The inverse market demand for a homogenous product is given by P=100-Q, where Q is the industry output and P the market price of the product in the market

The inverse market demand for a homogenous product is given by P=100-Q, where Q is the industry output and P the market price of the product in the market. There are two symmetric firms that produce the product in the market. Each firm has a per unit production cost equal to 20 (i.e., c1=c2=20).

a) Assume the firms compete in quantities (i.e., q1 and q2) and make their choices simultaneously (i.e., Cournot). What are the firms’ profits in equilibrium?

b) Suppose that Firm 1 has now discovered a cost-reducing technology. Firm 1 produces with a per unit cost of 10 (i.e., c1=10). What are the firms’ profits in equilibrium now?

c) Let the firms now compete in quantities in a sequential game (i.e., Stackelberg). The per unit costs of production are c1=10 and c2=20. What are the firms’ profits in equilibrium in this case? Compare and discuss your findings.