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 next week. A small caviar producer has a cost function given by 2 0.5 5 100, C q q = + + where qis 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. (We have not dealt with uncertainty in class as this is part of other courses from the chair of production economics. For the interested ones with more time, consult chapter 7 in Snyder Nicholson. For this problem I will give the necessary hints to solve it with the tools we have treated in class)

Expected profits= 0.5(30q-C(q))+0.5(20q-C(q)) = 25q-C(q) This is maximized at E(P)=50. To find the corresponding level of profits= E(P)=MC=q+5. Thus, q=20. E(profits)=500-400=100 In the two possible options, we have that, P=30, profit=600-400=200 P=20, profit= 400-400=0 Thus expected utility = 0.5(sqrt200)+0.5 sqrt(0)= 7.1 For all output levels between 13 and 19, the utility is more than that at q=20. Therefore, the reductions in profits due to producing less at a higher price…

is compensated in terms of utility by the rise in corresponding profits when the price is low. The maximum utility occurs at q=17. By setting P=MC, we have that, P=30, q=25, profit= 212.5 P=20, q=15 , profit= 12.5 Thus, expected profits= 112.5 Expected utility derived in this case= 0.5 sqrt(212.5)+0.5 sqrt(12.5) = 9.06