Question

Given the following function of the monopolist: average cost= 140+9Q+5Q2
Average revenue= 170 + 16Q + Q2
Calculate total cost, Total Revenue,marginal cost, marginal revenue, equilibrium output, profit or loss

Answer 1

Total cost is:

$TC = AC×Q = 140Q + 9Q^2 + 5Q^3.$

Total Revenue is:

$TR = AR×Q = 170Q + 16Q^2 + Q^3.$

Marginal cost is:

$MC = TC'(Q) = 140 + 18Q + 15Q^2.$

Marginal revenue is:

$MR = TR'(Q) = 170 + 32Q + 3Q^2.$

Equilibrium output is:

MR = MC,

$170 + 32Q + 3Q^2 = 140 + 18Q + 15Q^2,$

$6Q^2 - 7Q - 15 = 0,$

Q = (7 + 20.22)/12 = 2.27 units.

Profit is:

$TP = TR - TC = 170×2.27 + 16×2.27^2 + 2.27^3 - (140×2.27 + 9×2.27^2 + 5×2.27^3) = 57.38.$