If market inverse demands in two markets are P1Q1 a1 b1 Q1

If market inverse demands in two markets are P_1(Q_1) = a_1 - b_1 Q_1 and p_2(Q_2) = a_2 - b_2 Q_2 and the firm produces according to C(Q_1,Q_2) = c_1Q_1 + c_2Q_2? determine the firm\'s optimal quantity, price and profit level.

Solution

We are assuming that firm can discriminate.

for first market, firm\'s optimum quantity is where MC = MR

MR = a1-2b1

MC = c1

Equilibrium is established where

a1-2b1 = c1

for second market

MR = a2-2b2

MC = c2

Equilibrium is established where

a2-2b2 = c2