Question

In a Stackelberg model
P = a -bQ
Two firms are there
Q = Q1 + Q2

Solve following: a)  Let's say the inverse demand is given by P = 340 - 7Q and the costs are given by C1 = 10 and C2 = 12: Find the P *, Q1*,  Q2* , $\pi$1* , $\pi$2*
b)  Let's say the inverse demand is given by P = 200 - 3Q and the costs are given by C1 =12 and C2 =15. Find the P *, Q1*,  Q2* , $\pi$1* , $\pi$2* but the rms moved simul- taneously instead of sequentially (i.e. Cournot Model). Compare the Stackelberg results with the Cournot results.

Answer 1

In stackelberg game p = 340 - 7Q mc_1 = 10, mc_2 = 12 using backward induction pi_2 = [340 - 7 (q_1 + q_2) - 1] q_2 partial differential pi_2/ partial differential q_2 = 0 328 - 7 q_1 - 14 q_2 = 0 328 - 7 q_1/14 = q_2 (q_1) pi_1 = [340 - 7 (q_1 + q_2 (q_1)) - 10] q_1 pi_1 = [340 - 7 q_1 - 7 (328 - 7 q_1/14) - 10] q_1 partial differential pi_1/ partial differential q_1 = 0 166 - 14 q_1 + 7 q_1 = 0 166 = 7 q_1 q_1 = 23.7 q_2 = 11.6 p* = 93 pi_1* = 1967 pi_2* = 940