The Optimal Monetary And Exchange Rate Policy By An...

Summary This article derives the optimal monetary and exchange rate policy by an optimizing model under a small stochastic open economy with imperfect competition and short run price rigidity. After the exchange rate crises, lots of countries choose to adjust flexible exchange rate together with some monetary policies. However, history gives a different opinion of how monetary policy response to nominal and real exchange rate. In the 1970s, economists suggest a flexible exchange rate could help to insulate the economy from foreign real shocks, and floating can give monetary policy a measure of independence. Thus by this opinion we can set interest rate to attain internal balance and set exchange rate to secure external balance. However,†¦show more content†¦The basic model this paper applied has a home and a foreign economy. The representative home agent must choose the consumption of home and foreign varieties and tradable bonds in terms of foreign goods and a domestic bond in terms of home money to maximize the objective function subject to the consumption basket and to the inter-temporal budget constraint. Utility function:U_t^i=E_t {∑ââ€"’ã€â€"(1+ÃŽ ´)ã€â€"^(-(s-t)) [ã€â€"ã€â€"(Cã€â€"_s^i)ã€â€"^(1-Ï )/(1-Ï )-K_s/(1+V) ã€â€"(Y_s^i)ã€â€"^(1+v) ]} subject to C_t^i=(ã€â€"ã€â€"(Cã€â€"_(H,t)^i)ã€â€"^ÃŽ ± ã€â€"ã€â€"(Cã€â€"_(F,t)^i)ã€â€"^(1-ÃŽ ±))/(ÃŽ ±^ÃŽ ± ã€â€"(1-ÃŽ ±)ã€â€"^(1-ÃŽ ±) ) and B_t^(*i)-B_(t-1)^(*i)+(B_t^i-B_(t-1)^i)/P_(F,t) = r_(t-1)^* B_(t-1)^(*i)+i_(t-1) (B_(t-1)^i)/P_(F,t) +(P_(H,t)^i)/P_(F,t) Y_(H,t)^i-P_(H,t)/P_(F,t) T_t^i-P_(H,t)/P_(F,t) C_(H,t)^i-C_(F,t)^i Then we add asymmetries into the two economies by assuming that the home economy is small relative to the foreign economy. We set the home economy as a small open economy and the foreign economy as the rest of the world. Combine with the first order derivative of the Lagrange function, we can obtain a few functions which could link the exchange rate with a price level, consumption, and interest rate. We focus on the case that the current account is always zero. A zero current account for a small open economy and the rest of the world imply thatã€â€" Cã€â€"_t^*=Y_t^*-G_t^*; and C_t Q_t^((1-ÃŽ ±)/ÃŽ ±)=Y_t-G_t. With all the results we can express the equilibrium condition in logs. Price setting as a