Consider two duopolists whose demand functions are given by 91 = 2-2p1 - P2, and q2 = 2-2p2 - P1 where 91, 92, P₁ and p2 are quantities and prices. Their constant marginal costs are given by C1, C2 Assume that c2 = 1 is known to both firms, but c₁ is known only to firm 1. Firm 2 knows that c₁ car be either 1.2, or .8, with equal probabilities. The firms compete in prices in a simultaneous move game Define Firm 2's equilibrium price as p2. Define Firm 1's equilibrium as pth if its cost is high and pil i its cost is low. Then, equilibrium prices will be such that: 8 (a) pt¹ < p < p < 10 *h 10 (b) pil

Consider two duopolists whose demand functions are given by 91 = 2-2p1 - P2, and q2 = 2-2p2 - P1 where 91, 92, P₁ and p2 are quantities and prices. Their constant marginal costs are given by C1, C2 Assume that c2 = 1 is known to both firms, but c₁ is known only to firm 1. Firm 2 knows that c₁ car be either 1.2, or .8, with equal probabilities. The firms compete in prices in a simultaneous move game Define Firm 2's equilibrium price as p2. Define Firm 1's equilibrium as pth if its cost is high and pil i its cost is low. Then, equilibrium prices will be such that: 8 (a) pt¹ < p < p < 10 *h 10 (b) pil

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.4P

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1. 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?
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Assume that two companies (A and B) are duopolists that produce identical products. Demand for the products is given by the following linear demand functions:P=200-QA-QBwhere QA and QB are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies areTCA = 1500+55 QA +QA2TCB = 1200+20 QB +2QB2Assume that the firms form a cartel and maximize total industry profits,a. Determine the optimal output and selling price for each firm.b. Determine Frim A, Firm B, and total industry profits at the optimal solution foundin part (a).c. Show that the marginal cost of the two firms are equal at the optimal solutionfound in part (a).
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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…
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