Question #45251

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

Expert's answer

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

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

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