Question

Multi-Screen TV, Inc., is a Cleveland i-based importer and distributor of large screen HDTVs for residential and commercial customers. Revenue and cost relations are as follows:

TR = $1000Q - .1Q2

TC = $43,500 +100Q + 0.4Q2

A. Calculate output, marginal revenue, marginal cost, average cost, price, and profit at the average total cost-minimizing activity level. (Hint - MC passes through the minimum point on the ATC curve)

B. Calculate these values at the profit-maximizing activity level.

C. Compare and discuss your answers to parts A and B.

Answer 1

MR = dTR/dQ = 1000 - 0.2Q

MC = dTC/dQ = 100 + 0.8Q

ATC = TC/Q = (43,500/Q) + 100 + 0.4Q

(A) When ATC is minimized, ATC = MC.

(43,500/Q) + 100 + 0.4Q = 100 + 0.8Q

0.4Q = 43,500/Q

Q² = 43,500/0.4 = 108,750

Q = 330 (taking integer value for output)

MR = 1000 - (0.2 x 330) = 1000 - 66 = 934

MC = 100 + (0.8 x 330) = 100 + 264 = 364

ATC = MC = 364

Price = TR/Q = 1000 - 0.1Q = 1000 - (0.1 x 330) = 1000 - 33 = 967

Profit = TR - TC = (P x Q) - (ATC x Q) = Q x (P - ATC) = 330 x (967 - 364) = 330 x 603 = 198,990

(B) Profit is maximized when MR = MC.

1000 - 0.2Q = 100 + 0.8Q

Q = 900

P = 1000 - (0.1 x 900) = 1000 - 90 = 910

MR = 1000 - (0.2 x 900) = 1000 - 180 = 820

MC = MR = 820

ATC = (43,500/330) + 100 + (0.4 x 330) = 132 + 100 + 132 = 364

Profit = Q x (P - ATC) = 330 x (910 - 364) = 330 x 546 = 180,180

(C) Therefore, compared to ATC-minimizing levels, for profit-maximizing level of output, price is lower, output is higher, MR is lower, MC is higher, ATC is unchanged and profit is lower.