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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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QUESTION 3 A monopolist has a cost function of c(x) = x so that its marginal cost is constant at $1 per unit. It faces the following demand curve: D(p) = {100/p 100/p if p > 20 if p ≤ 20 A. What is the profit-maximizing choice of output/price for the monopolist? Graphically represent the monopoly market. B. If the government sets a price ceiling on the monopolist in order to force it to act as a competitor, what price should the government set? C. What output would the monopolist produce if forced to behave as a competitor? D. Based on the information in parts A - C, find the consumer-, producer-, and social surpluses before and after the government intervention.
a) Find and highlight the consumer surplus in the monopoly in the diagram.b) Draw a possible marginal cost curve for the monopolist into the diagram that is consistentwith all the other curves that are already given. c) Based on the marginal cost curve that you constructed in part (b), find and highlight themonopolist’s total costs at the monopoly price in the diagram. d) Briefly (200 words max) explain the shape of the marginal revenue curve as compared tothe demand curve in the diagram.
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3. A monopolist faces a demand curve of P = 120 – 2q and has a production function given by f (L, K) = L'/4K¼. Input prices are w = 1 and r = 4. (a) Calculate the monopolist's (long-run) marginal cost as a function of the quantity it produces. (b) Draw a diagram illustrating the monopolist's problem. Identify each of the following on the diagram and calculate its numeric value: (i) monopolist's profit-maximizing quantity, (ii) price charged, (iii) monopolist's profit, (iv) consumer surplus, (v) producer surplus, and (vi) deadweight loss. Two notes: (1) the area of a triangle is base * height, (2) if you are getting really messy answers here, you may have made a mistake in part (a). (c) The government is concerned about the monopoly and decides to impose a price ceiling. Illustrate the efficient price ceiling on your diagram. i. Illustrate and calculate the price ceiling that will result in an efficient outcome. ii. Compute consumer and producer surplus at the efficient outcome. iii.…
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Now suppose that the monopolist chooses q to maximise its profit. The consumer surplus at this profit maximising quantity would be?
Suppose a monopolist has a revenue function: R(y) = 20y Suppose further their cost of production is c(y) = 10y. Which of the following is true when the monopolist produces the optimal quantity? None of the other answers are correct Price is 10 Output is 6 O Price is 6 The cost of production is 25
Assume that the market for coal is a monopoly market. We have the following: ?(?) = ?? − ?? ????? ? > ? ??(?) = ?? ? − ?? ? + ?? + ??? a. Find the monopolist price and quantity. b. What is the value of Profit (or loss) at monopolist equilibrium price and quantity? c. What is the value of dead weight loss (DWL) at monopolist price and quantity?
1. A monopolist has a production function, Q = AL KB with 0 < a+B < 1. The cost of capital is r, the wage rate is w, and the monopolist takes both as given. The demand function for the monopolist is M Q 1+ exp {p} !! What is the long-run demand for labor?
The figure at right shows the demand line, marginal revenue line, and cost curves for a single-price monopolist. Now suppose the monopolist is able to charge a different price on each different unit sold. The profit-maximizing quantity for the monopolist is whole number.) (Round your response to the nearest D Price ($) 1000- 900- 800- 700- 600- 500- 400- 300- 200- 100- 0- 0 MC ATC D MR 50 100 150 200 250 300 350 400 450 500 Quantity 17
3. Suppose a software monopolist faces two markets for its software, students and professionals. The demand curve of professionals is given by Qp = 200-2Pp and the demand curve by students is given by Qs = 150 - 3Ps. The firm's cost function is C(Q) = 400+5Q. (a) If the firm can price discriminate, what price should it charge in each market to maximize profits? How much profit does it earn? (b) If the firm cannot price discriminate, what price should it charge? Verify that it sells to both markets at this price. How much profit does it earn? Hint: If the firm cannot price discriminate, this means it must treat the two markets as a single combined market.