Assume that the market demand and the costs of the duopolists are: P=120-0.4(QA + QB) TCA=5QA TCB= 0.2Q2B Also assume that firm B is the sophisticated leader, Determine: a. The reaction curve of A ,the reaction curve of B and the profit function of A b. Stackelberg equilibrium output level for firm A and Stackelberg equilibrium output level for firm B c. The market price

Assume that the market demand and the costs of the duopolists are: P=120-0.4(QA + QB) TCA=5QA TCB= 0.2Q2B Also assume that firm B is the sophisticated leader, Determine: a. The reaction curve of A ,the reaction curve of B and the profit function of A b. Stackelberg equilibrium output level for firm A and Stackelberg equilibrium output level for firm B c. The market price

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.2P

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Consider any market that has a demand curve given by: Qd = 240 - 2P. Where Qd is the total quantity demanded in the market, given in millions of units and P is the market price, calculated in monetary units. Imagine that there are 2 Cournot oligopolists operating in this market with Cmg = CVme = 15 and fixed monthly costs equal to 1,400. About this market, ask yourself: a) What is the reaction curve of oligopolists? b) What will be the production of each of the companies? c) What is the selling price practiced by oligopolists? d) What is the profit of each of the oligopolists? e) Imagine that one of the companies managed to implement a process innovation capable of halving its Cmg and CVme, so that they would go from 15 to 7.5. This investment implies an additional monthly expense of $1,800. Discuss the statement: "If this situation occurs, the innovative company will not implement variable cost reduction, as the quantity supplied in the market will increase very little; prices will…
(a) Firms A and B are Cournot duopolists producing a homogeneous good. The inverse market demand is given by P= 100 Q, where P is the market price and Q is the total quantity demanded. Each firm has marginal cost equal to 40 and there are no fixed costs. Calculate the total industry output in this market. Derive also (i) the market price, the total profit of the two firms and the consumer surplus. (ii) monopoly. Calculate the total industry output after the merger. Derive also the market price, profit and consumer surplus after the merger. Explain intuitively any changes in these variables if the merger occurs. Suppose the two firms propose to merge to become a
Q3. There are two firms selling differentiated products. Firm A faces the following demand for his product: e, = 20 – -P, + -P, 2. Firm B faces the following demand: 1 P. +-P, 2. 0, = 220- Assume that the marginal cost is zero both for firm A and firm B. What are the equilibrium prices of a simultaneous price competition? What would the equilibrium prices be if A is the leader and B is the follower?
Suppose you are employed at a monopolistic company as a research (pricing) economist and you are deriving the behavior of two markets based on demand curves given by: Di(P1) 3 50 — Pі D:(p>) — 50 — 2р2 Assume that the marginal cost is constant at $8 a unit. (a) If it can price discriminate, what price should it charge in each market in order to maximize profits? (b) If it can't price discriminate, what price should it charge?
Tom 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? -
2. Stackelberg Firms 1, 2 and 3 compete in quantities. The inverse market demand is given by p = 400 (91 +92 +93), where 91, 92 and q3 are the quantities produced by firms 1, 2 and 3, respectively. The marginal cost for firm 1 is c₁ = 20, and the marginal cost for both firm 2 and firm 3 is 40. The order of play is as follows: Firm 1 first sets a quantity q₁. Then, firms 2 and 3 observe q₁ and simultaneously set q2 and 93. Each firm sets its quantity to maximize its own profits. (a) Let us first consider the optimal action of firm 2. Given a value q₁ initially set by firm 1 and a value of q3 set by firm 3, what is the value of q2 that maximizes the profits of firm 2? Hint: Your answer should provide q2 in terms of 91 and 93. (b) Notice that, after firm 1 sets q1, a subgame starts, in which firms 2 and 3 simultaneously set q2 and 93. Given 91, find the values of q2 and q3 that firms 2 and 3 must set in a Subgame Perfect Nash Equilibrium. Hint: Your answer should provide q2 and q3 in…
Question 2: A market is contested by two firms, A and B, who compete in selling a homoge- neous good. Market demand is given by Q = 240 3p, where p is the price of the good. Firm A has constant marginal costs of 20 as long as it produces 100 units or fewer. Every unit above 100 costs 75 to produce. Firm B has the cost function CB = Q3, where QB is the quantity produced by firm B. The firms sequentially choose prices. A is the market leader and chooses its price first; B chooses its price after observing A's price. If they charge the same price each sells half of the demand at that price. The firms cannot turn away customers. What is the equilibrium price in this industry?
QUESTION THREE The market demand faced by duopolists is given by P=100-0.4Q and their respective cost functions are C1=5Q1,and C2=0.1Q22 where, Q1 and Q2 are quantities produced and supplied by duopolists 1 and 2 respectively so that Q= Q1+Q2 Derive the reaction equations Calculate quantity of the leader duopolist, Firm 1 Calculate quantity of the follower
Suppose two firms engage in simultaneous quantity competition. Both firms have 0marginal cost. Firm A : P(Q)= 24-Q Firm B: P(Q)= 24-2Q a) Find the Nash Equilibrium quantities q^NE and profits.(b) Find the Monopoly Quantity QM and Profit.(c) Now suppose the game is repeated infinitely and each firm has a common discountfactor δ. Find the required discount factor to sustain the following grim triggerstrategy as a SPNE: Play Q^M /2 if this has been played in every previous period,otherwise play q^NE.
1. The cost function for any potential firm in a manufacturing industry is C(y) = 2 + 8y + 2y? (if a firm exits the industry, then its cost is zero). The inverse market demand function is given by P(y) = 100 – 2y. (c) If the government wants to limit the number of firms to 5 in this industry by issuing only 5 licenses (all the firms are Cournot oligopolists), what is the highest price that the government can charge for the license?
Consider any market that has a demand curve given by: Qd = 240 - 2P. Where Qd is the total quantity demanded in the market, given in millions of units and P is the market price, calculated in monetary units. Imagine that there are 2 Cournot oligopolists operating in this market with Cmg = CVme = 15 and fixed monthly costs equal to 1,400. About this market, ask yourself: a) What is the profit of each of the oligopolists? b) Imagine that one of the companies managed to implement a process innovation capable of halving its Cmg and CVme, so that they would go from 15 to 7.5. This investment implies an additional monthly expense of $1,800. Discuss the statement: "If this situation occurs, the innovative company will not implement variable cost reduction, as the quantity supplied in the market will increase very little; prices will remain very close to what they are today and its profits will not increase"
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…