2. Two producers of the same good repeatedly compete in prices for T periods. They have the same discount factor 8. In thestage game, each firm chooses between three price levels 2, 4, and 10. The Bertrand stage game profits are given by:(12 - pi)(pi - 2),Pi < p-iui(pi, p-i) =-(12 Pi)(Pi-2), Pi = p-iPip-iIn each of the following parts you must explain your positive or negative answer. If your answer says that some path can beimplemented in an SPNE, then you must list the strategies. (a) Suppose T = 2, and 8 = 1. Can the path ((4, 4), (4, 4)) be implemented in a SPNE?Hint: Start by writing a 3 × 3 table representing the normal form of the stage game and find all stage NE.(b) Suppose T = 2, and 8 = 1. Can the path ((10, 10), (10, 10)) be implemented in a SPNE?(c) Suppose T = 2, and 8 = 1. Can the path ((10, 10), (4, 4)) be implemented in a SPNE?

Answered: Image /qna-images/answer/70b75d4c-f5cc-4d7b-a608-50b4e9b0e664.jpg

Answered: 2. Two producers of the same good…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider a duopoly market, where two firms sell differentiated products, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices p, and p2 simultaneously. The derived demand functions for the two firms are: D1 (P1, P2) = SG+P1)and D2 (P1, P2)= S(;+-P2), where S > 0 and the parameter t > 0 measures the 2t 2t degree of product differentiation. Both firms have constant marginal cost c> 0 for production. (a) Derive the Nash equilibrium of this game, including the prices, outputs and profit of the two firms. (b) From the demand functions, qi= D¡ (p; , p¡ )= SG+P), derive the residual inverse demand functions: p; = P; (qi , p¡) (work out: P; (qi , P;)). Show that for t > 0, P;(qi , P;) is downward 2t aPi (qi ,Pj) . sloping, i.e., c, i.e., firm į has market power. %3D (c) Calculate the limits of the equilibrium prices and profit as t → 0 ? What is P; (qi , p;) as t → 0? Is it downward sloping?…
Two rival companies competing in the same market need to decide their plans for future expansion of their stores. The Table below shows the possible outcomes of their mutually interdependent actions (payoffs are profits in £m) Giga Company Titanic Conglomerate No Change Refurbishment of existing stores Large Expansion No Change 30, 40 25, 35 15, 24 Refurbishment of existing stores 35, 30 28, 32 18, 33 Large Expansion 12, 22 18, 20 20, 25 The Nash equilibrium: (A) does not exist. (B) occurs when both firms choose Refurbishment of existing stores. (C) occurs when both firms choose Large Expansion. (D) occurs when both firms choose No Change.
QUESTION 13 Consider a market where two firms (1 and 2) produce differentiated goods and compete in prices. The demand for firm 1 is given by D₁(P₁, P2) = 140 - 2p1 + P2 and demand for firm 2's product is D2 (P1, P2) 140 - 2p2 + P1 Both firms have a constant marginal cost of 20. What is the Nash equilibrium price of firm 1? (Only give a full number; if necessary, round to the lower integer; no dollar sign.)
PROBLEM IV. Consider an industry consisting of two firms (i = 1,2) that are engaged in a Bertrand price competition. The demand function for the product of firm i is given by qi = 24 – 9p; + 6p;. The marginal cost of production for each firm is zero. Q12. The collusive price of the products is (a) 4 (b) 5 (c) 1 (d) 6 (e) 2
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.
7. Jie is a firm manager deciding its sales quantity strategy. His firm is in a market with another competitor, and he is the leader in the sequential game. Collusion is impossible. The market inverse demand function is P = 16 – Q, where Q is the total quantity of q? the production. The cost functions of Jie's firm and the other firm are c(g) and c(q) = q?, respectively. So Jie should set the quantity as С. 4 A. 8 В. 6 D. 2
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Plz solve this.
Initially there are six firms producing differentiated products. The demand function for the good produced by firm i, i=1,2..,6, is given by qi = 10-2pi+0.3 summation pj where the sum is taken over the five prices other than firm i. Each firm has the same marginal cost c. The firms choose prices simultaneously; that is, they are differentiated products Bertrand competitors. (a) Solve for the symmetric Nash equilibrium prices. (b) Suppose that you observe each firm to set a price of 4.8. What must c be? (c) Suppose that two of the six firms merge to become a single firm. The firm continues to produce both goods. Using the marginal cost you found in (b), derive the new post-merger Nash equilibrium prices.
8)Consider a market in which 5 companies operate, whose marginal and average costs are equal to c. The demand function is given by P(Q)= 1-Q, where P is the price and Q indicates the total quantity. Assume that companies compete with Cournot in choosing production levels. Assume that the game is repeated an infinite number of periods, that companies adopt trigger strategies and that the punishment is represented by Nash Reversion. 1)What is the value of the discount factor that allows companies to sustain tacit collusion in a balanced situation? 2) Assume now that companies are able to discover the defection of a rival company with K periods of delay. What do you think the effect on the sustainability of collusion can be? 3) Do you think that in this market collusion would be more easily sustainable if the companies compete with Bertrand? 4) If in a price-competitive market (Bertrand) N symmetrical companies operate, what would be the critical value of the discount factor that would…
There are two firms in the market (duopoly). These two firms are competingsimultaneously. The first firm chooses its output level (x) by predicting the second firm’soutput (y). Let c denote the total cost function c(x) = x and c(y) = y. Also, let’s assumethat the inverse demand function is p(Y) = 7 - Y where Y = x + y. (1) Obtain the reactionfunction of the first firm. (2) Find the equilibrium (output and profit of each firm) whentwo firms simultaneously compete
Two firms, Firm 1 and Firm 2, compete by simultaneously choosing prices. Both firms sell an identical product for which each of 100 consumers has a maximum willingness to pay of $40. Each consumer will buy at most 1 unit, and will buy it whichever firm charges the lowest price. If both firms set the same price, they share the market equally. Costs are given by ci(qi) = 16q;. Because of regulation, firms can only choose prices which are integer numbers, and they cannot price above $40. Answer the following: a) If Firm 1 chooses pi = 36, Firm 2's best response is to set what price?_________ b) If Firm 2 chooses the price determined in the previous question, Firm 1's best response is to choose what price?_________ C) If Firm 1 chooses pi = 11, Firm 2's best response is a range of prices. What is the lowest price in this range?__________ d) Now suppose both firms are capacity-constrained: Firm 1 can produce at most 31 units, and Firm 2 can produce at most 43 units. If firms set…

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