Donald Fribble is a stamp collector. The only things other than stamps that Fribble consumes are Hostess Twinkies. It turns out that Fribble’s preferences are represented by the utility function u(s, t) = s + ln t where s is the number of stamps he collects and t is the number of Twinkies he consumes. The price of stamps is ps and the price of Twinkies is pt. Donald’s income is m.

(a) Write an expression that says that the ratio of Fribble’s marginal utility for Twinkies to his marginal utility for stamps is equal to the ratio of the price of Twinkies to the price of stamps. 

(b) You can use the equation you found in the last part to show that if he buys both goods, Donald’s demand function for Twinkies depends only on the price ratio and not on his income. Donald’s demand function for Twinkies is:

(c) Notice that for this special utility function, if Fribble buys both goods, then the total amount of money that he spends on Twinkies has the peculiar property that it depends on only one of the three variables m,pt, and ps, namely the variable.

(d) Since there are only two goods, any money that is not spent on Twinkies must be spent on stamps. Use the budget equation and Don- ald’s demand function for Twinkies to find an expression for the number of stamps he will buy if his income is m, the price of stamps is ps and the price of Twinkies is p_t

(e) The expression you just wrote down is negative if m < ps. Surely it makes no sense for him to be demanding negative amounts of postage stamps. If m < ps, what would Fribble’s demand for postage stamps be? What would his demand for Twinkies be? 

(f) Donald’s wife complains that whenever Donald gets an extra dollar, he always spends it all on stamps. Is she right? (Assume that m > ps.)

(g) Suppose that the price of Twinkies is $2 and the price of stamps is $1. On the graph below, draw Fribble’s Engel curve for Twinkies in red ink and his Engel curve for stamps in blue ink. First draw the Engel curves for incomes greater than $1, then draw them for incomes less than $1.