PROBLEM 2: Theory of Demand

Randy chooses between two goods, x and y, with prices p_x and p_y, respectively. He has an income I and his preferences are represented by the utility function U (x, y) =x + y.

1. Assuming that an interior solution exists to the constrained utility maximization problem,

derive Randy's Marshallian demand function for each of the two goods. Are both goods

normal? Explain

2. Find the indirect utility function, V (p_x, p_y, I).

3. Derive Randy's Hicksian demand function for each of the two goods and the expenditure function. Compare the Marshallian demand for good x and the Hicksian demand for good x. Are these different functions? If so, why? If not, why not?

4. Suppose that I = 100, p_x = 1 and p_y = 2. How much of good x and good y will Randy

optimally choose?