Hi ... Can you please help with this. I'm confused with part (b) and (c) . CAN YOU PLEASE SHOW ME THE STEPS

ECON 641: Problem Set 12 Problem 1 - Cournot Model

Consider a market with two firms each selling an identical product and with identical costs of c(qi) = 1/2 q2i i = 1,2

where qi is the output of firm i. The market inverse demand is given by p(Q) = 20 Q

where y is the total market output, Q = q1 + q2. Each firm chooses its own output to maximize their own profit ("Cournot Competition").

(a) Write the profit function for firm 1 in terms of its own output as well as the output of the other firm: 1(q1,q2). Write out the profit for firm 2 as well: 2(q1,q2).

(b) Derive the NFOC for each firm to be maximizing its own profit with respect to its own output.

(c) Using the NFOC for firm 1, derive the optimal output of firm 1 in terms of the output of firm 2. That is, find the "best response" function for firm 1: q1 = BR1(q2). Do the same for firm 2.