DUOPOLIST CASE, and firms and products are IDENTICAL.

Given:

1. TOTAL inverse demand curve: p = 250 - (q(a) + q(b));
2. TOTAL cost curve for firm b: c(b) = 100 + 2q(b):
3. TOTAL cost curve for firm a: c(a) = 100 + q^2(a);

Solve the following questions:

a. We ONLY have" Firm a" in the market. In other words q(b) =0. Solve Monopoly equilibrium price, quantity and firm a's s profit.

b. Solve Nash (i) Cournot equilibrium price (ii) output level (iii) firms' profits.

c. Firm (a) is now the LEADER under Stackelberg case. Solve (i) equilibrium price (ii) output level (iii) firms' profits.

d. Firm (a) and Firm (b) are now under Caretel case. Solve (i) market price for each firm (ii) output level for each firm (iii) firms' profits.