Problem 1. Pizza restaurants are identical and exist in a market that is perfectly competitive. Marty’s pizza parlor faces the following demand and costs.
Q (pizzas) P ($) TC ($)
0 10 32
1 10 40
2 10 45
3 10 48
4 10 55
5 10 65
6 10 80
7 10 100
8 10 140
9 10 220
10 10 340
a) Derive the profit-maximizing output quantity and the profits that are achieved.
b) Is the market in long-run equilibrium. If not, describe what will happen in the market in the long run.
c) Now, suppose that the price of pizza increases to $15 dollars. Again, derive the profitmaximizing output quantity and the profits that are achieved.
Problem 2. Assume that the market for cardboard is perfectly competitive (if not very exciting). What should a cardboard-producing firm do in the short run in each of the following scenarios? Draw a diagram that illustrates the firm’s situation in each case.
a) Minimum ATC = $2.00; Minimum AVC = $1.50; Market price = $1.75.
b) MR = $1.00; Minimum AVC = $1.50; Minimum ATC = $2.00.
c) Price = $2,.00; Minimum ATC = Minimum AVC = $2.00.
d) MR = 1.75; Minimum AVC = $1.50.
Problem 3. The market for yo-yos is perfectly competitive. There are currently 3,000 identical firms in the market. Denote the market quantity by Q and the quantity of a firm by q. Each firm has a marginal cost given by and an average variable cost given by MC(q) = 0.01q and an average variable cost given by AVC = 0.005q.
The market demand is QD = 1,000 - 200,000P
a) Derive the short-run supply of a single firm.
b) Derive the short-run market supply.
c) Derive the short-run market equilibrium. How much does each firm produce in the short-run equilibrium?
Problem 4. The licorice industry is perfectly competitive. Each of the industry’s identical firms produces 2 million strings of licorice per year. The strings have an average cost of $0.20 each, and they sell for $0.30 each.
a) What is the marginal cost of strings? Why?
b) Is this industry in long-run equilibrium? Why or why not?
Problem 5. The industry for hockey pucks is perfectly competitive. All firms are identical with a coststructure that is independent of the number of firms in the industry. Each firm has a long-run average cost curve that has its minimum of $2.00 at a quantity of 2500 pucks. The demand for pucks is given by the following demand schedule.
P (US $) Q
3.00 200,000
2.50 400,000
2.00 600,000
1.50 800,000
1.00 1,000,000
0.50 1,200,000
a) Find long-run equilibrium price and output in the hockey puck market.
b) What is the long-run equilibrium production of each firm? How many of them are there in the long run? What are the profits of each firm?
c) Suppose that the expansion of the NHL into the sunbelt increases the demand for hockey pucks by 200,000 at every price. Derive the new long-run equilibrium price, market quantity, quantity supplied by each firm, number of firms, and profits per firm.
d) What is the shape of the long-run supply curve of hockey pucks. Explain why this is so.
6. Assume that the gold-mining industry is perfectly competitive.
a) Illustrate a long-run equilibrium using diagrams for the gold market and for a representative gold mine.
b) Suppose that an increase in jewelry demand induces a surge in the demand for gold. Using your diagrams, show what happens in the short run to the gold market and to each existing gold mine.
c) If the demand for gold remains high, what would happen to the price over time? Specifically, would the new long-run equilibrium price be above, below, or equal to the short-run equilibrium price in part b)? Is it possible for the new equilibrium price to be above the original long-run equilibrium price in part a)?