3. Consider a household in a three-period version of the dynamic consumption-savings model in real terms. The three peri

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3 Consider A Household In A Three Period Version Of The Dynamic Consumption Savings Model In Real Terms The Three Peri 1 (41.33 KiB) Viewed 50 times

3. Consider a household in a three-period version of the dynamic consumption-savings model in real terms. The three periods t = 1,2,3, are meant to represent youth, middle age, and old age. The household is assumed to have the preferences: u(C₁, C2, C3) In c₁ + Bln c₂ + ² In ca where is the household's subjective discount factor. Each period, the household enters with a predetermined amount of real wealth a-1 and earns real interest income rea-1. In periods 1 and 2, but not period 3, the household receives exogenous real labor income t For simplicity, assume that (i) the interest rate is constant so that r = r₁=₂=73, and (ii) the household neither receives an inheritance or leaves a bequest so that ao = a3 = 0. (a) Write down the real period-1, period-2 and period-3 budget constraints. (b) Using the sequential Lagrangian formulation, derive two intertemporal optimality conditions. (HINT: There will be one optimality condition for periods 1 and 2, and the other for periods 2 and 3.) (c) Solve for the optimal choices (ci, c, c) in terms of exogenous variables only. priv (d) Write down the expression for real private savings in period 1, si, in terms of exogenous variables only. Perform comparative static analysis to mathematically how an increase in the real interest rate would affect s