Investment and Interest Rate Policy in the Open Economy



2.3 Representative Agent

The representative agent chooses consumption C, domestic real money balances M/P ,
and leisure 1
- L, to maximize utility:

max


Eo∑βtU Ct, M
P
t


1 - Lt


(13)


t=0


where the discount factor is 0 < β < 1, subject to the period budget constraint

EtΓt,t+1Bt+1 +Mt +Pt (Ct + It)


Bt+Mt-1+PtwtLt+PtrrtKt+


1 Πtd(h)
0


- Υt. (14)


The agent carries Mt-1 units of money, Bt nominal bonds and Kt units of capital into
period
t. Before proceeding to the goods market, the agent visits the financial market
where a state contingent nominal bond
Bt+1 can be purchased that pays one unit of
domestic currency in period
t + 1 when a specific state is realized at a period t price
Γ
t,t+1. During period t the agent supplies labor and capital to the intermediate good
producing firms, receiving real income from wages
wt , a rental return on capital rrt ,
nominal profits from the ownership of domestic intermediate firms Π
t and a lump-sum
nominal transfer Υ
t from the monetary authority. The agent then uses these resources to
purchase the final good, dividing purchases between consumption
Ct and investment It .
The purchase of an investment good forms next period’s capital according to the law of
motion

Kt+1 = (1 - δ)Kt + It,                             (15)

where 0 < δ < 1 is the depreciation rate of capital.

For analytical simplicity we assume that the period utility function is separable among
its three arguments and the labor supply elasticity is infinite.
8 The first-order conditions
from the
home agent’s maximization problem yield:

βRtEt { ⅞(⅛τTP~i } = 1                   (16)

Uc(Ct) Pt+1

8Both Dupor (2001) and Carlstrom and Fuerst (2005) use the same functional form for their respective
closed-economy studies.



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