Problem 1. If the demand curve for wheat in the United States is P=12.4 - Q_D where is the P is the farm price of wheat (in dollars per bushel) and Q_D is the quantity of wheat demanded (in billions of bushels), and the supply curve for wheat in the United States is P= -2.6 + 2Q_S where Q_s is the quantity of wheat supplied (in billions of bushels), what is the equilibrium price of wheat? What is the equilibrium quantity of wheat sold? Must the actual price equal the equilibrium price? Why or why not?
Problem 2. The Haas Corporation's executive vice president circulates a memo to the firm's top management in which he argues for a reduction in the price of the firm's product. He says such a price cut will increase the firm's sales and profits.
a. The firm's marketing manager responds with a memo pointing out that the price elasticity of demand for the firm's product is about -0.5. What is this fact relevant?
b. The firm's president concurs with the opinion of the executive vice president. Is she correct?
Problem 3. In the following diagram, we show one of Jane's indifference curves and her budget line.
a. If the price of good X is $100, what is her income?
b. What is the equation for her budget line?
c. What is the slope of her budget line?
d. What is the price of good Y?
e. What is Jane's marginal rate of substation in equilibrium?
Problem 4. According to the chief engineer at the Zodiac Company, Q=AL^aK^B, where Q is the output rate, L is the rate of labor input, and K is the rate of capital input. Statistical analysis indicates that a=0.8 and B=0.3. The firm's owner claims the plant has increasing returns to scale.
a. Is the owner correct?
b. If B were 0.2 rather than 0.3 would she be correct?
c. Does output per unit of labor depend only on a and B? Why or why not?
Problem 5. The Haverford Company is considering three types of plants to make a particular electronic device. Plant A is much more highly automated than plant B, which in turn is more highly automated than plant C. For each type of plant average variable cost so long as output is less than capacity, which is the maximum output of the plant. The cost structure for each type of plant is as follows:
Average Variable Costs Plant A Plant B Plant C
Labor $1.10 2.40 $3.70
Materials 0.90 1.20 1.80
Other 0.50 2.40 2.00
Total $2.50 $6.00 $7.50
Total fixed costs $300,000 $75,000 $25,000
Annual capacity 200,000 100,000 50,000
a. Derive the average costs of producing 100,000, 200,000, 300,000, and 400,000 devices per year with plant A. (For output exceeding the capacity of a single plant, assume that more than one plant of this type is built.)
b. Derive the average costs of producing 100,000, 200,000, 300,000, and 400,000 devices per year with plant B.
c. Derive the average costs of producing 100,000, 200,000, 300,000 and 400,000 devices per year with plant C.
d. Using the results of parts (a) through (c), plot the points on the long-run average cost curve for the production of these electronic devices for outputs of 100,000, 200,000, 300,000 and 400,000 devices per year.
Problem 6. In 2008, the box industry was perfectly competitive. The lowest point on the long-run average cost curve of each of the identical box producers was $4, and this minimum point occurred at an output of 1,000 boxes per month. The market demand curve for boxes was
Q_D=140,000 - 10,000P
Where P was the price of a box (in dollars per box) and Q_D was the quantity of boxes demanded per month. The market supply curve for boxes was
Q_S=80,000 + 5,000P
Where Q_S was the quantity of boxes supplied per month.
a. What was the equilibrium price of a box? Is this the long-run equilibrium price?
b. How many firms are in this industry when it is in long-run equilibrium?
problem 7. The Wilson Company's marketing manager has determined that the price elasticity of demand for its product equals -2.2. According to studies she carried out, the relationship between the amount spent by the firm on advertising and its sales is as follows:
Advertising Expenditure Sales
$100,000 $1.0 million
$200,000 $1.3 million
$300,000 $1.5 million
$400,000 $1.6 million
a. If the Wilson Company spends $200,000 on advertising, what is the marginal revenue from an extra dollar of advertising?
b. Is $200,000 the optimal amount for the firm to spend on advertising?
c. If $200,000 is not the optimal amount, would you recommend that the firm spends more or less on advertising?
problem 8. Ann McCutcheon is hired as a consultant to a firm producing ball bearings. This firm sells in two distinct markets, each of which is completely sealed off from the other. The demand curve for the firm's output in the first market is P_1=160-8Q_1, where P_1 is the price of the product and Q_1 is the amount sold in the first market. The demand curve for the firm's output in the second market is P_2=80-2Q_2, where P_2 is the price of the product and Q_2 is the amount sold in the second market. The firm's marginal cost curve is 5+Q where Q is the firm's entire output (destined for either market). Managers ask Ann McCutcheon to suggest a pricing policy.
a. How many units of output should she tell managers to sell in the second market?
b. How many units of output should she tell managers to sell in the first market?
c. What price should managers charge in each market?
