11. a. Suppose David spends his income M on goods x1 and x2, which are priced p1 and p2, respectively. David's preference is given by the utility function

(1, 2) = 1 + 2.

(i) Derive the Marshallian (ordinary) demand functions for x1 and x2. (25 marks)

(ii) Show that the sum of all income and (own and cross) price elasticity of demand

b.for x1 is equal to zero. (25 marks) b. For Jimmy both current and future consumption are normal goods. He has strictly convex and strictly monotonic preferences. The initial real interest rate is positive. If the real interest rate falls, in each of the following cases, argue what will happen to his period 2 consumption level? Clearly illustrate your argument on a graph.

(i) He is initially a borrower. (25 marks)

(ii) He is initially a lender. (25 marks)