2. Adam, Brenda, and Casper each have $24, which they divide between goods 1 and 2. Adam's utility function has the form, UA(X1, X2) - min{axl, x2}, where a > 0 is a parameter. Brenda's utility function has the form, UB(X1, X2) - bx1 + 12, where b > 0 is a parameter. Casper's utility function is UC(X1, X2) = xx3, where c > 0 is a parameter. The price of good 1 is pi and the price of good 2 is p2. (30 points) (a) When the prices are p1 = 4 and p2 - 2, Adam purchases 3 units of good 1. What must be the value of a? How many units of good 2 does he purchase at these prices? Justify your answer mathematically. (8 points) (b) When the prices are p1 = 4 and p2 - 2, Brenda purchases 4 units of good 1. What must be the value of b? How many units of good 2 does she purchase at these prices? Justify your answer mathematically and explain, in words, how you arrived at your answer. ( points) (c) When the prices are p1 - 4 and p2 - 2, Casper purchases 3 units of good 1. What must be the value of c? How many units of good 2 does he purchase at these prices? Justify your answer mathematically. (8 points) (d) Starting from the initial prices p1 = 4 and p2 - 2, suppose the price of good 1 increases to 6. For Casper, compute the total effect of the price change on consumption of good 1 and decompose this into income and Slutsky substitution effects. Explain, in words, the process you followed to arrive at your answer. (6 points)