(I) Duopoly with homogeneous product: quantity and price competitionConsider a market with two firms (firms 1 and 2). The (inverse) demand curve is:p = 30 - 2q where q= q1 + q2Suppose Firm 1 has a marginal cost (c1) of 6 and Firm 2 has a marginal cost (c2) of 12.Assume neither firm has a fixed cost.(1) Suppose firms choose quantities sequentially: Firm 1 chooses q and after that decision is knownFirm 2 chooses q2. Calculate the SPNE.(2) Suppose firms choose prices sequentially: Firm 2 chooses its price first and after that decision isknown Firm 1 chooses its price. What is the SPNE? Justify.

A duopoly model with homogeneous products is a model where firms choose output or prices,…

Answered: I) Duopoly with homogeneous product:…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose that firms A and B have the same product in the same market, where Qd = Qa + Qb = 300 - 2p is demand And the firms have a simple cost curves of TCa = 5Qa and TCb = 10Qb Find Cournot Equilibrium & Find the Stackelberg equilibrium if A is the leader. Thanks!
Question 3 The inverse market demand for fax paper is given by P=100-Q. There are two firms who produce fax paper. Firm 1 has al cost of production of C₁= 15*Q₁ and firm 2 has a cost of production of C₂=20*Q₂. 1) Suppose firm 1 and firm 2 compute simultaneously in quantities. What are the Cournot quantities and prices? What are the profits of firm 1 and 2? 2) Suppose firm 1 and firm 2 compete simultaneously in prices. What are the Bertrand quantities and prices? What are the profits of firm 1 and 2? 3) Suppose that firm play a Stackelberg game. First firm 1 sets the quantity in t=1, then, knowing which quantity firm 1 has set, firm 2 chooses the quantity in t=2. What are the Stackelberg quantities and prices? What are the profits od firm 1 and 2? Compared to part a) which firm benefits and which firm loses?
Suppose the iceberg lettuce industry is a Cournot duopoly with two firms: Xtra Leafy (a) and Yummy Farms (y). Xtra Leafy produces q units of output and Yummy Farms produces qy units of output. Aggregate market output is Q = x + y. The (inverse) market demand schedule is: p = 176 - 2Q Both firms have identical cost structures: MC = MC₁ = ATC₂ = ATC₁ = $12 Find Xtra Leafy's Cournot reaction function of the form: 9x = a + bay Where "a" is the reaction function's intercept and "b" is its slope. Note: Please review the formatting instructions above. If any value is negative, be sure to include its negative sign. a. a= b. b = Hint: One of your answers will be negative. Think about why.
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Firm 1 is the leader and Firm 2 the follower in the model of price leadership. Thus, Firms 1 and 2 are the only two producers of a certain good; Firm 1 chooses the price p it will commit to maintain in the market; after having observed Firm 1's decision p, Firm 2 chooses the quantity yz it will produce. Here, the firms cost functions are as follows: c(y;)=3y, +y,?/2 and c2(Y2)= y2?/4. The inverse demand curve is p(Y)=70-Y. What is true about the quantity Firm 2 will produce at the equilibrium of this model? O a. It is between 40 and 42. O b. None of the other answers. It is between 44 and 45. O d. It is between 38 and 39. Oe. It is between 43 and 43.5.
The marginal cost of a product is fixed at MC = 20. The demand for the product is Q = 100 - 2P. (a) Now consider a Cournot model with two firms that are choosing quantities simultaneously. What is the best reply (best response) function for each firm? What is theNash equilibrium? What is the total surplus? (b)What do you expect the total surplus would be with three firms? Why? (You do not need to calculate an exact value. You can say ”total surplus is at least 100”, or ”total surplus is at most 80”)
= Two firms sell substitutable products; the market price is: P = 90-Q, where Q Q₁ + Q₂ is the total market quantity, which consists of Q₁ (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 = 10- 6Q₁ +Q². Firm 2's costs are C₂ = Q². Which is the best response function for Firm 2? O O O O Q₂ = 15. 1 Q₂ = 30 - ²0₁₁ 3 Q₂ = 42 + ²³² Q₁₁ 2 = 1. 3 Q₂ = 45. What is the equilibrium market quantity Q? O Q = 15.25. O Q = 30. Q = 46.5. O Q = 50. What is the equilibrium market price P? O P = 90. O P = 60. O P = 43.5. O P = 10.
The marginal cost of a product is fixed at MC = 20. The demand for the product is Q = 100 - 2P. (a) Now consider a Cournot model with two firms that are choosing quantities simultaneously. What is the best reply (best response) function for each firm? What is theNash equilibrium? What is the total surplus? (b)What do you expect the total surplus would be with three firms? Why? (You do not need to calculate an exact value. You can say ”total surplus is at least 100”, or ”total surplus is at most 80”)
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C2) Consider an industry with only two firms: firm A and firm B. The industry's inverse demand is P(Q) = 400 - ¹1/Q, 10 where P is the market price and Q is the total industry output. Each firm has a marginal cost of $10. There are no fixed costs and no barriers to exit the market. 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 NEA and NEB for each firm. marks] b) Suppose the two firms engage in Stackelberg competition, with firm A moving first, and firm B moving second. Find the equilibrium price PS in the industry, the equilibrium outputs QS and QBS, as well as the profits π and TSB for each firm. в c) For this subquestion only, suppose that firm B has a fixed cost of $200 000: What will firm B's optimal decision be, and what will be the resulting market structure? Now assume that instead of having two firms in the market, we have a monopoly facing the inverse…
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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