Consider a monopolist facing a linear inverse demand curve p(q) = a bq, where q denotes units of output and b > 0 represents the slope of the inverse demand curve. This rm faces cost function C (q) = F + cq, where F denotes its xed costs (can contain sunk costs), c represents the monopolist s (constant) marginal cost of production and assume a > c 0. Let us say that a regulator wants to induce the monopolist to produce q instead of qm. Would the monopolist have positive pro ts at q ? Suppose F represents only sunk costs, would the monopolist produce q in this case? Explain. Suppose F are only sunk costs and that the regulator of the monopoly establishes the price the monopoly takes as given and then decides to produce the level that maximizes pro ts. What is the price level the regulator would need to establish for the monopoly to be induced to produce the social optimum level q ? How would your conclusion change if F are xed costs? Explain.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter14: Monopoly
Section: Chapter Questions
Problem 14.9P
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Consider a monopolist facing a linear inverse demand curve p(q) = a bq, where q denotes units of output and b > 0 represents the slope of the inverse demand curve. This rm faces cost function C (q) = F + cq, where F denotes its xed costs (can contain sunk costs), c represents the monopolist s (constant) marginal cost of production and assume a > c 0.

  1. Let us say that a regulator wants to induce the monopolist to produce q instead of qm. Would the monopolist have positive pro ts at q ? Suppose F represents only sunk costs, would the monopolist produce q in this case? Explain.
  2. Suppose F are only sunk costs and that the regulator of the monopoly establishes the price the monopoly takes as given and then decides to produce the level that maximizes pro ts. What is the price level the regulator would need to establish for the monopoly to be induced to produce the social optimum level q ? How would your conclusion change if F are xed costs? Explain.
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