in which two firms compete. Firm 1 faces TC1(Q) = 18Q and firm 2 faces TC2(Q) = 9Q. Suppose that firm 1 chooses their quantity first, then firm 2 sees that quantity, and then firm 2 sets their quantity (Stackelberg duopoly). (a) Find the reaction function for firm 2 (b) What is the marginal revenue for firm 1 (given that they know that firm 2 will best respond)? (c) Find the Stackelberg equilibrium (d) Determine profits for each firm and consumer surplus. (e) Which firm is better off?

in which two firms compete. Firm 1 faces TC1(Q) = 18Q and firm 2 faces TC2(Q) = 9Q. Suppose that firm 1 chooses their quantity first, then firm 2 sees that quantity, and then firm 2 sets their quantity (Stackelberg duopoly). (a) Find the reaction function for firm 2 (b) What is the marginal revenue for firm 1 (given that they know that firm 2 will best respond)? (c) Find the Stackelberg equilibrium (d) Determine profits for each firm and consumer surplus. (e) Which firm is better off?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A community's demand for monthly subscription to a streaming music service is shown by the following table. Assume that there are only two firms serving this market (Firm A and Firm B), each firm offers the same quality of service and music selection, and that each firm’s marginal cost is constant and equal to 0 (zero). (please refer to table provided) If this market were highly competitive instead of a duopoly, the quantity of streaming movie subscriptions purchased each month would be ______ If the two firms agreed to each supply one half of the quantity a monopoly would supply, the contract would specify that each firm would supply ____
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Consider an industry with 4 firms with the same total cost function TC(q) = 20q. The demand function is p= 260 − 2Q. (a) Solve for Cournot equilibrium: how much each firm produces in equilibrium? What is an equilibrium price and profits? (b) What will be the profit of each firm if all the firms join the cartel? (c) If one of the firms wants to deviate from the cartel agreement, what output should it set? Calculate the profit of the cheating firm.
1. Consider two firms producing hats, A and B. The demand functions are as follows: qĄ(Pa, PB) = 592 – 8pA + 4pB and qB (PA, PB) = 400 – 8pg + 4pA Firm 1 has constant marginal cost c prices, i.e. the game's joint strategy space is {(pa, PB) E R² | Pa > 0,Pp > 0}. 10 per hat and firm 2 has c2 = 7. The firms decide on 1.1. What is the nature of the relationship between the hats produced by A and the hats produced by B? [No calculations required.] 1.2. Write down payoff functions for the two firms. 1.3. Derive best-response functions for the two firms.
Suppose two Bertrand competitors, F1 and F2, make identical products for a market with inverse demand P = 600 – 0.5Q. Both firms have the same costs Ci = 20qi, and each firm has sufficient capacity to supply the entire market. a. What prices will the firms choose? How much might each produce and what profit would they make? Is the result a Nash equilibrium? Explain. b. Suppose F1 improves its efficiency, reducing its cost to C1 = 16q1. What will happen in this market? Explain. c. Assume now that the firms have their original identical costs, but that F1 has only 100 units of capacity and F2 has only 200 units of capacity. What prices will the firms choose now? Explain why neither firm will want to decrease its price at the equilibrium you identify. Why would neither firm want to increase its price? Prove this for F1.
Two firms sell substitutable products; the market price is: P = 90-Q, where Q Q₁ + Q2 is the total market quantity, which consists of Q1₁ (the quantity produced by Firm 1) and Q2 (the quantity produced by Firm 2). The firms choose their quantities simultaneously. Firm 1's costs are C₁ 6Q₁ + Q². Firm 2's costs are C₂ = Q². = O Which is the payoff function for Firm 2? O π₂ = 90Q₂ - 2 Which is the best response function for Firm 1? O π₂ = 90Q₂ - Q²². πT2 π₂ = 45 - Q² Q₁ Q₂₁ 2 O π₂ = 45 - 1²/20₁². Q₁ Q₁ 3 = 16. ²/Q²-Q₁2. = 32- 2- 1/1/202₂. 3 Q₁ = 45. Q1 = 40 + ²/Q₂₁ 2.2. = 10- -
2 firms are engaged in Cournot competition; firm A faces the cost curveCA(yA)=40yAand firm Bfaces the cost curveCB(yB)=40yB. The inverse market demand curve isP(y)=100y, whereyrepresents market level of output. a)Define the Cournot game. b)In 1 or 2 sentences explain why a firm has no incentive to deviate from the Cournot Nash equilibrium(holding their opponent’s strategy constant). c)Find the Cournot Nash Equilibrium. d)Now suppose instead of playing their strategies at the same time, firm A moves first and then firm B moves second(sequentialgame).Does firm A earn higher profits in this game or the game in part c)?
2. Consider a Cournot competition environment with one good and two firms, Firm 1 and Firm 2. The (pure) strategy space of Firm 1 is S₁ = [0, 1], and the strategy s₁ of Firm 1 corresponds to the amount of the good they produce. Similarly, the (pure) strategy space of Firm 2 is S2 = [0, 1], and the strategy s2 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity s₁ and Firm 2 were to produce quantity s2, the prevailing price in the good market would be 1 — 81 — 82, the utility of Firm 1 would be their profit, u₁ (81, 82) = (1-81-82 - c)81, and the utility of Firm 2 would be their profit, u2($1, $2) = (1-81-82-c)s2, where 0 ≤ c< 1 is the marginal cost of production for both firms. (a) Find the pure-strategy Nash equilibria of this game. (b) Are there other Nash equilibria in this game.
Suppose two firms, Firm A and Firm B, are competing by setting quantities (Cournot competition). Firm A has a constant marginal cost of $10 per unit; Firm B has a constant marginal cost of $15 per unit. Assume fixed costs are equal to 0 for both firms. Hint: since fixed costs are zero and the marginal cost is constant, MC = AC. The two firms choose between producing 50 units or 100 units. If the total output is 100 units, the price is $20 per unit; if total output is 150 units, the price is $15 per unit; if total output is 200 units, the price is $10 per unit. Based on the information provided, fill in the firms’ profits in the payoff matrix below with Firm A choosing the row and Firm B choosing the column. QB=100 QB=50 QA=100 , , QA=50 , , The resulting equilibrium is for Firm A to produce ____ (50 or 100)units and Firm B to produce_____ (50 or 100) units.
Note: the answer should be typed.
Does Firm 1 have a dominant strategy? a)No b)Yes. Advertise c)Yes. Do not advertise Does Firm 2 have a dominant strategy? a)No b)Yes. Advertise c)Yes. Do not advertise
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