Question

Commercial Recording, Inc. is a manufacturer and distributor of mixing consoles for commercial recording studios. Revenue and cost relations are:

TR = $3,000Q - $0.5Q2

MR

TC = $100,000 + $1,500Q + $0.1Q2

MC

1. Calculate output, marginal cost, average cost, price, and profit at the average cost- minimizing activity level.
2. Calculate these values at the profit-maximizing activity level.
3. Compare and discuss your answers to parts A and B.

= TR/ Q=$3,000-$1Q

= TC/ Q = $1,500 + $0.2Q

2

Answer 1

(A)

TR = 3,000Q - 0.5Q²

MR = dTR/dQ = 3,000 - Q

TC = 100,000 + 1,500Q + 0.1Q²

MC = dTC/dQ = 1,500 + 0.2Q

ATC = TC/Q = (100,000 / Q) + 1,500 + 0.1Q

Average cost is minimized when dATC/dQ = 0.

- (100,000 / Q²) + 0.1 = 0

100,000 / Q² = 0.1

Q² = 1,000,000

Q = 1,000

MC = 1,500 + (0.2 x 1,000) = 1,500 + 200 = 1,700

Since MC intersects ATC at its minimum point, when ATC is minimized, ATC = MC = 1,700.

P = TR / Q = 3,000 - 0.5Q = 3,000 - (0.5 x 1,000) = 3,000 - 500 = 2,500

Profit = Q x (P - ATC) = 1,000 x (2,500 - 1,700) = 1,000 x 800 = 800,000

(B)

Profit is maximized when MR = MC.

3,000 - Q = 1,500 + 0.2Q

1.2Q = 1,500

Q = 1,250 (Quantity is higher by (1,250 - 1,000) = 250)

MC = 1,500 + (0.2 x 1,250) = 1,500 + 250 = 1,750 (MC is higher by (1,750 - 1,700) = 50)

ATC = (100,000 / 1,250) + 1,500 + (0.1 x 1,250) = 80 + 1,500 + 125 = 1,705 (ATC is higher by (1,705 - 1,700) = 5)

P = 2,000 - (0.5 x 1,250) = 2,000 - 625 = 1,375 (Price is lower by (2,500 - 1,375) = 1,125)

Profit = 1,250 x (1,375 - 1,705) = 1,250 x (- 330) = - 412,500 (Profit is lower by (800,000 + 412,500) = 1,212,500