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) find out 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?