Answer to Question #278488 in Microeconomics for Aussie

Question

EXPLAIN WITH THE HELP OF GRAPH, A monopolist has a cost

function 200q + 15Q2

and faces a demand function given by P= 1200 – 10Q. Calculate total

revenue, marginal revenue, output and price that maximize profit-maximizing? What is its

maximal profit?

Answer 1

Total revenue is:

$TR = P×Q = 1200Q - 10Q^2.$

Marginal revenue is:

$MR = TR'(Q) = 1200 - 20Q.$

At MR = MC output and price maximize profit, so:

$MC = TC'(Q) = 200 + 30Q,$

1200 - 20Q = 200 + 30Q,

50Q = 1000,

Q = 20 units,

P = 1200 - 10×20 = 1000.

Total profit is:

$TP = TR - TC = 1000×20 - (200×20 + 12×20^2) = 11200.$