Question 1 Firm A and B are the only producers of soft drinks for the market....

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Question 1 Firm A and B are the only producers of soft drinks for the market. The inverse market demand curve is given by P = a - Q where Q is the total supply to the market. The price will be zero if O > a. Firm A has constant marginal cost of production c, while B's cost of production is c2. The two firms make their production decisions independently of each other. Derive the Nash equilibrium of this game. You may assume that the marginal costs are such that an interior solution exists. (a) [5marks] [5marks] (b) (c) What is the equilibrium level Assume now that before this interaction Firm A can invest in processes that will affect its marginal cost of production. In particular assume that profit for Firm A arising from this equilibrium? q = 0.5a - Vr Where r is the cost of the investment incurred, rs Assuming that the outcome of the second stage is the Nash equilibrium, show that the anticipated profit for Firm A is -r. [5marks] (d) Solve for the equilibrium level of investment r, given that a=12 and c = 6. [5marks] (e) What are the subgame perfect equilibrium strategies of this game? [10marks] Questions 2 A. Derive the profit function for a firm with the Cobb-Douglas technology y xx. What restrictions on a and ß are required to ensure that the profit function is well defined? Explain. [5marks] Question 1 Firm A and B are the only producers of soft drinks for the market. The inverse market demand curve is given by P = a - Q where Q is the total supply to the market. The price will be zero if O > a. Firm A has constant marginal cost of production c, while B's cost of production is c2. The two firms make their production decisions independently of each other. Derive the Nash equilibrium of this game. You may assume that the marginal costs are such that an interior solution exists. (a) [5marks] [5marks] (b) (c) What is the equilibrium level Assume now that before this interaction Firm A can invest in processes that will affect its marginal cost of production. In particular assume that profit for Firm A arising from this equilibrium? q = 0.5a - Vr Where r is the cost of the investment incurred, rs Assuming that the outcome of the second stage is the Nash equilibrium, show that the anticipated profit for Firm A is -r. [5marks] (d) Solve for the equilibrium level of investment r, given that a=12 and c = 6. [5marks] (e) What are the subgame perfect equilibrium strategies of this game? [10marks] Questions 2 A. Derive the profit function for a firm with the Cobb-Douglas technology y xx. What restrictions on a and ß are required to ensure that the profit function is well defined? Explain. [5marks]

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