Assignment:
George Sr. has preferences over frozen bananas (B) and ice cream sandwiches (I), and has $60 to spend. The price of ice cream sandwiches is pI = 3, but he has the option of purchasing a membership to Quantity Plus (a Costco-like retailer) for 10 dollars. If he purchases the membership, he can go to Quantity Plus and buy ice cream sandwiches for pI = 2. Unfortunately, Quantity Plus does not sell frozen bananas. They must be purchased at an outside banana stand for the price of pB = 1.
(a) Write down a mathematical expression for George Sr.'s budget constraint in two cases: one where he buys a membership to Quantity Plus, and one where he does not. Carefully sketch both budget constraints on the same diagram, labeling all intercepts and intersection points. Put bananas on the horizontal axis, and ice cream sandwiches on the vertical axis. (Carefully drawn sketches will be useful in solving the remaining parts of the problem)
(b) Suppose we know that George's preferences are well-behaved and satisfy diminishing MRS. Can we say for sure whether or not he will choose to buy a membership? Argue your answer using sketches on the diagram.
(c) Suppose now that we do market research, and learn that George has the following preferences: min{2qB; qI}, where qB is the quantity of bananas consumed, and qI is the quantity of ice cream sandwiches consumed. Now can we say for sure whether or not he will choose to buy a membership? Show your work.