Problem Set Number 6
due April 9, 2008
A telecommunications firm provides local telephone service to two markets. The marginal cost of supplying each market is constant at $5 per month per customer, and the incumbent firm incurs a fixed cost of $4 million per month for serving the two markets combined. Through market research and experience, the firm understands the demand relationships in the two markets -- residential and commercial -- to be as follows:
| Price ($ per month) | Residential lines demanded (thousands) | Commercial lines demanded (thousands) |
| 10 | 200 | 300 |
| 20 | 175 | 250 |
| 30 | 150 | 200 |
| 40 | 125 | 150 |
| 50 | 100 | 100 |
The public agency that regulates the local telecommunications markets agrees to allow the firm to charge whatever it wants to the commercial customers, as long as it charges no more than $10 to residential customers.
1a. Calculate marginal revenue in each market for each price level in the table.
b. How much would the firm charge each group of customers, how many residential customers would it serve, and how much would the firm earn overall?
2. Now suppose another firm -- firm B -- begins to look at the local telephone market, and offers to serve the commercial market only. Firm B concludes from its market research that it can get a 50% market share if it charges what firm A charges. If firm B charges more than A it gets no customers, and if it charges less, firm A will lower its price to match B. Assume the total number of commercial customers is still determined from firm A's price and demand schedule. Firm B will need to spend a fixed cost equal to $2 million per month in order to enter the market on this limited basis, and has the same marginal cost per customer as firm A.
a. Suppose firm A wants to try to lower its prices in the commercial market to keep out firm B. How low would firm A have to set its rates in order to keep out firm B (by making it unprofitable for B to enter)?
b. Which is ultimately more profitable for firm A: lowering the price to keep out B, or letting B enter and splitting the market as in question 2?