I. (15 points)Alf's preferences are given by the following utility function:U(x; y) = x-1/y.

A.(5 points)Are his preferences rational? Explain.

B.(5points)Dotheysatisfytheassumptionofmonotonicity?Whyorwhynot?

C.(5points)Supposexcosts$4andycosts$1,andAlf'sincomeis$30.Howmanyunitsofxandy

would he buy? Show your work.

II. (10 points)Jake is consuming two goods: good Y and good X. We know that his preferences over two goods satisfy rationality (of course), monotonicity and the diminishing MRS assumptions. We also know that for him X is an inferior good and Y is a normal good.

Draw Jake's preferences for X and Y (put Y on the horizontal axis). Use (hypothetical) budget constraint (s) and optimal choice(s) to demonstrate that good X is inferior and good Y is normal.

III. (20 points)John and Jane are avid readers and consume only electronic books and paper books. For John e-books and paper books are perfect substitutes that he likes equally well. That is, John does not care which format (electronic or paper) the book is in, he only cares about having as many books of either kind as he can afford.

For Jane the two goods are less substitutable. She also likes paper books more than the electronic ones.

a) (6 points)Draw the indifference curves that represent John's and Jane's preferences for e-books

and paper books on separate graphs. Put paper books on the horizontal axis. How are the two

graphs different?

b) (7points) Suppose both John and Jane have the same income( M) and buy their e-books and

paper books at the same market at respective pricesP(EB)andP(PB). Suppose also that paper books cost a little bit more, that is,P(PB)> P(EB).Add the budget constraints to the graphs from A and show the optimal choices. Can you tell who would optimally buy more electronic books, John or Jane? Explain.

c) (7points)Suppose the price of paper books and incomes stay the same, while the price of electronic books increases so thatP(EB)=P(PB). Find the new optimal consumption bundle(s) for each consumer. What are the substitution and income effects of this price change on consumption of paper books for each consumer? What consumer has larger substitution effect and why?