Assume a monopolist firm X that faces the following inverse demand:
(i) P(q) = a - bq, where q is quantity and a, b > 0. Assume, furthermore, that the monopolist firm has the following cost function:
(ii) C(q) = d + kq, where d, k > 0 and k < a.
Assume now that another firm (Y) enters the market, where inverse demand is still given by
(i). The cost function for firm Y is the same as for the original firm (X), i.e. it is also given by
(ii). First, consider the case where both firms simultaneously choose their quantities.
a) Derive the best-response functions (reaction functions) of the two firms.
b) Calculate the quantity that each firm will produce. What will be the market price?
Now assume that as the incumbent firm X can choose quantity first. Then, based on firm X's decision, firm Y chooses its quantity.
c) What quantities will the two firms produce? What will be the market price?