Question

1. Ann’s utility function from consuming x and y is given by U(x, y) = x 1 4 y 1 4 .

a) Write down the budget constraint and rationality condition.

b) Find Ann’s demand curves of x and y.

c) Now suppose Ann’s income is $100. The price of x is $1 and the price of $y is 2. What’s the optimal bundle?

d) If the price of x increases to $2, and other things are the same as in part c). What’s the new optimal bundle? If Ann wants to enjoy the same utility as in part c), while consuming an optimal bundle. How much money Ann should borrow from banks?

e) If Ann’s income increases to $200, and other things are the same as in part c). How many x and y should Ann consume now to maximize her utility?

Answer 1