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Imagine a saver that can deposit at a bank but the return is risky. In the good state they receive (1+r)d and in the bad state they only get e. Expected utility is given by
EU = Ln(c1) + b[qc21 + (1-q)c22]
where 1 > b > 0, c1 = w - d, c21 = (1+r)d, and c22 = e.

A. Find the deposit function.

Banks make loans that pay (1+r)d or e. The investor borrows b and must repay it in the good state plus interest. In the bad state, the investor only pays e and essentially defaults. Expected profit is q[Ak - k2/2 - (1+r)k] + (qe - (1-q)e), where A > 1+r.

B. Find the optimal investment k.

Equilibrium requires s = d = l = b = k, or s = k.

C. Solve for k using s.

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Microeconomics, Economics

Category:- Microeconomics
Reference No.:- M938737

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