The market for caviar depends on the weather. If the weather is good, the caviarsells form $30 and if the weather is bad, it sells for $20. Caviar produced one weekwill not keep until the next week. The caviar producer's cost function is given by

C(q) = q²/2+ 5q + 100

where q is weekly caviar production. Production decisions must be made before the price of caviar is known, but it is known that good weather and bad weather each occur with probability 1/2

a) How much caviar should the firm produce if it wishes to maximize the expected value of its profits?

b) Suppose the owner of the firm has a utility function of the form utility =√πwhere π is weekly profits. What is the expected utility of the output strategy defined in part a)?

c) Can the firm owner obtain a higher utility of profits by producing some otheroutput than specified in parts a) and b)? Explain.

d) Suppose that the firm could predict next week's weather (and hence, prices).What strategy would maximize expected profits in this case? What would expected profits be?

Thank you very much. It is actually due this morning by 9am. It would be great if I can get any feedbacks by then :)