Problem 1. 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.
(b) If the price of cow feed is p and her income is m, how much hay does Lolita choose?
(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?
Problem 2. F. Flintstone has quasi-linear preferences and his inverse demand function for Brontosaurus Burgers is P(b) = 30 − 2b. Mr. Flintstone is currently consuming 10 burgers at a price of 10 dollars.
(a) How much money would he be willing to pay to have this amount rather than no burgers at all? What is his level of (net) consumer’s surplus?
(b) The town of Bedrock, the only supplier of Brontosaurus Burgers, decides to raise the price from $10 a burger to $14 a burger. What
is Mr. Flintstone’s change in consumer’s surplus?