Lolita, an intelligent and charming Holstein cow, consumes only two goods, cow feed (made of ground corn and oats) and hay. Her preferences are represented by the utility function U(x, y) = x−x2 / 2+y, where x is her consumption of cow feed and y is her consumption of hay. Lolita has been instructed in the mysteries of budgets and optimization and always maximizes her utility subject to her budget constraint. Lolita has an income of $m that she is allowed to spend as she wishes on cow feed and hay. The price of hay is always $1, and the price of cow feed will be denoted by p, where 0 < p ≤ 1.
(a) Write Lolita’s inverse demand function for cow feed. (Hint: Lolita’s utility function is quasilinear. When y is the numeraire and the price of x is p, the inverse demand function for someone with quasilinear utility f(x) + y is found by simply setting p = f` (x).)
(b) If the price of cow feed is p and her income is m, how much hay does Lolita choose? (Hint: The money that she doesn’t spend on feed is used to buy hay.)
(c) Plug these numbers into her utility function to find out the utility level that she enjoys at this price and this income.
(d) Suppose that Lolita’s daily income is $3 and that the price of feed is $.50. What bundle does she buy? ________. What bundle would she buy if the price of cow feed rose to $1? ________.
(e) How much money would Lolita be willing to pay to avoid having the price of cow feed rise to $1? _______. This amount is known as the _______ variation.
(f) Suppose that the price of cow feed rose to $1. How much extra money would you have to pay Lolita to make her as well-off as she was at the old prices? _______. This amount is known as the compensating variation. Which is bigger, the _______ or the equivalent variation, or are they the same? _______.
(g) At the price $.50 and income $3, how much (net) consumer’s surplus is Lolita getting?