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6. Consider a monopolist facing a linear inverse demand curve p(q) = a bg, where q denotes units of output and b > O represents the slope of the inverse demand curve. This rm faces cost function C (q) = F + cg, 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. a. Find the monopolisť's profit maximizing output and label it gm. Verify if it is positive. b. What is the market price pm and the profit level m? Is the profit level always positive? If not what is the condition for the profit level to be positive? Explain c. Find the absolute value of the price elasticity of demand n Is the elasticity greater than one? Find the markup on price or Lerner index, defined as evaluated at gm as defined in the textbook.

6. Consider a monopolist facing a linear inverse demand curve p(q) = a bg, where q denotes units of output and b > O represents the slope of the inverse demand curve. This rm faces cost function C (q) = F + cg, 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. a. Find the monopolisť's profit maximizing output and label it gm. Verify if it is positive. b. What is the market price pm and the profit level m? Is the profit level always positive? If not what is the condition for the profit level to be positive? Explain c. Find the absolute value of the price elasticity of demand n Is the elasticity greater than one? Find the markup on price or Lerner index, defined as evaluated at gm as defined in the textbook.

Essentials of Economics (MindTap Course List)
Essentials of Economics (MindTap Course List)
8th Edition
ISBN:9781337091992
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter14: Monopoly
Section: Chapter Questions
Problem 9PA
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6. Consider a monopolist facing a linear inverse demand curve p(q) = a bg, where q denotes units of output and b > O represents the slope of the inverse demand curve. This rm faces cost function C (q) = F + cg, where F denotes its xed costs (can contain sunk costs), c represents the monopolist s (constant) marginal cost of production and assume a >с 0. a. Find the monopolist's profit maximizing output and label it Verify if it is positive. b. What is the market price pm and the profit level Tm? Is the profit level always positive? If not what is the condition for the profit level to be positive? Explain c. Find the absolute value of the price elasticity of demand Is the elasticity greater than one? Find the markup on price or Lerner index, defined as p(q)-C'(q) evaluated at qm as defined in the textbook. L (q) p(q) at gm. What happens with L when n increases? Is it true that "A proft maximizing monopolist decreases its markup as demand becomes more price elastic. Explain. d. 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, gm, that you found in part (a)? Is it true that q* = 2qm? Explain. e. Illustrate gm 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.
Transcribed Image Text:6. Consider a monopolist facing a linear inverse demand curve p(q) = a bg, where q denotes units of output and b > O represents the slope of the inverse demand curve. This rm faces cost function C (q) = F + cg, where F denotes its xed costs (can contain sunk costs), c represents the monopolist s (constant) marginal cost of production and assume a >с 0. a. Find the monopolist's profit maximizing output and label it Verify if it is positive. b. What is the market price pm and the profit level Tm? Is the profit level always positive? If not what is the condition for the profit level to be positive? Explain c. Find the absolute value of the price elasticity of demand Is the elasticity greater than one? Find the markup on price or Lerner index, defined as p(q)-C'(q) evaluated at qm as defined in the textbook. L (q) p(q) at gm. What happens with L when n increases? Is it true that "A proft maximizing monopolist decreases its markup as demand becomes more price elastic. Explain. d. 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, gm, that you found in part (a)? Is it true that q* = 2qm? Explain. e. Illustrate gm 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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