Assume that two firms, say firm 1 and firm 2, sell differentiated goods and face the following demand functions:
q1 = 4/3 - 2/3a - 4/3 p1 + 2/3 p2 and q2 = 4/3a - 2/3 + 2/3 p1 - 4/3 p2
where a > 1. In addition assume that the firms target own profit maximization, compete (simultaneously) in quantities and have marginal costs equal to c1 = c2 = c. Assume that 1 > c > or equal to 0. Describing the necessary mathematical steps, and providing the related mathematical intuition,
1. Find the inverse demands faced by the two firms (Hint: Solve the two demands simultaneously with respect to prices.
2. Derive each firm's best response function. Are quantities strategic substitutes or complements.
3. Derive the equilibrium in quantities.
4. Explain the economic meaning of parameter a. What happens to the equilibrium quantities and profits if a increases?
The instruction for this question is that I have to make sure to use proper mathematical notation used.
Assume that two firms, say firm 1 and firm 2, sell differentiated goods and face the following demand functions:
q1 = 4/3 - 2/3a - 4/3 p1 + 2/3 p2 and q2 = 4/3a - 2/3 + 2/3 p1 - 4/3 p2
where a > 1. In addition assume that the firms target own profit maximization, compete (simultaneously) in quantities and have marginal costs equal to c1 = c2 = c. Assume that 1 > c > or equal to 0. Describing the necessary mathematical steps, and providing the related mathematical intuition,
1. Find the inverse demands faced by the two firms (Hint: Solve the two demands simultaneously with respect to prices.
2. Derive each firm's best response function. Are quantities strategic substitutes or complements.
3. Derive the equilibrium in quantities.
4. Explain the economic meaning of parameter a. What happens to the equilibrium quantities and profits if a increases?
The instruction for this question is that I have to make sure to use proper mathematical notation used.
