Problem Set 2
Due Date: Oct31, Monday – between 9 & 11 AM in room S 2.132 Please keep a copy of your assignment and show all your work clearly.
(1) Mr. J. Bond, a retired movie actor, consumes only grapes and the composite good Y (i.e. price of Y is £1). His income consists of £10000 a year from his investment fund plus the proceeds of whatever he sells of the 2000 bushels of grapes he harvests annually from his vineyard in Tuscany. Last year, grapes sold at £2 per bushel and Bond consumed all 2000 bushels of his grapes, in addition to 10,000 units of Y. This year, the price of grapes is £3 per bushel (and the price of the composite good Y is the same as before). If Bond has well-behaved preferences, will his consumption of grapes this year be greater than, less than or the same as last year’s? How about his consumption of the composite good? (Hint: Graph both years’ budget constraints and think about whether last year’s bundle is affordable to Mr. R).
(2) Suppose Carmela’s income is £100 per week, which she allocates between sandwiches and books. Sandwiches cost £2 each. Books cost £10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to £5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Carmela might have more than one utility-maximizing solution?
(3) Fiona requires a minimum level of consumption, to derive additional utility. For Fiona, U(X,Y) = 0 if X+Y<5
= X+Y otherwise.
Which of our usual assumptions about well-behaved preferences are violated in Fiona’s case?
(4) Consider the following utility functions over goods A and B. U = AB, and V = A2B. Compute the MRS for each of these functions, and evaluate these at the point (3,4). Explain whether these functions represent the same preference ordering....