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Question 13) Jane is a vegetarian who consumes only two goods: apples and spinach. Let x denote the quantity of apples, and y denote the quantity of spinach that Jane consumes every week. Both x and y are measured in pounds. Jane's preferences are represented by the Cobb-Douglas utility function u(x, y) = x3'4y1'4. Jane's weekly income is I. The price of one pound of apples is p,, and the price of one pound of spinach is pv. (a) Find the Marshallian demand functions for apples and spinach, x(px, pV,I) and y(px, pv, I) by writing down Jane's optimization problem and solving it with the Lagrange method. (b) What is Jane's demand for each of the goods at pX = $3, py = $1, and I = $56? What is the highest utility level, U', that Jane can achieve ifpx= $3, py = $1, and I = $56? The government appreciates Jane's healthy eating habits and wants to subsidize her. The government is considering three policies. 0 The first policy is to subsidize only apples (as more expensive good) at the rate s =$1 (which means that effectively, Jane will be paying p"x =$2 per pound of apples). 0 The second policy will subsidize both goods at the same rate 0