Ahab's Coffee has 150 customers. Fifty of them are small and 100 are big, with appetites for coffee matching their size. Small people value coffee at $0.10 per ounce for the first 8 ounces and nothing for more than that. Large people value coffee at $0.15 cents per ounce for the first 10 ounces and nothing for more than that. Coffee costs $0.05 per ounce to produce.
a. What is Ahab's profit-maximizing strategy if it can sell a small cup to small people and a large cup to large people and prevent anyone from buying one or more of the other sized cups (either for their own consumption or to resell to other people). How much profit does Ahab's earn, and how much surplus does each type of consumer obtain?
b. For the rest of the question, suppose it is illegal for Ahab's to charge prices based on people's size. Show that the strategy from part a would not work now by computing the surplus big customers would get from buying a small cup and showing this is more than their surplus from buying a large cup.
c. What is the most Ahab's can charge for a 10-ounce cup and an 8-ounce cup and still have some customers buy each sized cup? Calculate the profit Ahab's can earn from such a pricing strategy.
d. Show that Ahab's can do better than in part c by reducing the size of the small cup from 8 ounces to 6 ounces.