2.1 A an easy cash-in-advance model

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Our description of the version used in this section deserve to be brief, because it will certainly be familiar to most readers. The energy of the representative household is

where ct is consumption. Each duration is divided into 2 exchanges: in the gaue won exchange, the household receives its endowment, pays its taxes, and also trades assets. In the products exchange the follows, the family members must salary for intake goods through money, causing the familiar cash in breakthrough constraint

where Mt is money and also Pt is the price level. The household spending plan constraint because that the financial exchange is

where Bt space nominal federal government bonds, that is the gross nominal interest rate, y is the fixed household endowment, and also τt is a lump-sum tax.

and a transversality condition that we specify later. If that > 1, climate the family members cash in development constraint is binding. The government likewise faces a cash in advancement constraint; therefore in equilibrium

where because that simplicity we will let government spending (g) be continuous over time. The model is fairly monetarist, through velocity set equal come one. Due to the fact that government spending is constant, consumption is also continuous (since ct = y − g), and the Euler equation reduces come

where St ≡ Pt(τt − g) is the major surplus. Us will permit the bump sum-tax (τt) to fluctuate randomly, over time; this is the just stochastic element in our simple CIA model.

Sebastian Schmidt, Volker Wieland, in Handbook of Computable basic Equilibrium Modeling, 2013 Households

The model economy consists of a large number of identical households. The representative household is characterized by the adhering to preferences concerning consumption, labor and real money balances:

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Equation (22.1) represents households’ meant discounted lifetime utility, wherein Ct denotes the household’s consumption of a basket of differentiated goods, Mt procedures the end-of-period money balances, Pt is the price of the consumption great basket in regards to money and also Ht denotes the variety of hours worked. The consist of of genuine money balances in the utility function is a traditional short-cut to catch their transaction solutions (see, e.g. Woodford, 2003).1 The usage goods basket Ct is composed of a continually of identified goods:

where ɛ>1 and Ct(i) denotes consumption of an excellent i. The price table of contents Pt is then defined as the minimum expenditure at which the family can buy one unit of Ct: