4721_HW4 - Econ 4721 Money and Banking Fall 2008 Homework 4...

Econ 4721: Money and Banking, Fall 2008
Homework 4
Due Monday, December 8, at the beginning of class.
Problem 1. Bank Runs
Consider an economy in which consumers live for three periods (called period 1, 2, and 3). Each consumer
has an endowment of 20 goods when young, and nothing when middle-aged and when old. Utility from
consumption depends on what ”type” a consumer is, as follows:
u ( c
1
, c
2
, c
3
) =



log [ c
2
] for type 1 — impatient
log [ c
2
+ c
3
] for type 2 — patient
There are 200 consumers, and half will become each type. However, consumers only learn their type
in period 2. Assume no one else can observe the types (an agent knows her type only).
There are two assets available in the economy, money and capital, offering the following rates of
return:
One-Period Return Two-Periods Return
Fiat Money 1 1
Capital 0 . 9 1 . 5
(a) Suppose a consumer, on her own, saves half her goods in each asset in period 1. After finding out
her type, she consumes all the savings in the appropriate period. Calculate the consumption the
consumer would receive in either period.