24.Competition à la Cournot with homogenous goods and symmetric convex costfunctions. Consider an industry with N > 2 firms competing à la Cournot, facing inverse demand functionp(Q) = a – bQ, where Q = E1 9i and symmetric cost function c(q;) = cq; + q where a > c, d > 0, b > 1and d+ 26 > 0. (You may also assume that < - to avoid settings with negative costs). As a remark,note that marginal costs in this setting are c(qi) = c+ dq; , which is increasing in firm i's output.26+d d.Find the equilibrium price and profits for each firm at equilibrium. What happens to thesewhen the number of firms increase? Explain.According to your results determine whether the following statement is true or false. "Moreе.firms in an industry à la Cournot decrease profits for all firms in the industry while decreasing the price inthe market". Justify your answer.

Given information Cournot model with 2 firms Inverse demand function P=a-bQ Q=q1+q2 identical cost…

24. Competition à la Cournot with homogenous goods and symmetric convex cost functions. Consider an industry with N > 2 firms competing à la Cournot, facing inverse demand function p(Q) = a – bQ, where Q = 1q; and symmetric cost function c(qi) = cq; + q? where a > c, d > 0, 6 > 1 and d+ 2b > 0. (You may also assume that note that marginal costs in this setting are c(qi) = c+ dq; , which is increasing in firm i's output. < - to avoid settings with negative costs). As a remark, a-c 26+d %3|

24. Competition à la Cournot with homogenous goods and symmetric convex cost functions. Consider an industry with N > 2 firms competing à la Cournot, facing inverse demand function p(Q) = a – bQ, where Q = 1q; and symmetric cost function c(qi) = cq; + q? where a > c, d > 0, 6 > 1 and d+ 2b > 0. (You may also assume that note that marginal costs in this setting are c(qi) = c+ dq; , which is increasing in firm i's output. < - to avoid settings with negative costs). As a remark, a-c 26+d %3|

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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
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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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Problem 3. Longer problem. Consider 2 firms F1 and F2 that produce identical products and have identical cost functions c₁ (31) = y2 and c₂ (y2) = y2. The demand function is p (yr) = 24 - yr where yry1 + y2 is the output produced by the two firms. i) Find a competitive equilibrium including the price, quantity and profit in which price = marginal cost. ii) Find the monopoly solution including the price, quantity and profit in which marginal revenue marginal cost. iii) Find the oligopoly (duopoly) Nash equilibrium including the price, quantity and profit in which both firms engage in Cournot competition. iv) Suppose that the oligopolists form a cartel and play a repeated game. Assume that they maximize infinite discounted profits for periods t = 0, 1, 0, ..., specifically, To ++ (1+r)² + .... The duopolists can remain in cartel forever and share the monopoly profit equally so each of them gets Tm 2 + 2 77m 2(1+r) 2(1+r)² cheating + + Alternatively, one of them can decide to break the…
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Consider a homogeneous good duopoly with linear demand P(q) = 12- q,where q is the total industry output, and constant marginal costs c = 3. 1. Suppose that firms simultaneously set quantities. Determine the equilibrium (price, quantities, profit, welfare). 2. The firms consider to merge although their production costs are not affected. Determine the optimal price and quantity after merger. 3. Is such a merger profitable? 4. What are the welfare effects of such a merger?
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