Department of Economics
University of Maryland
Economics 325
Intermediate Macroeconomic Analysis
Practice Problem Set 5
Professor Sanjay Chugh
Spring 2011
1.
Infrequent Stock Transactions.
Consider a representative consumer at time t
seeking to maximize the sum of discounted lifetime utility from t on,
0
(
)
s
t
s
s
u c
E
f
±
¦
subject to the infinite sequence of flow budget constraints
2
2
t
t
t
t
t
t
t
t
t
Pc
S a
S a
D a
Y
²
²
±
±
±
,
where the notation is as in class:
t
a
is holdings of a real asset (a “stock”) at the end
of period t,
t
S
is its nominal price in t,
t
D
is the nominal dividend that each units of
assets carried into t
from period t2
pays out,
t
Y
is nominal income in t,
t
c
is
consumption in t, and
t
P
is the nominal price of each unit of consumption in t.
Note
well how the budget constraint is written:
it is assets accumulated in period t2 that
pay off in period t – thus, in this model, stocks (for some reason…) must be held for
two periods, rather than being able to be traded every period.
Construct the
Lagrangian to compute the stock price
t
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 Spring '08
 chugh
 Economics, Quantum Field Theory, Lagrangian, instantaneous utility function, habit persistence

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