Question

Assume a firm is perfectly competitive. Assume a firm's toatal cost curve can be represented as follows:

                    TC= 10+ 4q + 2q^2

Assume the market price for this good is $100 per unit.

A. What is the profit maximizing level of output for this firm?

B. At the profit maximizing level of output, how much economic profit is this firm earning?

C. At this profit maximizing level of output what is ATC?, AVC?, AFC?

D. At what output is ATC at ist minimum?

E. At what output is AVC at its minimum?

Answer 1

(A)

TC = 10 + 4q + 2q²

Calculate MC -

MC = dTC/dq = d(10+4q+2q²)/dq = 4 + 4q

Market Price, P = $100 per unit

A perfectly competitive firm maximizes profit when it produce that level of output corresponding to which market price equals marginal cost.

MC = Market price

4 + 4q = 100

4q = 96

q = 96/4

q = 28 units

The profit-maximizing level of output for this firm is 28 units.

(B)

Calculate the economic profit -

Economic profit = TR - TC

Economic profit = (P*q) - (10 + 4q + 2q²)

Economic profit = (100 * 28) - (10 + (4*28) + 2(28)²)

Economic profit = 2,800 - (10 + 112 + 1,568)

Economic profit = $1,110

This firm will earn economic profit of $1,110.

(C)

Profit-maximizing level of output, q = 28 units

TC = 10 + 4q + 2q²

ATC = TC/q = (10 + 4q + 2q²)/q = (10/q) + 4 + 2q = (10/28) + 4 + (2*28) = $60.36

The ATC is $60.36

TVC = 4q + 2q²

AVC = TVC/q = (4q + 2q²)/q = 4 + 2q = 4 + (2*28) = $60

The AVC is $60

TFC = 10

AFC = TFC/q = 10/q = 10/28 = $0.36

The AFC is $0.36

(D)

ATC is at its minimumwhen it is equal to MC.

Equating ATC and MC

(10/q) + 4 + 2q = 4 + 4q

(10/q) - 2q = 0

2q² = 10

q = 2.23

ATC is at its minimum when output is 2.23 units.

(E)

AVC is at its minimum when it is equal to MC

Equating AVC and MC

4 + 2q = 4 + 4q

2q = 0

q = 0

AVC is at its minimum when output is 0 units.