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. No graph is required but you may draw one if you find that helpful in your explanation.