3. Consider a three-period overlapping generations economy with N young people born eachperiod. Each young person receives y goods, but nothing when middle-aged or when old.People can access a storage technology that yields one good next period for every goodput in storage in the current period. Alternatively, there is a capital good, with one unitof the consumption good acquiring one unit of capital. For each unit of capital acquiredin date t, 1.2 units of the consumption good will be received at date t+2. If the personliquidates the capital after one period, though, then only .8 units of the consumption goodcan be obtained at date t + 1. Assume that there is a 50% probability that a person willwant to consume only when middle-aged and a 50% probability that a person will wantto consume only when old. Whether someone is an "early" or "late" consumer will berevealed only at time t + 1.(a) Derive the equilibrium in this economy without an intermediary bank. How muchwould people invest in the storage technology if they are risk-neutral? How wouldyour answer change if you assume instead that agents are risk averse, so they preferless variance for the same expected return? (25%)(b) Derive the equilibrium with a bank, assuming the bank operates under perfect com-petition (no profits). Assume also that the bank does not expect a bank run to occur.What is the advantage of pooling risk? (25%)(c) What is the outcome in case of an (unexpected) bank run, assuming that the bankequally splits the value of its portfolio among all depositors? (25%)(d) Compare and rank outcomes from points a., b. and c., both in terms of ex-anteexpected consumption (before agents are revealed whether they are early or lateconsumers) and ex-post actual consumption for early and late consumers. (25%)

Solving all parts (a), (b), (c) and (d) stepwise below.

(a) Derive the equilibrium in this economy without an intermediary bank. How much would people invest in the storage technology if they are risk-neutral? How would your answer change if you assume instead that agents are risk averse, so they prefer less variance for the same expected return? (25%) (b) Derive the equilibrium with a bank, assuming the bank operates under perfect com- petition (no profits). Assume also that the bank does not expect a bank run to occur. What is the advantage of pooling risk? (25%) (c) What is the outcome in case of an (unexpected) bank run, assuming that the bank equally splits the value of its portfolio among all depositors? (25%) (d) Compare and rank outcomes from points a., b. and c., both in terms of ex-ante expected consumption (before agents are revealed whether they are early or late consumers) and ex-post actual consumption for early and late consumers. (25%)

(a) Derive the equilibrium in this economy without an intermediary bank. How much would people invest in the storage technology if they are risk-neutral? How would your answer change if you assume instead that agents are risk averse, so they prefer less variance for the same expected return? (25%) (b) Derive the equilibrium with a bank, assuming the bank operates under perfect com- petition (no profits). Assume also that the bank does not expect a bank run to occur. What is the advantage of pooling risk? (25%) (c) What is the outcome in case of an (unexpected) bank run, assuming that the bank equally splits the value of its portfolio among all depositors? (25%) (d) Compare and rank outcomes from points a., b. and c., both in terms of ex-ante expected consumption (before agents are revealed whether they are early or late consumers) and ex-post actual consumption for early and late consumers. (25%)

ECON MACRO

5th Edition

ISBN:9781337000529

Author:William A. McEachern

Publisher:William A. McEachern

Chapter8: Productivity And Growth

Section: Chapter Questions

Problem 1.2P

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