Investment and Interest Rate Policy in the Open Economy

Uc(Ct) =βEtUc(Ct+1)[Etrrt+1 +(1-δ)]                  (18)

^um(mt)   Rt ^{- 1}

Uc(Ct) =   Rt

where Rt denotes the gross nominal yield on a one-period discount bond defined as R_t^-1 ≡
Et{Γt,t+1}. Equation (16) is the consumption Euler equation for the holdings of domestic
bonds and the money demand equation is given by (19). Equations (17) and (18) are the
respective labor supply and optimal investment conditions. Optimizing behavior implies
that the budget constraint (14) holds with equality in each period and the appropriate
transversality condition is satisfied. Analogous conditions apply to the foreign agent.

From the first-order conditions for the home and foreign agent, the following risk-
sharing conditions can be derived:

Rt = R*Et {et+¹}

Q = _o ^uc(Ct )                                 (21)

Q^{t q}0 Uc(Ct)                                     ⁽ )

where the constant q₀ = Q₀ [U^c(C2) j. Equation (20) is the standard uncovered interest
rate parity condition and equation (21) is the risk sharing condition associated with
complete asset markets, which equates the real exchange rate Q with the marginal utilities
of consumption.

2.4 Monetary Authority

The monetary authority can adjust the nominal interest rate in response to changes in
domestic price inflation π_t^h_+v or to changes in consumer price inflation πt+v , according to
the rules:

Rt = μ (∏h+v) = R (^π∏r) ,                       (22)

Rt = μ (∏t+v ) = R (^πt+v )^μ,                          (23)

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