This preview shows pages 1–2. Sign up to view the full content.
Econ 387L: Macro II
Spring 2006, University of Texas
Instructor: Dean Corbae
Problem Set #8 Due 3/28/06
I. This question explores the equivalence between time 0 ArrowDebreu forward markets
and Arrow’s sequential representation in a nonstochastic exchange economy. There are
I
households and the horizon is in
f
nite. Goods are nonstorable and household
i
has an
endowment of goods
y
i
>
0
each period. Household
i
’s utility function is given by
∞
X
t
=0
¡
β
i
¢
t
u
i
(
c
i
t
)
where
u
i
is strictly increasing and concave, continuously differentiable.
1. Write household
i
’s budget constraint in a forward markets economy where
p
t
is the
forward price of the consumption good delivered at time
t
set at time
0
.
2. Write household
i
’s budget constraint in a sequential markets economy where
q
t
is the
spot price of the consumption good in period
t, a
i
t
+1
are loans (if positive) or borrowings
(if negative) by household
i
between time
t
and
t
+1
,
and
r
t
is the interest paid at
t
on
assets chosen at
t
−
1
.
Assume that
a
0
=0
.
3. Show under what conditions the two constraints equivalent. Would a borrowing
constraint be suf
f
cient to generate the equivalence?
4. De
f
ne a competitive forward market equilibrium.
5. Can the value of a household’s income be in
f
nite in a competitive forward market
equilibrium? What implications does this have for the value of the aggregate endowment?
How is this used in the proof of the
f
rst welfare theorem for this economy (i.e., that a
competitive forward market equilibrium is Pareto optimal)?
6. What are the conditions which characterize a forward market equilibrium? Count
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '07
 CORBAE

Click to edit the document details