Cathy chooses between two goods, :3 and y, with prices pm and py, respectively. She has an income I and her preferences are represented by the utility function U($, y) = 4mg. 1. Assuming that an interior solution exists to the constrained utility maximization problem, derive Cathy 's Marshallian demand function for each of the two goods. Are both goods normal? Explain 2. Find the indirect utility function, V(p$, py, I). 3. Suppose that I = 100, 30m = 5 and pg = 4. How much of good a: and good y will Cathy optimally choose? 4. Now the price of good :1: rises to p;c = 10, while income (I = 100) and the price of good y, pg 2 4, remain unchanged. What quantities does Cathy buy and what is her resulting utility? Illustrate graphically