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
Pt
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
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)
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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