Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Question
Chapter 15, Problem 15.2P
a)
To determine
To determine profit maximising
b
To determine
Nash
c)
To determine
Nash
d)
To determine
Nash equilibrium quantities for
e)
To determine
To show
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Suppose that firms’ marginal and average costs are constant and equal to c and that inverse market demand is given by P = a – bQ, where a, b > 0
(a) Calculate the profit-maximizing quantity-price combination and for a monopolist.
(b) Calculate the Nash equilibrium quantities for Cournot duopolists, which choose quantities and for their identical products simultaneously. Also compute market output and market price.
(c) Calculate the perfectly competitive equilibrium price and market output.
(d) Suppose now that there are n identical firms in a Cournot model (oligopoly). Compute the Nash equilibrium quantities as functions of n. Also compute market output and market price.
(e) Verify (i) that the monopoly outcome from part (a) can be reproduced in part (d) by setting n = 1;
(ii) that the duopoly outcome from part (b) can be reproduced in part (d) by setting n = 2;
(iii) that letting n approach infinity yields the same market price and output as…
Suppose that firms’ marginal and average costs are constant
and equal to c and that inverse market demand is given by
P = a – bQ, where a, b> 0.
a. Calculate the profit-maximizing price-quantity combi-
nation for a monopolist. Also calculate the monopolist's
profit.
b. Calculate the Nash equilibrium quantities for Cournot
duopolists, which choose quantities for their identical
products simultaneously. Also compute market output,
market price, and firm and industry profits.
Please
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- Pleasearrow_forwardCournot duopolists face a market demand curve given by P = 60 – 1/2Q, where Q is total market demand in units. Each firm can produce output at a constant marginal cost of $15/unit. a) What is the equilibrium price and quantity produced by each firm? b) What if the firm's engaged in Bertrand competition? c) What if one of the firms chose its quantity before its competitor? What is the name for this sort of competition? d) Which of the three forms of competition gives the greatest social surplus?arrow_forwardA monopolist can produce at a constant average and marginal cost of ATC = MC = $5. It faces a market demand curve given by Q = 53 - P. Suppose there are N firms in the industry, all with the same constant MC = $5. Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also show that as N becomes large, the market price approaches the price that would prevail under perfect competition. (Hint: your answers will be functions of N)(BONUS)arrow_forward
- Imagine any market divided by 2 Cournot oligopolists who have identical costs Marginal cost = Average cost = 200. About this market, ask yourself: a) If the demand curve for this market is given by Q = 1250 - 2.5P, where Q is the total quantity demanded in the market and P is the selling price, both given in units, what is the reaction curve of the oligopolists? b) What will be the quantity produced and the selling price of the oligopolists? c) A strategist considers that a good marketing campaign would be able to expand the Demand of this market to Q = 1,500 - 2.5P and that in this way, oligopolists could produce the same amount and make significantly greater profits. Such a campaign would generate a reduction in profits in the order of 70,000. Is it worth making this investment in marketing?arrow_forwardConsider two Cournot oligopolists, firm 1 and firm 2, in a homogenous product market. The market demand is P = 100 - 3Q and each firm has a constant marginal cost MC=10. The market price of equilibrium and total quantity in the market is: Select one: a. P* 30 and Q* = 20 O b. P* 40 and Q* = 20 ○ c. P* = 40 and Q* = 30 O d. P*20 and Q* = 30arrow_forwardIn a market with a Duopoly, if Market Demand is P=300-Q find the Cournot reaction curves and the Cournot Quantity solutions then deduce the Price in the case where Marginal Costs curves for either of the Duopoly firms is MC1=q1+30 and MC2=q2+30. Compare your results to the case where a Monopolist that has a MC=Q+30 replaces the Duopoly. What are the Monopoly Quantity and Price? Which quantities are bigger, Cournot or Monopoly? What is the Consumer Surplus in both cases? Set-up the Oligopoly model in a game theoretical prisoner’s dilemma framework. Explain briefly the strategies and how you reach the Nash Equilibrium.arrow_forward
- Suppose the inverse demand function for two Cournot dupolists is given by P= 10 – (Q1+Q2) and their cost are zero.a) What is each firm marginal revenue?b) What are the reaction function for the two firmsc) What are the Cournot equilibrium outputd) What is the equilibrium price?arrow_forwardTom is a monopolist input supplier to Dic and Harry. Tom's marginal cost is 1. Dic and Harry are duopolists with production function q = x1/2. No firm has fixed costs. The demand for the final product is given by Q = 100 – p. a) Assume Dic and Harry buy the input from Tom at price k. What are their cost functions? b) Find the Cournot equilibrium quantities. c) What price, k, should Tom set? -arrow_forward1. Consider two duopolists who each have a constant marginal cost c = e2 = 3 and face inverse demand P = 15 – Q,where Q = Q1 + Q2 is the total output of both firms. 1. Find the Cournot equilibrium quantity for each firm, the resulting market price, and the profits for each firm. 2. Find the Stackelberg equilibrium quantities for each firm, and the price, and the profits for each firm supposing that Firm 1 is the industry leader. 3. Suppose that Firm 2 figures out a way to lower its marginal cost to ez = 0 while firm 1 still has a marginal cost equal to 1: c = 3. How does this affect the Cournot equilibrium quantities, price, and profits? 4. How does this affect the Stackelberg equilibrium (with Firm 1 still as the leader) quantities, price, and profits?arrow_forward
- Assume firms' marginal and average costs are constant and equal to c and that inverse market demand is given by P = a - bQ where a, b > 0. Suppose now the market is served by 2 firms (one leader, and one follower) that choose quantities for their identical products. Calculate: i. ii. iii. iv. The Nash equilibrium quantities for the Stackelberg duopolists Market output Market price Firm profitarrow_forwardMy question is, Assuming the firms are Bertrand duopolists, what is likely to happen? Explain verbally?arrow_forwardPlease see the attached photo, and provide detialsarrow_forward
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