- A. MODEL DERIVATIONS Consider the problem of individual household i. We define W t+1(i) ≡ m t(i)+ b t(i) and x t+1(i) = m t(i). Then the household’s problem can be solved by the very same Lagrangian as in Evans and Honkapohja (2007), i.e., L = E t ( ∞ X t=0 βt (1 − Ã1)−1 c t(i)(1−Ã1) + A(1 − Ã2)−1 (x t(i)À−1 t )(1−Ã2) −βt+1 1,t+1 W t+1(i) − y + ct(i) + Ät − x t(i)À−1 t − Rt−1À−1 t (W t (i) − x t(i)) −βt+1 2,t+1 x t+1(i) − m t(i)
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