Question

Emil has access to a perfect capital market1 with interest rate r ∈ (0, 1). He has preferences over bundles (x, y) ∈ R2+ of money for consumption in period 1 (x) and money for consumption in period 2 (y) that can be represented by the following utility function

u(x, y) = x2 · y

Emil has an endowment of E = (2000, 1200), that is his income in period 1 is m1 = 2000 and his income in period 2 is m2 = 1200.

1. Emil can use his endowment and save or borrow money in the capital market with interest rate r. Determine Emil’s budget constraint.

2. Suppose Emil chooses bundle (c1,c2) at interest rate r ̄. Given this choice, how would you determine whether Emil is saving or borrowing? If he is indeed saving, how do you compute the amount s(r ̄) which he saves in period 1?

3. Determine the interest rates for which Emil would be a saver (rather than a borrower) without solving for Emil’s demand.

4. For these interest rates at which Emil becomes a saver, determine the amount he saves, s, as a function of the interest rate, r.

Answer 1