A perfectly competitive firm has total revenue and total cos

A perfectly competitive firm has total revenue and total cost curves given by:

TR = 100Q

TC = 5,000 + 2Q + 0.2 Q2

A. Find the profit-maximizing output for this firm.

B. What profit does the firm make?

Solution

(A) TR = 100Q

     MR = 100

    TC = 5,000 +2Q + 0.2Q²

     MC = 2 + 0.4Q

The firm will maximize profit when MR = MC

2 + 0.4Q =100

0.4Q = 98

Q = 98/0.4 = 245 units

Therefore, the profit-maximizing output for this firm is 245 units

(B) Profit = TR - TC

             = 100Q - (5,000 +2Q + 0.2Q² )

             = 100Q - 5,000 - 2Q - 0.2Q²

     Profit = 98Q - 5000 - 0.2Q²

Substituting the value of Q in the profit function, we can get

    Profit = 98 * 245 - 5000 - 0.2(245)²

            = 24,010 - 5000 - 12,005

So, Profit = $7005