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EC 813A
PROBLEM SET 3
TO BE HANDED IN ON FRIDAY OCTOBER 17TH
Exercise 1. Infinite horizon pure consumption economy (Difficulty: Easy/Average)
Consider the household maximizing the utility of consumption from present to future
under certainty:
Ȉ
t=0
¡
ȕ
t
ln c
t
(ln x is natural log of x)
Subject to the budget constraint:
B
t+1
=RB
t
+y
t
 c
t
Taking as given the initial asset RB
0
, real gross interest rate R and the path of the wage
income y
t
.
(i)
Derive the relationship between permanent income and the initial asset and
the wage income from present to future.
(ii)
Write down the Bellman equation. Derive the value function.
(iii)
Show that the consumption is proportional to the permanent income.
(iv)
Suppose that the wage grows at constant rate: y
t+1
=(1+
Ȗ
) y
t
, where
(1+
Ȗ
)<R. Derive the relationship between consumption and the initial asset
and the current wage explicitly.
Exercise 2. Infinite horizon production economy with uncertainty (Difficulty: High)
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 Spring '08
 MINETTI
 Macroeconomics, Utility

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