3) Two firms produce a homogeneous product. Inverse demand is P(Q) = D− Q. Firm 1 has a constant marginal cost of c₁ and firm 2 has a constant marginal cost of c₂. Assume that D> C₂ > C₁ > 0. a) Solve for the competitive equilibrium price and output level for each firm. b) Solve for the Cournot equilibrium price and output level for each firm. c) What is the total deadweight loss arising from Cournot competition in this market? d) Productive inefficiency refers to the extra costs to produce a given amount relative to the lowest cost method of producing that amount. How much of this loss is due to productive inefficiency rather than market power?

3) Two firms produce a homogeneous product. Inverse demand is P(Q) = D− Q. Firm 1 has a constant marginal cost of c₁ and firm 2 has a constant marginal cost of c₂. Assume that D> C₂ > C₁ > 0. a) Solve for the competitive equilibrium price and output level for each firm. b) Solve for the Cournot equilibrium price and output level for each firm. c) What is the total deadweight loss arising from Cournot competition in this market? d) Productive inefficiency refers to the extra costs to produce a given amount relative to the lowest cost method of producing that amount. How much of this loss is due to productive inefficiency rather than market power?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.
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.
A) Suppose there are just two firms, 1 and 2, in the oil market and the inverse demand for oil is given by P = 90 – 3Q. The marginal cost for each firm is €18. Calculate the level of output that each firm would produce at the Cournot equilibrium. B) Suppose there are just two firms, 1 and 2, in the oil market and the inverse demand for oil is given by P = 60 – Q. The marginal cost for each firm is €36. What price should Firm 1 charge at the Cournot equilibrium? C) Consider the production function Q = 10KL. Will the MRTS for this production function remain constant along the Q = 200 isoquant? Explain briefly.
Suppose that there are two firms in an industry and they face market demand y=400-0.5p where y=y1+y2 . The total cost functions of the firms are C1(y1)= 40y1 and C2(y2)= 2y22. a) Assume initially that the firms enter into Cournot competition. Calculate the equilibrium market price and each firm’s equilibrium output. That is, find y1c, y2sand pc.b) Calculate the equilibrium market price and each firm’s equilibrium output assuming that firm 2 is the Stackelberg leader and firm 1 is the follower. That is, find y1s, y2sand ps.
The inverse demand curve for a product is p = 20 - 0/5, where Q is the total volume brought to the market. At present two firms serve this market. Firm 1 has constant marginal costs of 5, while Firm 2 has constant marginal costs of 2. Both firms have fixed costs of 100. a) Assuming the fixed costs are sunk, calculate the equilibrium quantities, price and profits for the two firms. b) Now assuming the fixed costs are not sunk, calculate the equilibrium quantities, price and profits for the two firms. c) Discuss any competition issues raised by your answer in part b). d) Discuss the theoretical relevance of sunk costs to competition in markets.
a) Suppose that the two firms engage in Cournot competition. Find the equilibrium price PNE in the industry, the equilibrium outputs QANE and QBNE, as well as the profits πANE and πBNE, for each firm. b) Suppose the marginal cost for firm B increases from $20 to $140, while everything else remains unchanged. Find the new equilibrium price PNE in the industry, the new equilibrium outputs QANE and QBNE, as well as the new profits πANE and πBNE for each firm. c) Suppose that, in addition to the marginal cost increase from $20 to $140 from sub question b), firm B also has a fixed cost of $2500, out of which $2100 may be recouped if it shuts down; everything else remains unchanged. In this case, what will firm B’s optimal output be? (Justify your answer.) What will firm A’s profit be?
. The market for widgets consists of two firms that produce identical products. Competition in the market is such that each of the firms independently produces a quantity of output, and these quantities are then sold in the market at a price that is determined by the total amount produced by the two firms. Firm 2 is known to have a cost advantage over firm 1. A recent study found that the (inverse) market demand curve faced by the two firms is P = 280 – 2(Q1 + Q2), and costs are C1(Q1) = 3Q1 and C2(Q2) = 2Q2. a. Determine the marginal revenue for each firm. b. Determine the reaction function for each firm.
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.
Two firms produce a homogeneous product. Inverse demand is P(Q)=D-Q. Firm 1 has a constant marginal cost of c1 and firm 2 has a constant marginal cost of c2. Assume that D>c2 >c1 >0. a) Solve for the competitive equilibrium price and output level for each firm. b) Solve for the Cournot equilibrium price and output level for each firm. c) What is the total deadweight loss arising from Cournot competition in this market d) Productive inefficiency refers to the extra costs to produce a given amount relative to the lowest cost method of producing that amount. How much of this loss is due to productive inefficiency rather than market power?
1. marginal costs e, = c, = c, = 20. The inverse demand function is given by P = 100 - Q. where Q = q, + 4: + 93- Consider a market with three firms (i - 1, 2, 3). which have identical a) Identify the reaction functions for each firm and compute the Cournot equilibrium, i.e., the market price and quantity. b) What happens to the market price if all three firms merge compared to part (a)?
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?
Here is a market with three firms: 1, 2, and 3. The demand curve is P=100-Q. There is no fixed cost but the marginal cost 10 for all firms. Firm 1 is a leader firm so that it decides the quantity Q1 first. Then two firms respectively decide their quantities Q2 and Q3 simultaneously. 1) At an equilibrium (SPE), Q1 is Q2=Q3= 2) At the equilibrium, (the market quantity) Q= and (the market price) P= 3) The profit of firm 1 is while the profit of firm 2 and 3 respectively is