Homework 7
Graduate Macroeconomics. Viktor Tsyrennikov
Question 1.
Exercise 9.3.
Assume
u
(
c
) =
ln
(
c
). Ignore part (c).
Question 2.
Time is discrete.
There is one perishable good at each
date.
Uncertainty is fully summarized by a firstorder Markov process
s
t
with transition density
F
(
s
t
+1

s
t
).
Individuals live for 3 periods: age 0,1,2. An individual born at history
s
t
ranks different consumptions streams according to:
U
(
c

s
t
) =
E
bracketleftbig
ln
(
c
(
s
t
)) +
γln
(
c
(
s
t
+1
)) +
ln
(
c
(
s
t
+2
))
bracketrightbig
,
γ
greaterorequalslant
1
.
Note that every individual values consumption in the second period of her
life more than in other periods.
Financial markets trade one unit of stock paying
d
(
s
t
) units of good in
state
s
t
. Stock is traded at the exdividend price
q
(
s
t
). Individuals’ initial
endowment of stock is zero.
Individuals receive 1 unit of good in the first period that they live and
no income in later periods of their life.
Assume that the economy starts
at
t
=
∞
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 Spring '11
 ViktorTsyrennikov
 Macroeconomics, Period, stationary competitive equilibrium

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