Calculate the quantity that each firm will produce.

Assume that another firm (Y) enters the market, where inverse market demand is given by

P(q) = a – bq, where q is quantity and a, b > 0. (i). The cost function for firm Y is the same as that for the original firm: C(q) = d + kq, where d, k > 0 and d < a.

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?