ECN 713 Spring 2010
Natalia Kovrijnykh
Problem Set 6: Due on Thursday, April 15, in class
(100 points total)
1. [25 points] Consider the following endowment economy. There is a continuum of
consumers on the unit interval. Each has preferences given by
E
1
X
t
=0
t
u
(
c
t
; ±
t
)
;
where
c
t
is consumption in period
t
and
±
t
is a preference shock. The preference shock
Q
(
±
t
; ±
t
+1
)
. This
process is the same for all individuals and the realizations are i.i.d. across individuals. For
each individual the value of
±
0
is given. Each individual also faces a stochastic endowment
of the consumption good, denoted by
y
t
, with the transition function
P
(
y
t
; y
t
+1
)
, where
again this process is the same for all individuals and realizations are i.i.d across individuals.
The processes for preference shocks and endowment shocks are assumed to be uncorrelated.
Consider the following market structure. In each period there is a market for the single
consumption good and a market for one period ahead borrowing and lending. Individuals
are not allowed to have debt below
b
. All individuals begin with zero as their net asset
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 Spring '10
 natalia
 Limit of a function, Limit of a sequence, Limit superior and limit inferior, recursive competitive equilibrium, Natalia Kovrijnykh

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