Question

A profit maximization perfectly competitive firm face the following function total cost function. TC=10Q^2+50 and marginal revenue (MR)=10 based on the above information
a) calculate total revenue function
b) find or determine the OPTIMAL LEVEL OF OUTPUT or profit maximization output
c) calculate the maximum profit or loss at optimal level of output

Answer 1

TC=10Q^2+50, MR = 10
a) calculate total revenue function
For a perfectly competitive firm MR = MC = P, so P = MR = MC = 10 and TR =
P*Q = 10Q
b) find or determine the OPTIMAL LEVEL OF OUTPUT or profit maximization output
Profit maximization output is in the point, where MR = MC = P.
MC = TC' = 20Q
MR = 10, so:
20Q = 10
Q = 0.5 units
c) calculate the maximum profit or loss at optimal level of output
Maximum profit will be: TP = TR - TC = P*Q - 10Q^2 - 50 = 10*0.5 - 10*0.25
- 50 = 5 - 2.5 - 50 = -$47.5