Adam's utility function is U = B1/2 A1/2 where B, A represent the number of bananas and apples respectively that he consumes.

(a) Write down Adam's demand functions for A and B. If his income is $120 and PA = $8 and PB = $9, how much A and B will he buy?

(b) Suppose a rationing scheme is introduced. Adam is given 38 ration coupons. The ration coupon "prices" of A and B are set at 3 and 2 coupons respectively. Adam continues to have to pay the money prices also. (In other words, to buy one unit of A he must pay $8 and 3 coupons.) How much A and B will he now buy?

(c) Suppose the ration coupon "prices" had been 6 for apples and 3 for bananas, and Adam's allocation was 48 coupons. What would be his consumption?

(d) Finally, suppose a black market for coupons develops and the black market price of a coupon is $1. Assuming his coupon allocation is as in (c), how much A and B will Adam buy, and how many coupons will he buy or sell?