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9.1. THE REDUX MODEL 265Home CountryForeign Countryz z*0 n1Figure 9.1: Home and foreign households lined up on the unit interval.provides individuals with indirect utility because higher levels of realcash balances help to lower shopping (transactions) costs.We assume that households have identical utility functions and wewill work with a representative household.Representative agent (household) in Redux model. Letc t (z) bethehome representative agent’s consumption of the domestic good z, andc t (z ∗ ) be the agent’s consumption of the foreign good z ∗ .Peoplehavetastes for all varieties of goods and the household’s consumption basketis a constant elasticity of substitution (CES) index that aggregatesacross the available varieties of goodsC t ==·Z 10·Z n0c t (u) θ−1θ du¸ θθ−1c t (z) θ−1θ dz +Z 1n¸ θc t (z ∗ ) θ−1 θ−1θ dz∗ , (9.1)where θ > 1 is the elasticity of substitution between the varieties. 1Let y t (z) bethetime-t output of individual z, M t be the domesticper capita money stock and P t be the domestic price level. Lifetimeutility of the representative domestic household is given byU t =∞Xj=0⎡β j ⎣ln C t+j +γà ! ⎤1−²Mt+j− ρ 1 − ² P t+j 2 y2 t+j (z) ⎦ , (9.2)⇐(147)1 In the discrete commodity formulation with N goods, the index can be written¸ θ·PNas C =z=1 c θ−1 θ−1θz ∆z where ∆z = 1. The representation under a continuumof goods takes the limit of the sums given by the integral formulation in (9.1).