Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm I faces a demand function of q₁ = 100 - 2p₁ + P2, where q₁ is Firm 1's output, p₁ is Firm 1's price, and P2 is Firm 2's price. Similarly, the demand function Firm 2 faces is q2 = 100 - 2p2 + P₁. Solve for the Nash-Bertrand equilibrium.

Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm I faces a demand function of q₁ = 100 - 2p₁ + P2, where q₁ is Firm 1's output, p₁ is Firm 1's price, and P2 is Firm 2's price. Similarly, the demand function Firm 2 faces is q2 = 100 - 2p2 + P₁. Solve for the Nash-Bertrand equilibrium.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.4P

See similar textbooks

Similar questions

Problem 1. HHI in the Bertrand Triopoly Equilibrium It's a Bertrand Triopoly - hence we know there are 3 firms in the industry-in-question, who competes in "price". The inverse demand functions for Firm 1, 2, and 3 are as follows: q1 = 40 - 1.5p1 +0.5p2 +p3 q2 = 40 + 1.5p1 - 3p2+p3 q3 = 40 + 2p1 + 1.5p2 - 4p3 For each firm, the marginal cost of production is $2.50/unit produced and sold. Apparently, the firms' products are differentiated. You cannot impose symmetry across firms. Therefore, please solve each firm's profit maximization problem, impose equilibrium, and solve for each firm's "action" in equilibrium. After that, please calculate the Herfindahl- Hirschman Index (HHI) in the industry in equilibrium.
8. Suppose there are two identical firms in an industry who compete by setting quantities. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by 92. Each firm faces a constant marginal cost of 3. Let Q denote total output, 1.e. Qq1 +42. The inverse demand curve in the market is given by P-15-Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. (b) If the firms could collude, what would be the total output in the mar- ket? Assuming each firm produces half of the collusive output, what is the profit of each firm?
8. Suppose there are two identical firms in an industry who compete by setting quantities. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by 92. Each firm faces a constant marginal cost of 3. Let Q denote total output, 1.e. Q-91 +42. The inverse demand curve in the market is given by P-15-Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. "// (b) If the firms could collude, what would be the total output in ket? Assuming each firm produces half of the collusive output, the profit of each firm? the mar- what is (c) Suppose each firm produces half of the collusive output identified in part (b). Firm 1 considers a deviation from this arrangement. What would be the best deviating output of firm 1 and its deviation profit? (d) Suppose firms interact repeatedly over an infinite horizon, and firms have a common discount factor & € (0,1). Specify a trigger strategy for each firm to sustain the collusive arrangement as an…
Suppose that identical duopoly firms have constant marginal costs of $0 per unit. Firm 1 faces ademand function of q1 = 100 – 2p1 + p2, where q1 is Firm 1’s output, p1 is Firm 1’s price, and p2 isFirm 2’s price. Similarly, the demand Firm 2 faces is q2 = 100 – 2p2 + p1. Please solve for theBertrand equilibrium.
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?
6. Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm 1 faces a demand function of q1 = 100– 2p1+p2, where q1 is Firm l's output, pi is Firm l's price, and p2 is Firm 2's price. Similarly, the demand Firm 2 faces is q2 = 100– 2p2+P1. Solve for the NE.
Consider a duopoly market with 2 firms. Aggregate demand in this market is given byt Q = 500 – P, where P is the price on the market. Q is total market output, i.e., Q = QA + QB, where QA is the output by Firm A and QB is the output by Firm B. For both firms, marginal cost is given by MC = 20, i=A,B. « Assume the firms compete a la Cournot. e a) Find the inverse demand in this market. Note that marginal revenue for both firms is given by MRA=500-2QA-QB, MRB=500-QA-2QB. b) Describe what a best-response curve is and how to find it. c) Derive the best-response function for each firm. d) What are the equilibrium quantities? e) What is the total quantity supplied on this market? f) What is the equilibrium price in this market?
3. Consider a duopoly with a demand curve given by P = a -bQ, where a and b are positive constants and Q is the total production by the two firms. Firms sell identical goods and have an identical constant marginal cost of production c. Fixed costs are equal to zero. We assume firms choose quantities simultaneously (Cournot competition). a. Obtain the first order condition of profit maximization for each firm. Use graphical analysis and economic intuition to explain what they represent. b. Obtain the profit maximizing quantity for each firm. Explain what they represent using game theory concepts c. Demonstrate using relevant graphical analysis and economic intuition that the results obtained in b are not a Pareto Optimum for the firms involved. d. How would the graphical analysis in part a change if Firm A had a fixed cost of production
Help me please
Suppose that identical duopoly firms have constant marginal costs of $10 per unit. Firm 1 faces a demand function of where q, is Firm 1's output, p, is Firm 1's price, and p., is Firm 2's price. Similarly, the demand Firm 2 faces is Solve for the Bertrand equilibrium. In equilibrium, p, equals $ and p2 equals $ (Enter numeric responses using integers.) 9₁-160-2p₁ + 1P2 92 = 160-2p₂+1P1-
E1 Find Bertrand equilibrium and its outputs for the following asymmetric duopoly:q 1(p1, p2) = 16 - p1 + 0.5 p2, C1(q1) = 4q1;q 2(p1, p2) = 16 + 0.5 p1 - p2, C2(q2) = 6q2.(Note that the average and marginal costs are: AC1=MC1 = c1 = 4, AC2=MC2 = c2 = 6)
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 k firms that choose quantities for their identical products simultaneously. Calculate: i. ii. iii. iv. The Nash equilibrium quantities for the Cournot firms as functions of k. 2 Market output and price as a function of k Firm profit as a function of k Using your answers in i, ii, iii and iv, describe what happen to firm output, market output, market price and firm profit as the number of firms increases.