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?