Question

Casey’s Sprocket, Inc.’s short-run cost curve is C= ((25q^2)/K) +15K where q is the number of sprockets produced and K is the number of robot hours Casey hires. Currently, Casey hires 10 robot hours. The short-run marginal cost curve is MC=50(q/k) Suppose the sprocket market is perfectly competitive. Answer the following questions:
If the market price for a sprocket is $250, what is the profit-maximizing output level for Casey’s firm?

Assume all fixed costs are sunk. If the market price for a sprocket drops to $50, will Casey shut down the firm? Why or why not?

Answer 1

Answer:

At 10 robot hours producing 50 sprocket It maximizes his profit to $ 6,100

At a price of 50 per sprocket Casey will drop production to 10 where it can still earn a gain of 100 dollars.

Explanation:

K = 10

MC = 50(q/k) = 50(q/10)

The profit maximization point is that marginal cost = marginal revenue

MR = 250

MR = MC

250 = 50(q/10)

250/50x10 = q = 50

Revenue: 250 x 50 = 12,500

Cost: (25q^2)/K+15K = 25(50^2)/10 + 15*10

C = 6,250 + 150 = 6,400

Profit: 12,500- 6,400 = 6,100

If price drops to 50 and already hired 10 robo hours:

Then:

50 = 50(q/10)

50/50*10 = q = 10

Revenue: 50 x 10 = 500

Cost (25q^2)/K+15K  = 25(10^2)/10 + 15*10

C = 250 + 150 = 400

Profit: 500 - 400 = 100