Question

Consider a Cournot model of a duopoly where Firm ?? and Firm ?? operate with asymmetric costs. The inverse market demand function is ?? = ?? ???, the marginal cost of Firm ?? is zero, the marginal cost of Firm ?? is ??, and we impose ?? > ?? > 0 and ?? > 2??. The market output ?? is equal to ???? +????, where ???? and ???? are the output levels of Firms ?? and ??, respectively. There are no fixed costs.

1. Show the best-response function of each firm.

2. Calculate the profit-maximizing output level for each firm.

3. Show that the more efficient firm (i.e., the one with less marginal cost) will supply more.

4. What is the market output? What is the market price?

5. Calculate the profit of each firm.

6. Show that the more efficient firm will have a higher profit.

Answer 1