Question 1:
Suppose that the demand for long-distance telephone service is D(P) = 50 - 2P, where P is price. Prior to recent deregulation, this market was monopolized by AT&T. Assume that AT&T's cost function is C(q) = 100 + 5q.
a. If AT&T had been an unregulated monopolist, derive the price that it would have charged.
b. Derive the price that a regulatory agency would set if it was interested in maximizing consumer welfare subject to AT&T earning at least normal profits.
Since deregulation, AT&T has continued to be the dominant firm. Suppose AT&T's competitors are small price-taking firms that can be represented by the supply function S(P) = 2P - 20.
c. Using the static dominant firm model, derive the price that AT&T would charge. Derive AT&T's market share.
d. How much is AT&T willing to pay to be an unregulated monopolist?
Suppose that we extend this model to a multiperiod setting, and assume that the fringe finances growth through retaining earnings.
e. Will AT&T's current price be higher or lower than that derived in part c?
Question 2:
Ace Washtub Company is currently the sole producer of washtubs. Its cost function is C(q) = 49 + 2q, and the market demand function is D(P) = 100 - P. There is a large pool of potential entrants, each of which has the same cost function as Ace. Assume the Bain-Sylos postulate. Let the incumbent firm's output be denoted q ^ i.
a. Derive the residual demand function for a new firm.
b. Given that the incumbent firm is currently producing q ^ i, if a potential entrant was to enter, how much would it produce?
c. Find the limit price. Hint: Find the output for Ace such that the slope of a new firm's average cost curve equals the slope of a new firm's residual demand curve.
Suppose, instead of assuming the Bain-Sylos postulate, that we assume active firms expect to achieve a Cournot solution.
d. Does entry depend on qI? Explain. e. Will there be entry?
e. Will there be entry?