The market for high-quality caviar is dependent on the weather. If the weather is good, there are many fancy parties and caviar sells for $30 per pound. In bad weather it sells for only $20 per pound. Caviar produced one week will not keep until the next week. A small caviar producer has a cost function given by
C = 0.5q2+ 5q + 100,
whereq is weekly caviar production. Production decisions must be made before the weather (and the price of caviar) is known, but it is known that good weather and bad weather each occur with a probability of 0.5.
a. How much caviar should this firm produce if it wishes to maximize the expected value of its profits?
b. Suppose the owner of this firm has a utility function of the form utility= vp, where p is weekly profits. What is the expected utility associated with the output strategy defined in part (a)?
c. Can this firm owner obtain a higher utility of profits by producing some output other than that specified in parts (a) and (b)? Explain.
d. Suppose this firm could predict next week's price but could not influence that price. What strategy would maximize expected profits in this case? What would expected profits be?