Posted: November 28th, 2014

two firms, say firm 1 and firm 2, sell differentiated goods and face the following demand functions: 4 2 qi = 1 — /33_ + p2 and q2 = 4 -I- 2 1401 4 ,,.., 3 a 3, _ – 31,2 where a >

two firms, say firm 1 and firm 2, sell differentiated goods and face the following demand functions: 4 2 qi = 1 — /33_ + p2 and q2 = 4 -I- 2 1401 4 ,,.., 3 a 3, _ – 31,2 where a >

1. In addition assume that firms target own profit maximisation, compete (simultaneously) in quantities and have marginal costs equal to ci = c2 = c. Assume that 1 > c > 0. Describing the necessary mathematical steps and providing the related economic intuition,
1. find and describe the inverse demands faced by the two firms (HINT: solve the two demands simultaneously with respect to prices) [15 marks] 2. derive and describe each firm’s best response function. Are quantities strategic substitutes or complements? [25 marks] 3. derive and describe the equilibrium quantities [30 marks] 4. explain the economic intuition behind parameter a. What happens to the equilibrium quantities and profits if a increases? Provide economic intuition. [30 marks]
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