Consider an industry with 2 firms producing homogeneous product. The cost function for firm 1 and...

  

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Consider an industry with 2 firms producing homogeneous product. The cost function for firm 1 and firm 2 are c₁ (y₁) = a+by₁+cy? and c2 (y2) = a'+b'y2+c'y, respectively. y1, y2 are outputs of firm 1 and firm 2, and others are parameters which are all positive. The market demand is P(y) = 100 - 2(y1 + y2). Suppose firm 1 is the quantity leader. It decides and announces its output y₁ first; firm 2 then observes y₁ and chooses its output. (a) (5 points) Suppose a = 1, b = 3,c=1; a' = 2,b' = 2, d = 1. What are the equilibrium price, outputs, and profits for each firm? (b) (6 points) Suppose the firms are operating in a country with loose anti-trust law, and the two firms realize that collusion may increase total profits. i. Solve for the collusion price and outputs for each firm. Given the outputs and price, how much is the total profits and profits for each firm? ii. Is the collusion result stable? Explain why. (c) (5 points) Does firm 1 have incentive to become the quantity leader, compared with being the quantity follower and Cournot competitor? You don't need to solve the problem numerically. Just use a graph to explain your answer clearly. Consider an industry with 2 firms producing homogeneous product. The cost function for firm 1 and firm 2 are c₁ (y₁) = a+by₁+cy? and c2 (y2) = a'+b'y2+c'y, respectively. y1, y2 are outputs of firm 1 and firm 2, and others are parameters which are all positive. The market demand is P(y) = 100 - 2(y1 + y2). Suppose firm 1 is the quantity leader. It decides and announces its output y₁ first; firm 2 then observes y₁ and chooses its output. (a) (5 points) Suppose a = 1, b = 3,c=1; a' = 2,b' = 2, d = 1. What are the equilibrium price, outputs, and profits for each firm? (b) (6 points) Suppose the firms are operating in a country with loose anti-trust law, and the two firms realize that collusion may increase total profits. i. Solve for the collusion price and outputs for each firm. Given the outputs and price, how much is the total profits and profits for each firm? ii. Is the collusion result stable? Explain why. (c) (5 points) Does firm 1 have incentive to become the quantity leader, compared with being the quantity follower and Cournot competitor? You don't need to solve the problem numerically. Just use a graph to explain your answer clearly.

Answer rating: 100% (QA)

a To find the equilibrium outputs and price we first need to determine the reaction functions of both firms The profit function of firm 1 is given by 1 100 2y1 y2y1 a by1 cy2 Taking the derivative wit... View the full answer