3. The market for highequality caviar is dependent on the weather. If the weather is good, there are many fancy parties and caviar sells for $30 per pound. ln 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 = 0.59;2 + 5q+ 100 where q is the 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. Hint: Expected prot = E(:r) = 0.5 (30g C ((1)) + 0.5 (20:; C(q)) (a) How much caviar should this rm produce if it wishes to maximize the expected value of its prots? (b) Suppose the owner of this rm has a utility function of the form 1 Utility = :23 where 2: is weekly prots. What is the expected utility associated with the output strategy dened in part (a)? (c) Can this rm owner obtain a higher utility of prots by producing some output other than that specied in parts (a) and (b)? Explain. (d) Suppose this rm could predict next week's price but could not influence that price. What strategy would maximize expected prots in this case? What would expected prots be