Question

Given P = 24-0.1Q, where Q = q1+q2 and q1 = q2, TC1 = 0.075q1^2, TC2 = 0.05q2^2, (i) Show the profit equation of each form. (ii) Determine the output and price of low cost firm. (iii) Calculate the profit of low cost firm. (iv) What profit maximizing price level the high cost firm would have charged had it been a leader?

Answer 1

(i) The profit equations of each form are:

TP1 = P×q1 - TC1,

TP2 = P×q2 - TC2.

(ii) The output and price of low cost firm is:

P = 24 - 0.1(q1 + q2),

MR = MC,

MR2 = TR'(q2) = 24 - 0.1q1 - 0.2q2,

MC2 = TC'(q2) = 0.1q2,

24 - 0.1q1 - 0.2q2 = 0.1q2,

0.1q1 + 0.3q2 = 24,

q2 = 80 - 1/3q1,

P = 24 - 0.1(q1 + 80 - 1/3q1) = 16 - 1/15q1.

(iii) The profit of low cost firm is:

$TP2 = (16 - 1/15q_{1} )×q_{2} - 0.05q_{2}^2.$

(iv) The profit maximizing price level the high cost firm would have charged would be higher if it had been a leader.