Answer to Question #177113 in Macroeconomics for Boakye Charlotte

Question

Consider the firm with the following total monthly cost function.

Tc= 1000 + 0.01Q².

The firm operates in a perfect competitive industry and sells its product at the market determining price of $ 10.

To maximize total profit, what should be the firm's monthly output level and how much economic profit will the firm earn each month.

Answer 1

Solution:

Profit = Revenue function – Cost function

Revenue function = price x quantity = 10 x Q = 10Q

Profit function = 10Q – 1000 + 0.01Q²

 

At the total level of profit maximizing output: MR = MC

MR = derivative of the Revenue function

MR = derivative of 10Q = 10

MR = 10

MC = derivative of the Total cost function

MC = derivative of 1000 + 0.01Q²

MC = 0.02Q

MR = MC

10 = 0.02Q

Q =$\frac{10}{0.2} = 500$

Q = 500 units

Monthly output level to maximize total profit = 500 units

Profit = 10Q – 1000 + 0.01Q²

Profit = $10(500) - (1000 + 0.01(500)^{2} )$

Profit = $5000 - (1000 + 2500)$

Profit = 5000 – 3500 = 1,500

Economic profit earned each month = 1,500