Question

If a firm's marginal cost function is MC(Q) = (b/2) + aQ and the demand curve is P = b - aQ (where a and b are both positive numbers), then the firm's profit-maximizing quantity equals what?

a) 0

b) b/(2a)

c) b/(3a)

d) b/(6a)

Answer 1

Ans: b/6a

Explanation:

P = b - aQ

TR = P * Q = bQ - aQ^{​​​​​2}

MR = b - 2aQ

The profit maximization condition is

MR = MC

b - 2aQ = (b/2) + aQ

3aQ = b - (b/2)

3aQ = (2b - b)/2 = b/2

Q = (b/2) / 3a = b/(6a)

Thus, option [d] is correct answer.