuades the Japanese governments to impose "voluntary export restrictions" on their exports of cars to the United States. Suppose that the Japanese agree to restrain their exports by requiring that every car exported to the United States must have an export license. Suppose further that the Japanese government agrees to issue only 236,000 export licenses and sells these licenses to the Japanese firms. If the Japanese firms know the American demand curve and if they know that only 236,000 Japanese cars will be sold in America, what price will they be able to charge in America for their cars?
D(p) = 250-2p. The Japanese firms will set the price so that D(p) = 236,000. So 250 -2p = 236 Y 2p = 14, and p = 7,000.
(e) How much will a Japanese firms be willing to pay the Japanese government for an export license? (Hint: Think about what it costs to produce a car and how much it can be sold for if you have an export license.)
The firms will be willing to pay $2,000, as they will receive a net of $5,000 per car.
(f) How much will be the Japanese government's total revenue from the sale of export licenses?
($2,000/car)*236,000 cars = $472,000,000.
(g) How much money will Americans spend on Japanese cars?
Americans will spend ($7,000/car)*236,000 cars = $1,652,000,000.
(h) Why might the Japanese "voluntarily" submit to export controls?
The voluntary export controls currently used allow the Japanese to keep all of the extra revenues. In this example, the Japanese would increase revenues by $1,652,000,000 -$1,2000,000,000 = $452,000,000. Since they would be producing 4000 fewer cars, they would decrease costs by $5,000*4,000 = $20,000,000. The total extra surplus for the Japanese manufacturers is thus $452,000,000 + $20,000,000 = $472,000,000. Equivalently, the extra surplus kept by the Japanese = (7-5)*$236,000 = $472,000,000.