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4.2. THE ONE-MONEY MONETARY ECONOMY 115and the lump-sum monetary transferW t = P t−1(ω xt−1 x t−1 + ω yt−1 q t−1 y t−1 )P t| {z }Dividends+ ω xt−1 e t + ω yt −1e ∗ t| {z }+Ex-dividend share values∆M t2P t| {z }Money transfer. (4.26)In the securities market, the domestic household allocates W t towardscash m t to Þnance shopping plans and to equitiesW t = m t+ ω xt e t + ω yt e ∗ tP . (4.27)tThe household knows that the amount of cash required to Þnance thecurrent period consumption plan ism t = P t (c xt + q t c yt ). (4.28)The cash-in-advance constraint is said to bind. Substituting (4.28) into(4.27), and equating the result to (4.26) eliminates m t and gives thesimpler consolidated budget constraintc xt + q t c yt + ω xt e t + ω yt e ∗ t = P t−1P t[ω xt−1 x t−1 + ω yt−1 q t−1 y t−1 ]+ ∆M t2P t+ ω xt−1 e t + ω yt−1 e ∗ t . (4.29)The domestic household’s problem is therefore to maximize⎛∞XE t⎝j=0⎞β j u(c xt+j ,c yt+j ) ⎠ , (4.30)subject to (4.29). As before, the terms that matter at date t areu(c xt ,c yt )+βE t u(c xt+1 ,c yt+1 ),so you can substitute (4.29) into the utility function to eliminate c xt andc xt+1 and to transform the problem into one of unconstrained optimization.The Euler equations characterizing optimal household behaviorare⇐(81-83)