Four Seasons Hair Salon is the only women\'s hair stylist in Lake View. A busine

Question

Four Seasons Hair Salon is the only women's hair stylist in Lake View. A business consultant has estimated its monthly cost functions as follows: TC = 2000 + 80 Q + 0.05 Q 2 MC = 80 + 0.1 Q The firm is faced with the following demand: Qd = 800 - 4 P a. Determine the profit maximizing level of the output for this firm. b. What price should the firm charge to maximize its profit? c. What is the firm's profit at the profit-maximizing output? d. What is its average variable cost at this level of output? e. What price should it charge if it were to maximize its revenue? f. At what level of output is the firm's average total cost minimized?

Explanation / Answer

P = 200-Q/4

For profit maximization of a monopolist, MR=MC

R = PQ = 200Q-Q2/4

MR = 200 - Q/2

200-Q/2 = 80+.1Q

.6Q = 120

Q=200

P=200-Q/4 = 150

Profit = R-C

= 200*200 - 200*200/4 -2000 - 80*200 - .05*200*200

= 10000

AVC = 80 + .05Q

= 80 + 10 = 90

for revenue max, MR=0

200 - Q/2 = 0

Q = 400

P = 200 - 400/4 = 100

ATC = 2000/Q + 80 + .05Q

to min, d(ATC)/dQ=0

-2000/Q2 + .05 = 0

Q2 = 2000/.05

Q = 200

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