Consider a market with three firms (i - 1, 2, 3), which have identical marginal costs e = c = Cg = 20. The inverse demand function is given by P = 100 – Q. where Q = q, + 9; + 9s- a) Identify the reaction functions for each firm and compute the Cournot equilibrium, ie, the market price and quantity. b) What happens to the market price if all three fims merge compared to part (a)?

Consider a market with three firms (i - 1, 2, 3), which have identical marginal costs e = c = Cg = 20. The inverse demand function is given by P = 100 – Q. where Q = q, + 9; + 9s- a) Identify the reaction functions for each firm and compute the Cournot equilibrium, ie, the market price and quantity. b) What happens to the market price if all three fims merge compared to part (a)?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.3P

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6. Two firms, Firm 1 and Firm 2 and are competing in quantities. The demand they are facing is given by p=1-91-92, with p being the price of the good, and 9₁ and 92 the quantities produced by firm 1 and 2 respectively. The total cost of firm 1 is TC1 (91) = 9₁ and the one of firm 2 is TC₂ (92) = 292. (a) Find the Cournot equilibrium. (b) The government decides that it wants to make the market more competitive. As such it decides to offer to Firm 1 a license to become the leader in the market. The licence costs F, and if Firm 1 buys it, it will be allowed to choose its quantity before Firm 2. What is the maximum Firm 1 would be willing to pay for this license?
1. The market (inverse) demand function for a homogeneous good is P(Q) = 10 - Q. There are two firms: firm 1 has a constant marginal cost of 2 for producing each unit of the good, and firm 2 has a constant marginal cost of 1. The two firms compete by setting their quantities of production, and the price of the good is determined by the market demand function given the total quantity. a. Calculate the Nash equilibrium in this game and the corresponding market price when firms simultaneously choose quantities. b. Now suppose firml moves earlier than firm 2 and firm 2 observes firm 1 quantity choice before choosing its quantity find optimal choices of firm 1 and firm 2.
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2. A homogenous good industry consists of two firms (firm 1 and firm 2). Their cost functions are cq and cq2, respectively, where c<2. The market demand function is p=10-Q, where Q=q₁+q₂. (a) Assume that the two firms play the Bertrand price game. Find the firms' choices in the Bertrand-Nash equilibrium. (b) Assume that the two firms play the Cournot quantity game. Find the firms' choices in the Cournot-Nash equilibrium. (c) Assume the two firms play the Stackelberg game with firm 1 as the leader. Find the firms' equilibrium choices in the Stackelberg equilibrium.
1-Consider two firms facing the demand curve P = 20 – 5Q. The firms' cost functions are MC1=MC2=10. a. Determine reaction curves and Cournot equilibrium point.
QUESTION 1A) Two cournot competitors face inverse demand P = 50 - Q. Where, Q = q1+q2, is the total output of firms 1 and 2. What are the equilibrium output levels for q1 and q2, If firm 1 marginal cost is 1, and firm 2's marginal cost is 12? QUESTION 1B. Continuing with the inverse demand, P = 50 - Q, if each firm has a marginal cost of 0, what is the difference between the equilibrium price under Cournot competition and under Bertrand competition? b. C. d. a. The Cournot price is higher than the Bertrand price by 50. The Cournot price is lower than the Bertrand price by 25. The Cournot price is higher than the Bertrand price by 50/3. Equilibrium prices under Cournot and Bertrand are the same, so the difference is zero.
The inverse market demand curve for salmon is given by P(Y) = 100 – 2Y, and the total cost function for any firm in the industry is given by TC(y) = 4y. a. Suppose that two Cournot firms operated in the market. What would be the reaction function for Firm 1 and the reaction function of Firm 2? (Notes: The marginal cost is not zero). If the firms were operating at the Cournot equilibrium point, what would the industry output and price be? b. For the Cournot case, draw the two reaction curves and indicate the equilibrium point on the graph
4. In 2056, there are two mining firms operating on the moon, extracting Helium 3. Once both firms have entered the market, they compete a la Cournot. The market inverse demand function is given by P(Q) = 8 – Q. Assume that both firms have the total cost functions = 2+ 2q. Let the star superscript* denote equilibrium quantities/prices/profits. Which C(q): of the following statements is true? (a) qi = 4 = 4 (b) qi > qž (c) p* = 6 (d) nj < T (e) Tỉ = = 2 5. Assume the same demand and cost structures as in question 4, but now firm 1 enters the market first and firm 2 follows, as in the Stackelberg model from lecture (both firms are guar- anteed to enter; the only choice is quantities produced). Which of the following statements regarding the equilibrium outcome is FALSE? (a) The first mover produces a greater quantity than the second mover (b) Total market output is Q* = 4.5 (c) The second mover will receive a negative profit (d) The first mover will receive a greater profit than the…
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