4) Suppose there are two firms that compete in prices, say firms 1 and 2, but that thefirms produce differentiated products. Suppose that the demand for firm 1 is9₁(P₁, P2) = 10 - 2p₁ + P₂ and the demand for firm 2 is q2 (P2, P₁) = 10 - 2p₂ + P₁.Also, assume that firm 1 has a constant marginal cost of c₁ = 2 and firm 2 has a constantmarginal cost of c₂ = 3.a) What are the reaction functions for both firms?Solve for the Bertrand equilibrium in prices.b)c) Now, suppose firms 1 and 2 agree to merge. However, under the merger onlyfirm 1 will operate and firms 1 and 2 will split the resulting profits equally. Willboth firms agree to such a plan or do they prefer the Bertrand outcome?

Given information q1=10-2P1+P2 q2=10-2P2+p1 MC1=2 MC2=3

Answered: 4) Suppose there are two firms that…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.4P

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5. Consider a market where there are two mers with inverse demand func- consu tions p(q1) = 10 -91 and p(q2) = 5-92. (a) Suppose there is a single firm with inverse supply function p(q) = }q. Find the competitive equilibrium. (b) Find the elasticity of demand and supply at the equilibrium. (c) Suppose instead that there are three firms with the identical inverse sup- ply function given in part (a). Find the competitive equilibrium.
A4
1 Consider two identical firms with a unit cost of production of $10 and a market demand of p= 60-y. (a) What is firm 1’s optimal output level as a function of firm 2’s output? (b) What is firm 2’s optimal output level as a function of firm 1’s output? (c) What is the Cournot equilibrium output level for these firms? (d) What is the Cournot equilibrium price level? Show your work step by step.
Please no written by hand solution Considerthe following problem. There are five firms producing a homogenous good and competing in quantities simultaneously. The demand function for this good is given by D(p) = 100−p, where p denotes price. The marginal cost is the same for all firms and equals 40 Answer the following questions. (a) Compute the equilibrium quantities and profits of each firm. (b) Now suppose that two of these firms (say firms 1 and 2) want to merge. (The remaining firms stay unchanged.) Merging, however, is costly. To merge, each merging firm has to pay a fixed cost F. Determine the highest fixed cost F that the two firms would be willing to pay in order to proceed with the merger.
6. Suppose the market demand for a homogeneous product is given by P = a-bQ, where a and b are positive constants. There are n identical firms, each of which is capable of producing the product at constant marginal cost c > 0. Assume c
2) Assume that there are 2 firms producing an identical product. Both firms have the same total cost function TC(q) =q2. The inverse demand function for the firms' output is p=120 Q, where Q is the total output and p is price. 1. What are the equilibrium price, output and profits of each firm if they are competing with each other? (Hint: Consider the equilibrium in a Cournot game.) 2. What happens if they form a cartel? Calculate the equilibrium price, output, and profits for the cartel? 3. If a single firm cheated, what would its output and profits be, assuming the other firm maintains the cartel price? Calculate the new outputs and profits for bath firms: 4. Discuss why it is hard to enforce a cartel. Explain using words. DO NOT do any calculations. DO NOT draw any graphs. 5. What can the cartel members do to enforce the cartel agreement? Propose a method. Describe the method using words. DO NOT do any calculations. DO NOT draw any graphs.
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3. The (market) inverse demand function for a good is as follows: 12- 2q if q = [0,6], if q> 6. Pp(q) = { 12 There are two firms: N = {1,2}. Each firm's cost function is such that producing a units of the good incurs cost 2r. We consider the Cournot competition of the two firms. That is, they simultaneously choose their quantities. The firms are profit-maximizers. (1) Find a Nash equilibrium. (2) What is the size of the deadweight loss incurred by the Duopoly, compared to the competitive equilibrium allocation?
an Problem 5. Consider following price competition between 2 firms. Both firms choose their prices (p, and p2) simultaneously and the market demand function given by q 10-min{p₁, P2}. Assume production costs are 0 for both firms. Thus, the payoff (profit) function for firm i is: u.(Pi. Pj) (10-P.)Pi (10-pi)Pi 2 Notice that this function is not continuous in pi 1 if Pi Pj
2.- Each of two firms, firms 1 and 2, has a cost function C(q) = 1 2 q; the demand function for the firms' output is Q = 1.5-p, where Q is the total output. Firms compete in prices. That is, firms choose simultaneously what price they charge. Consumers will buy from the firm offering the lowest price. In case of tying, firms split equally the demand at the (common) price. The firm that charges the higher price sells nothing. (Bertrand model.) (a) Formally argue that there could be no equilibrium in prices other than p1 = p2 = 1 2. (b) Solve the same problem, but this time assuming that firms compete in quantities.Now, suppose that firm 1 has a capacity constraint of 1/3. That is, no matter what demand it gets, it can serve at most 1/3 units. Suppose that these units are served to the consumers who are willing to pay the most. Thus, even if it sets a price above that of firm 1, firm 2 may be able to sell some output. (c) Obtain the (residual) demand of firm 2 (as a function of its own…

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