4721_HW3_AK

4721_HW3_AK - Econ 4721 Money and Banking Fall 2008...

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Unformatted text preview: Econ 4721: Money and Banking, Fall 2008 Homework 3 Answer Key 1 Problem 1. Risky Lending (20 points) Consider a standard two-period OLG economy, where population grows according to the process N t = 1 . 08 N t- 1 and the stock of fiat money is constant. Suppose that agents in this economy are able to hold fiat money (a perfectly safe asset), or may lend to some other agents who have a 10% chance to default on their debt. In case of no default, the borrower repays the loan back and offers a gross real return of r per unit of consumption. (a) Calculate the rate of return r in the stationary equilibrium, assuming that agents are risk-neutral. (b) Now assume that everybody in this economy became risk-averse. Explain what you expect to happen to the equilibrium value of r . 1.1 Answer (a) First, the rate of return on fiat money here is: v t +1 v t = n z = 1 . 08 1 = 1 . 08 Since people are risk neutral, they only care about expected returns when consider risky assets like lending here. A risk-neutral lender would be willing to make a loan if the expected real interest rate is equal to 1 . 08. We know that borrowers default on the loans in 10% of cases, and pay back the rate r in other cases. This gives us the expected value of interest rate E [ r ]: E [ r * ] = 0 . 9 r + 0 . 1(0) = 0 . 9 r Thus we are only left to solve a very simple equation: . 9 r = 1 . 08 r * = 1 . 2 and hence the equilibrium rate will be equal to 1 . 2 (b) We know that a risk-neutral person will accept an expected rate r * = 1 . 2. We also know that a risk- averse person would demand an extra premium for the fact that s/he may lose the lended amount altogether. Hence we would expect r * to increase beyond 1 . 2 to get to a new equilibrium level. 1 2 Problem 2. Risky Assets (40 points) Consider an individual consumer who lives for two periods, endowed with y = 40 goods when young and nothing when old. The consumer wants to save half of the endowment (thus, 20 goods). Saving can be done in either a safe (risk-free) asset (asset a ) or a risky asset (asset b ). The real rate of return on asset b is uncertain, and depends upon which event occurs in the second period, as summarized in the following table: Event H Event L Probability of occurence π H = 1 2 π L = 1 2 Return on asset a r a H = 1 . 25 r a L = 1 . 25 Return on asset b r b H = 2 r b L = 0 . 5 where the notation r i j denotes the real rate of return on asset i if event j occurs in the second period....
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4721_HW3_AK - Econ 4721 Money and Banking Fall 2008...

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