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%)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

3. Consider a three-period overlapping generations economy with N young people born each
period. 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 good
put in storage in the current period. Alternatively, there is a capital good, with one unit
of the consumption good acquiring one unit of capital. For each unit of capital acquired
in date t, 1.2 units of the consumption good will be received at date t+2. If the person
liquidates the capital after one period, though, then only .8 units of the consumption good
can be obtained at date t + 1. Assume that there is a 50% probability that a person will
want to consume only when middle-aged and a 50% probability that a person will want
to consume only when old. Whether someone is an "early" or "late" consumer will be
revealed only at time t + 1.
(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%)

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