## OPEN-ECONOMY MARKET: Nominal Income Targeting 4

Labor is immobile across countries and, in addition to being an employer of labor, each household is endowed with one unit of potential work-time each period, which it supplies inelastically to the domestic labor market. Governments, both domestic and foreign, are assumed not to issue debt, but each country has a private security denominated in units of its own output. Source Domestic households may purchase the domestic security for (1+r,)”1 per unit in period t, and it is redeemed for one unit of domestic output in period /+1.

Foreigners purchase only the bond denominated in their own output, which they may purchase for (1+r,*)”1 units of foreign output and which is redeemed for one unit of foreign output one period later. Domestic households may also purchase this bond, but the price they must pay (expressed in foreign output units) is (1+к,)”1(1+а*,*)“м6 Let Bt+i and BHi* denotes the quantity of domestic and foreign bonds, respectively, purchased in t by the representative household.

The household also receives TR{ in lump-sum real transfers from the home government. The budget constraint for a typical household, expressed in real terms, is therefore

As labor supply is inelastic, another optimality condition is Nts ~ 1 for all t. However, with the price adjustment specification that we employ (detailed in the next section), the level of output will in general differ from its natural — i.e., flexible-price — value; output will be demand-determined and producers will hire the required level of labor input. Thus, there will not be labor market clearing: the realized value of labor supplied will vary from period to period depending on demand conditions, usually departing from the desired level Nts= 1.

As a producer, each household chooses the optimal values of its inputs, Nf and lMtd. This leads to the following pair of conditions for the typical household:

Equations (4.11) and (4.12) indicate that, in a symmetric equilibrium, the aggregate markup (i.e., the ratio of the price level to aggregate marginal cost) is given by (&t /£). The household has one more decision to make, namely its choice of Pt.