A consumer's utility is given by U(A, B) = A 1/2B 1/4 , where A is consumption of apple and B is consumption of banana. Let pA and pb denote the prices of apple and banana, and let m be the consumer's income.

(a) State the "optimality condition" characterizing the best affordable bundle.

(b) Derive the consumer's demands for apple and banana.

(c) What is the consumer's optimal consumption if pA = pB = 1 and m=120?

(D)Suppose that the price of Apple rises to pA = 2 and at the same time income increases to m=160? Is the bundle (A , B ) in (c) still affordable? Is the consumer off or worse off as a result of the change in price and income?