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?

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

answer; i believe the answer is 40,600,000;