Consider the consumer problem with two goods, apples and oranges. Let x be the amount of apples and y be the amount of oranges, and let u(z,y) = 24/x + y be the utility function of the consumer. Let p, be the price of apples, p, be price of oranges, and I be the income of the consumer. (a) Using the condition that the MRS is equal to the relative prices, that is, du/dx _ ps du/dy py' derive the demand functions of apples and oranges. (b) Even though the demand function of apples does not explicitly contain I, it is assumed that I cannot be too small. Explain why this assumption is necessary. (c) Let I = 90 and suppose that p, = 6. Consider a price increase of apples from 2 to 3 that leaves the price of oranges unchanged at 6. Calculate the substitution effect and the income effect from this price change regarding the demand for apples