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:

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

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
Γt,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 Πt and a lump-sum
nominal transfer Υt 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)

U_c(C_t) P_t+1

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

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