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 fixed costs (can contain sunk costs), c represents the monopolist’s (constant) marginal cost of production and assume a > c ≥ 0.Find the socially optimal output level q* which is the value that maximizes consumer surplus (price equals marginal cost). Is it larger or smaller than the profit maximizing output, qm, that you found in part (a)? Is it true that q* = 2qm?Illustrate qm and q* in a graph where price is the vertical axis and q is the horizontal axis. Be sure to include the MR and MC curves as well as the inverse demand curve.

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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 fixed costs (can contain sunk costs), c represents the monopolist’s (constant) marginal cost of production and assume a > c ≥ 0.

Find the socially optimal output level q* which is the value that maximizes consumer surplus (price equals marginal cost). Is it larger or smaller than the profit maximizing output, q^m, that you found in part (a)? Is it true that q* = 2q^m?
Illustrate q^mand q* in a graph where price is the vertical axis and q is the horizontal axis. Be sure to include the MR and MC curves as well as the inverse demand curve.

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