Question 1: Choice and Demand with Weft-Behaved Utiiity Functions. (50 pts) Consider the following utility function: \"(x1,x2) 2 xi\" 175-3? (a) Given income level m, prices p1 and p2, nd the demand for both goods, 1:: = x1(p1, p2, m) and x3 = I2(PI,P2,m)- Hint: use method 1 as seen in class with the condition M R3 = 5; (12 pts} (b) Let a = %, m = 24 and p1 = p2 = 4. Draw the budget s_et, the optimal points and the indifference curve in a graph. Make sure to label your axes appropriately and indicate the origin. No need for a precise indifference curve, the general shape is sufcient. (10 pts) (c) Now, let pi = 8. i.e. there is a change in price of good 1, but everything else stays the same. Draw the new graph (budget set, optimal points, origin and the indifference curve). (10 pts) (d) Now, suppose that a = 411, but that all the other variables are as in (b): p1 = p; = 4 and m = 24. Draw the new graph (budget set, optimal points, origin and the indifference curve). (10 pts) (e) Why are the values of .153 the same in (b) as in (c)? Why are they not the same in (b) as in (d)? (3 PtS)