For each of the following questions, explain you answer and show your work. Make sure your answers are backed up by numbers.
1. Suppose that individual demand for a product is given by Q = 1200 - 5P. Marginal revenue is
MR = 200 - 0.4Q, and marginal cost is constant at $ 20. There are no fixed costs.
a. The firm is considering a quantity discount. The first 400 units can be purchased at a price of $120, and further units can be purchased at a price of $80. How many units will the consumer buy in total?
b. Show that this second- degree price- discrimination scheme is more profitable than a single monopoly price.
2. A monopolist sells in two geographically divided markets, the East and the West. Marginal cost is constant at $50 in both markets.
Demand and marginal revenue in each market are as follows:
Qe = 1200 - 2Pe
MRe = 600 - Qe
Qw = 800 - Pw
MRw = 800 - 2Qw
Where e represents the east, and w represents the west market.
a. Find the profit- maximizing price and quantity in each market.
b. In which market is demand more elastic? How can you tell? Describe.
c. Under what conditions, price discrimination is effective and why?
3. Consider a market with a monopolist and a firm that is considering entry. The new firm knows that if the monopolist "fights" (that is, sets a low price after the entrant comes in), the new firm will lose money. If the monopolist accommodates (continues to charge a high price), the new firm will make a profit
Entrant
Enter Don't Enter
Monopolist Price High 20, 10 50, 0
Price Low 5,-10 10, 0
A. Is the monopolist's threat to charge a low price credible? That is, if the entrant has come, would it make sense for the monopolist to charge a low price? Explain.
B. What is the Nash equilibrium of this game?
C. How could the monopolist make the threat to fight credible?
4. Jill resigns from her job, at which she was earning $ 40,000 per year, and uses her $120,000 savings, on which she was earning 5 percent interest, to start a business. In the first year, she earns revenue of $200,000, and her costs are as follows:
Rent $25,000
Utilities $12,000
Wages $30,000
Materials $20,000
a. Calculate Jill's accounting profit.
b. Calculate Jill's economic profit.
c. What makes economic profit different from accounting profit?