Question

# Consider a consumer with preferences over current and future consumption given by U (c1, c2) =...

Consider a consumer with preferences over current and future consumption given by U (c1, c2) = c1c2 where c1 denotes the amount consumed in period 1 and c2 the amount consumed in period 2.

Suppose that period 1 income expressed in units of good 1 is m1 = 20000 and period 2 income expressed in units of good 2 is m2 = 30000. Suppose also that p1 = p2 = 1 and let r denote the interest rate.

1. Find the optimal consumption bundle when r=0.15. Is the consumer a saver or a borrower?

2. Let p1 = p2 = 1 and r = 0:2. Suppose the consumer is asked to choose between two bundles, (c1; c2) = (25; 16) and (c1; c2) = (9; 36): Which one would she choose?

3.Consider again our consumer from above, and suppose that (m1; m2)=(110; 100), p1 = 1, and r = 0: What are the inflation rates that make her be a saver and what are the ones that make her be a borrower?

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