2.1 A simple cash-in-advance model
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Our description of the model used in this section can be brief, since it will be familiar to many readers. The utility of the representative household is
where ct is consumption. Each period is divided into two exchanges: in the financial exchange, the household receives that is endowment, pays its taxes, and trades assets. In the products exchange that follows, the household must pay for consumption goods through money, bring about the familiar cash in breakthrough constraint
where Mt is money and Pt is the price level. The household spending plan constraint because that the jae won exchange is
where Bt space nominal government bonds, it is the gross nominal interest rate, y is the fixed family endowment, and also τt is a lump-sum tax.
and a transversality problem that we specify later. If that > 1, climate the household cash in development constraint is binding. The government likewise faces a cash in breakthrough constraint; therefore in equilibrium
where because that simplicity we will certainly let government spending (g) be continuous over time. The design is rather monetarist, with velocity collection equal to one. Because government security is constant, consumption is also continuous (since ct = y − g), and also the Euler equation reduces come
where St ≡ Pt(τt − g) is the major surplus. We will enable the bump sum-tax (τt) to fluctuate randomly, over time; this is the only stochastic element in our straightforward CIA model.
Sebastian Schmidt, Volker Wieland, in Handbook the Computable basic Equilibrium Modeling, 2013
The design economy contains a large number of similar households. The representative family members is characterized by the following preferences regarding consumption, labor and real money balances:
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Equation (22.1) to represent households’ intended discounted lifetime utility, wherein Ct denotes the household’s usage of a basket of identified goods, Mt actions the end-of-period money balances, Pt is the price the the consumption good basket in terms of money and Ht denotes the variety of hours worked. The consist of of genuine money balances in the utility role is a conventional short-cut to capture their transaction solutions (see, e.g. Woodford, 2003).1 The consumption goods basket Ct is composed of a continually of differentiated goods:
where ɛ>1 and Ct(i) denotes intake of an excellent i. The price index Pt is then defined as the minimum expenditure at which the household can buy one unit of Ct: