Suppose you have an income of $24 and the only two goods you consume are apples (x1) and peaches (x2). The price of apples is $4 and the price of peaches is $3.
A. Suppose that your optimal consumption is 4 peaches and 3 apples.
(a) Illustrate this in a graph using indifference curves and budget lines.
(b) Now suppose that the price of apples falls to $2 and I take enough money away from you to make you as happy as you were originally. Will you buy more or fewer peaches?
(c) In reality, I do not actually take income away from you as described in (b) but your income stays at $24 after the price of apples falls. I observe that, after the price of apples fell, you did not change your consumption of peaches. Can you conclude whether peaches are an inferior or normal good for you?
B. Suppose that your tastes can be characterized by the function u(x1,x2) = x1α x2(1−α) .
(a) What value must α take in order for you to choose 3 apples and 4 peaches at the original prices?
(b)What bundle would you consume under the scenario described in A(b)?
(c) How much income can I take away from you and still keep you as happy as you were before the price change?
(d)What will you actually consume after the price increase?