Answer to Question #51462 in Microeconomics for William Waso Wasonga K Omole

Question

Under a perfect competition the price as sh. 6 per unit has been determined. An individual firm has a total cost function given by C=10+15Q - 5Q^2+Q^3/3. Find:
1. Revenue function
2. The quantity produced at which profit will be maximum profit
3. Maximum profit

Answer 1

P = 6 per unit
C=10+15Q - 5Q^2+Q^3/3.
i) Revenue function is:
TR = P*Q = 6Q
ii) The quantity produced at which profit will be maximum profit is in
the point, where marginal revenue equals marginal cost: MR = MC
MR = TR' = 6
MC = C' = 15 - 10Q + Q^2
15 - 10Q + Q^2 = 6
Q^2 - 10Q + 9 = 0
Q1 = 9 units, Q2 = 1 unit (may not be profit maximizing).
iii) Maximum profit is:
TP = TR - TC = 6*9 - (10 + 15*9 - 5*81 + 729/3) = 54 - 17 = $37