Please write down the detailed solution procedure, thanks!

Q1 Consider the following inverse demand function, 39(9) = 3 29, Q : q1 + :12 +q3, where {1, denotes rm i's output, 1' = 1, 2, 3 ('11 denotes rm 1's output, in denotes rm 2's output, and q3 denotes rm 3's output). The three rms choose prioes simultaneoust and non cooperatively (Bertrand competition). Firm i's marginal cost of production is constant and equal to c, 2::- 0 (c1 denotes rm 1's marginal cost, 02 denotes rm 2's marginal cost, and c3 denotes rm 3's marginal cost). Assume that c1 3 c2 and that c1 5 c3. a) Derive the best response function of rm 1. b) Find the Bertrand-N ash equilibrium price set by rm 1. c) Find the Bertrand-Nash equilibrium output sold by each rm. d) Show that, if c1 =22 c2 and c1 =2: (:3, rm 1 makes higher prots than the other rms