Donald is a stamp collector. The only things other than stamps that Donald consumes are Harold's doughnuts. It turns out that Donald's preferences are quasilinear, represented by the utility function U(d, s) = lnd + s, where d is the number of doughnuts he consumes and s is the number of stamps he collects. The price of doughnuts is pd and the price of stamps is ps. Donald's income is m.

(a) Write the equation that says that the absolute value of Donald's MRS is equal to the price ratio. Use it to nd Donald's demand for doughnuts.

(b) Since there are only two goods, any money that is not spent on doughnuts must be spent on stamps. Use the budget equation and Donald's demand for doughnuts to nd Donald's demand for stamps.

(c) If you did not make any mistakes, the expression you just wrote down is negative if m < ps. Surely it makes no sense for Donald to be demanding negative amounts of stamps. If m < ps, Donald's demand for stamps would be s = 0. What would his demand for doughnuts be?

(d) Suppose that the price of doughnuts is $2 and the price of stamps is $1. On a graph with doughnuts on the horizontal axis and income on the vertical, draw Donald's Engel curve for doughnuts. On a separate graph with stamps on the horizontal axis and income on the vertical, draw Donald's Engel curve for stamps.