OPEN-ECONOMY MARKET: Nominal Income Targeting 3

The model depicts an open economy that is small in a sense that will be spelled out below. This economy is populated by a continuum of households over (0,1). A typical household maximizes P7 w(C,+/, C,+/_ь Mt+Jf /*%), where Ct is an index of household consumption in period f, Л/,/7*4, denotes its end-of-period real money holdings (which facilitate period t transactions), F4, is the general price level, and u(Ch Ct~u М/ F*t) is the instantaneous utility function. The appearance of Ct~i in w(*) implies that preferences are not time-separable with respect to consumption; however, we assume that «(•) is separable across consumption and money balances, taking the specific functional form
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with с > 0, у > 0, a * 1, у Ф 1, and Ле[0,1). Preferences over consumption thus incorporate habit formation, with the functional form used in (4.1) being a special case of that in Carroll, Weil and Overland (1995), the special case being suggested by Fuhrer’s (1998) estimates.11 In (4.1), v, is a preference shock whose behavior we specify in Section 7. Households consume many goods — all of them domestically produced. The C, variable appearing in (4.1) is the quantity consumed in / of an aggregate of these goods, with the index constructed in the Dixit-Stiglitz (1977) manner, with C, = [J 1oC,(/)(0“1)/e<#]e/(0_1), where Ct(j) denotes the household’s period t consumption of good j\ and 0 > 1. All goods are differentiated from each other.
While a typical household consumes an aggregate of all goods, it specializes in production, using the CES technology
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where а^ОД], and vj e(-oo,oo). In (4.2), At is an exogenous technology shock entering all households’ production functions; N? is the amount of labor hired by the household in period t\ and IMf is the quantity purchased by the household of the foreign-produced good, which is an input in production. There is only one type of foreign good explicitly recognized, but it too could be viewed as a Dixit-Stiglitz aggregate with different goods being used by different domestic producers. Due to its monopoly power over the good it produces, household / treats the good’s price, which is Pt in domestic-currency units, as a choice variable, while taking the domestic aggregate price level PAi, the nominal exchange rate Sty and the foreign price level Pt* as given.

Having chosen Ph the household produces whatever quantity of its output is demanded. The household has two types of buyer for its good: domestic residents (i.e., other households in the same country) and the rest of the world (to which it may export its good). The household may not price-discriminate, so the price of good / to foreign purchasers is simply (Pt/ St).13 Let DY? be the total quantity demanded by all domestic households of the representative household’s output, and let EX? be the quantity of the good demanded by foreigners. (Thus, Y? = DY? + EX?). It may be shown (e.g., Obstfeld and Rogoff, [1996, ch. 101) that domestic households’ demand function for good / is given by payday loans with bad credit

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