Economics Assignment

Economics Assignment

In recent years, the new Keynesian economics that incorporates imperfect competition and nominal rigidities into a dynamic general equilibrium structure for an open economy have been developed. The theoretical development in the new Keynesian literature has made it possible to analyze the dynamic effects of monetary shocks in the presence of (in)complete international capital mobility and nominal rigidities. Considering the empirical fact that the nominal rigidities are important in understanding the real effects of monetary policy, it is natural to incorporate the nominal rigidities and explore the behavior of the macroeconomic variables such as exchange rates and the current account in the open economy.

We assume an open economy which consists of domestic economy and world economy that is great deal larger than the domestic one. Economic subjects of both domestic and large economy maximize their objective function under the same condition; the difference between the two subjects is the relative importance of foreign goods in domestic consumption.

Assume that a typical consumer of domestic economy maximizes one's utility function throughout lifetime under a certain capital and time constraint

(1)

where Ct is a composite consumption index defined by

(2)

Here s-1 is the intertemporal elasticity of substitution and ? is the intratemporal elasticity of labor supply. Here Cht and Cft are indices of domestic and foreign consumption goods, and ? and 1 - ? represent the share of domestic consumption allocated to domestic goods, and imported goods. The indices are given by the following CES aggregator of the quantities consumed of each variety of good:

(3)

Here ? and measure the elasticity of substitution between domestic and foreign goods, and the elasticity of substitution among goods within each category. ß is the household's discount factor, and Et denotes the expectation operator conditioned on the information available in period t. Nt represents the domestic household's labor supply in period t. Here Zt is the home country resident's preference shock process at period t. We assume that the preference shock follows an AR(1) process.

log Zt=?z log Zt-1+?zt, -1
where ?At is .

The household faces a time constraint such that

(4)

where Lt and denote the leisure hours and time endowment of the home resident, respectively.

Since the monetary policy is specified in terms of an interest rate rule, money is not introduced in the model. The optimal allocation for each differentiated good yields the demand functions:

(5)

for all j  [0,1], where and are the price indexes for domestic and foreign goods, both expressed in home currency.

The optimal allocation of expenditures between domestic and foreign goods implies:

(6)

where the consumer price index (CPI) is given by

(7)

Here Pft is the price index for foreign goods, expressed in domestic currency.

There exists a complete asset market in the economy. Let Bt+1 denote the nominal payoff in domestic currency units of the portfolio purchased in period t and ?t,t+1 be the corresponding nominal stochastic discount factor in period t. Then the riskless one-period domestic nominal interest rate in period t is given by Rt(= 1 + rt) = [Et?t,t+1]-1 Then the household's wealth in the beginning of the period t is given by

(8)

where Wt and Gt denote the domestic nominal wage ...