Problem 1. Suppose that, in a large city, 200 identical street vendors compete in a competitive market for hot dogs.
1. Fore each vendor i, total costs to produce qi hot dogs is, Ci(qi) = 1/4 qi + 1/8qi2
What is the marginal cost function of each firm?
2. Given your answer from above, how many hot dogs will each vendor produce if offered a price of $4 per hot dog?
3. What is the aggregate supply curve for this market?
4. Let demand for hot dogs be Q = 2500-100P, what is the short run equilibrium price?
5. What is the total quantity of hot dogs sold in short-run equilibrium?
6. In the long run, would you expect this industry to experience entry or exit? Explain your answer.
Problem 2. In the same city as before, a new "wave" technology is discovered, firms using this new technology have a total cost function C˜i(qi) = 2qi+1/20 q2i. While the 200 existing firms keep their old technology. Ten new firms enter using "wave" technology.
The hot dogs produced by the two technologies are exactly the same (that is, the hot dogs are homogeneous). You may assume there is free entry in both technologies in the long run.
1. The promoters of "wave" technology point out that although it may appear more expensive at first, it benefits from greater "economies of scale" than standard technology. Explain what they mean, feel free to use a numerical example.
2. What is the individual supply curve of a firm using "wave" technology? Let q˜i(P) stand for the individual supply of a firm using the wave technology and qi(P) remain the individual supply of a firm using the original technology from Problem 1.
3. Given that there are now 200 "standard" firms and 10 "wave" firms, what is the aggregate supply curve for this market?
4. What is the new short-run equilibrium price in this market?
5. Is the market in long-run equilibrium? Explain why or why not.
6. You are hired as a consultant by a firm using wave technology. What do you suggest they do?
Problem 3. Suppose Monolith Enterprises has gained exclusive rights to sell ball point pens in State College. The demand for ball point pens is described by Q = 1500 - 10P, Monolith's total cost function for producing pens is C(Q) = 2Q.
1. What is the marginal cost function for Monolith?
2. Write down the monopolist's optimization problem, assume the monopolist chooses quantities.
3. What quantity of pins should Monolith produce?
4. What is the price at this level of output?
5. Is this outcome efficient? If so, why? If not, what is the efficient level of output?
6. What is the Lerner Index for Monolith?
7. Suppose Monolith's cost function changed to C(Q) = 10 + 2Q. Would Monolith's optimal quantity of pens be different? Explain why or why not.
Problem 4. The following firms compete within the same industry:
|
Name
|
Sales (millions)
|
|
ACME Industries
|
38
|
|
Beta Inc.
|
10
|
|
Caltech
|
15
|
|
Douglass Ltd.
|
4
|
|
Gramen Inc.
|
12
|
|
Houghton Enterprises
|
22
|
|
Jenentech
|
7
|
1. Use this information to calculate CR3
2. Calculate CR5 for the industry.
3. What is the HHI for the industry?
4. Can you use this information alone to calculate the Lerner Index? Explain why or why not.