problem 9. . The Xerxes Company is composed of a marketing division and a production division. The marketing division packages and distributes a plastic item made by the production division is
P_0=200-3Q_0
Where P_0 is the price (in dollars per pound) of the finished product and Q_0 is the quantity sold (in thousands of pounds). Excluding the production cost of the basic plastic item, marketing division's total cost function is
TC_0=100+15Q_0
Where TC_0 is the marketing division's total cost (in thousands of dollars). The production division's total cost function is
TC_1=5+3Q_1 + 0.4Q_1^2
Where TC_1 is total production cost (in thousands of dollars) and Q_1 is the total quantity produced of the basic plastic item (in thousands of pounds). There is a perfectly competitive market for the basic plastic item, the price being $20 per pound
a. What is the optimal output for the production division?
b. What is the optimal output for the marketing division?
c. What is the optimal transfer price for the basic plastic item?
d. At what price should the marketing division sell its product?
problem 10. James Pizzo is president of a firm that is the industry price leader; that is, it sets the price and the other firms sell all they want at that price. In other words, the other firms act as perfect competitors. The demand curve for this industry's product is P=300-Q, where P is the price of the product and Q is the total quantity demanded. The total amount supplied by other firms is equal to Q_r, where Q_r = 49P. (P is measured in dollars per barrel; Q, Q_r and Q_b are measured in millions of barrels per week.)
a. If Pizzo's firm's marginal cost curve is 2.96Q_b, where Q_b is the output of his firm, at what output level should he operate to maximize profit?
b. What price should he charge?
c. How much does the industry as a whole produce at this price?
d. Is Pizzo's firm the dominant firm in the industry?
problem 11. The Boca Raton Company announces that if it reduces its price subsequent to a purchase, the early customer will get a rebate so that he or she will pay no more than those buying after the price reduction.
a. If the Boca Raton Company has only one rival, and if its rival too makes such an announcement, does this change the payoff matrix? If so, in what way?
b. Do such announcements tend to discourage price cutting? Why or why not?
problem 12. Your company is bidding for a broadband spectrum license. You have been asked to submit an optimal bidding strategy. You expect that bidders will have independent private values for the licenses because each bidder presently has a different structure in place. You elieve the valuations for these licenses will be $200 million and $700 million. Your own valuation is $650 million. There is some uncertainty about the auction design that will be used, so you must suggest an optimal bidding strategy for the following acution designs:
a. Second-price, sealed-bid auction
b. English auction.
c. Dutch auction
problem 13. William J. Bryan is the general manager of an electrical equipment plant. He must decide whether to install a number of assembly robots in his plant. This investment would be risky because both management and the workforce have no real experience with the introduction or operation of such robots. His indifference curve between expected rate of return and risk is as hsown in the figure.
a. If the riskiness () of this investment equals 3, what risk premium does require?
b. What is the riskless rate of return
c. What is the risk-adjusted discount rate?
d. In calculating the present value of future profit from this investment, what interest rate should be used?
problem 14. Suppose the typical Florida resident has wealth of $500,000, of which his or her home is worth $100,000. Unfortunately Florida is infamous for its hurricanes, and it is believed there is a 10 percent chance of hurricane that could totally destroy a house (a loss of $100,000). However, it is possible to retrofit the house with various protective devices (shutters, roof bolts, and do on) for a cost of $2,000. This reduces the 10 percent chance of a loss of $100,000 to a 5 percent chance of a loss of $50,000. The homeowner must decide whether to retrofit and thereby reduce the expected loss. The problem for an insurance company is that it does not know whether the retrofit will be installed and therefore cannot quote a premium conditioned on the policyholder choosing this action. Nevertheless, the insurance company offers the following two policies from which the homeowner can choose: (1) The premium for insurance covering total loss is $12,000 or (2) the premium for insurance covering only 50 percent of loss is $1,500. The typical homeowner has a utility function equal to the square root of wealth. Will the homeowner retrofit the house, and which insurance policy will homeowner buy? Will the insurance company make a profit (on average) given the homeowner's choice?
problem 15. The market for digital cameras is relatively new. Ajax Inc. produces what it regards as a high-quality digital camera. Knockoff Inc. produces what it regards as a low-quality digital camera. However, because the market is so new, reputations for quality have not yet developed, and consumers cannot tell the quality difference between an Ajax digital and a Knockoff digital just by looking at them.
If consumers knew the difference, they'd be willing to pay $200 for a high-quality camera, and they'd be willing to pay $100 for a low-quality camera. It costs Ajax $85 to produce a high-quality camera, and it costs Knockoff $55 to produce a low-quality camera.
A recent MBA hire at Ajax suggests that Ajax could differentiate its camera from Knockoff's by offering a full-coverage warranty (which would fully cover any defect in the camera at no cost to the customer). The MBA estimates that it would cost Ajax $20 per year to offer such a warranty. The MBA also estimates that it would cost Knockoff $40 per year should Knockoff attempt to copy Ajax's warranty strategy. Consumers will feel that the camera with the longest warranty is high-quality and that with the shortest warranty is low-quality. The camera companies want to maximize the profit per camera.
problem 16. The cost of pollution (in billions of dollars) originating in the paper industry is
Cp=2P +P^2
Where P is the quantity of pollutants emitted (in thousands of tons). The cost of pollution control (in billions of dollars) for this industry isCc=5 - 3)
a. What is the optimal level of pollution?
b. At this level of pollution, what is the marginal cost of pollution?
c. At this level of pollution, what is the marginal cost of pollution control?