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 x square divided by x+ 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. p = f(x)

(b) If the price of cow feed is p and her income is m, how much hay does Lolita choose?

(c) Suppose that Lolita's daily income is $3 and that the price of feed is $.50. What bundle does she buy?