Olive has the utility function U(X,Y) = X1/3Y2/3, where X is the number of apples consumed and Y is the number of oranges consumed. Let the income I = 90.

(a) Suppose the price of apples is PXa = 2 and the price of oranges is PY = 2. What are the quantities demanded of apples and oranges when Olive maximizes her utility subject to her budget constraint?

(b) Suppose the price of apples decreases to PXb = 1 and the price of oranges remains constant at PY = 2. What are the quantities of apples and oranges demanded by Olive after this price change?

(c) What is the substitution effect of the previous price change? [Hint: What is a way to minimize expenditure to achieve the profit level in part (a) at the prices in part (b)?]

(d) What is the income effect of the previous price change? [Hint: What is the difference between the total effect of part (b) and the substitution effect of part (c)?]