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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 functionU(x, y) =
x 22 + , 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, where0 < ≤ 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_________ variation. Which is bigger, the compensating 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? _________
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