The organic apple market is perfectly competitive, with apples currently selling at $22 per case. A study commissioned by the organic apple association shows that the short-run total cost of production for a typical producer is T C = 8, 000 + 0.02q 2 , and MC = 0.04q where q is the number of cases sold per year.

(a) Calculate the short-run profit-maximizing quantity (number of cases) for the typical producer.

(b) In the short-run, should the typical producer shut down? Show your work and explain, clearly laying out the logic in support of your answer.