Consider a representative household in the two-period consumption-savings model whose preferences are given by: u(c, c)=...

 

 

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Consider a representative household in the two-period consumption-savings model whose preferences are given by: u(c₁, c₂)=√ +8 √₂ In the first period the household receives exogenous real labor income 1 and real interest income rao on their wealth endowment of ao, which they split between real consumption expenditures c1 and saving s1. In the second period they again receive exogenous real labor income y2 and real interest income rai on their wealth a1. spending any remaining lifetime income on consumption while leaving behind no assets so that a2 = 0. You may assume that the subjective discount factor and real interest rate are equal to B = 1/1.1 andr= 0.1, and the initial wealth endowment is equal to ao = 0: (a) Write down the period-1 and period-2 budget constraints in real terms. (b) Set up the sequential Lagrangian, derive the consumption-savings optimality con- dition, and solve for the optimal levels of period-1 and -2 consumption. (₁,₂). in terms of the exogenous variables, yı and y2. priv (c) Compute the numerical values of (ci,c) and si for: i. y₁ = 6, y2 = 11 11. = 10, 3/2 = 6.6. Interpret your answers above in terms of the permanent income hypothesis'. (The computations are messy and the final answers do not necessarily work out 'nicely'.) (d) Suppose that lenders impose a borrowing constraint on households such that they are not allowed to be in debt at the end of period 1. Determine whether this constraint affects the household's desired consumption levels in part (c)(i) or in (c)(ii). Consider a representative household in the two-period consumption-savings model whose preferences are given by: u(c₁, c₂)=√ +8 √₂ In the first period the household receives exogenous real labor income 1 and real interest income rao on their wealth endowment of ao, which they split between real consumption expenditures c1 and saving s1. In the second period they again receive exogenous real labor income y2 and real interest income rai on their wealth a1. spending any remaining lifetime income on consumption while leaving behind no assets so that a2 = 0. You may assume that the subjective discount factor and real interest rate are equal to B = 1/1.1 andr= 0.1, and the initial wealth endowment is equal to ao = 0: (a) Write down the period-1 and period-2 budget constraints in real terms. (b) Set up the sequential Lagrangian, derive the consumption-savings optimality con- dition, and solve for the optimal levels of period-1 and -2 consumption. (₁,₂). in terms of the exogenous variables, yı and y2. priv (c) Compute the numerical values of (ci,c) and si for: i. y₁ = 6, y2 = 11 11. = 10, 3/2 = 6.6. Interpret your answers above in terms of the permanent income hypothesis'. (The computations are messy and the final answers do not necessarily work out 'nicely'.) (d) Suppose that lenders impose a borrowing constraint on households such that they are not allowed to be in debt at the end of period 1. Determine whether this constraint affects the household's desired consumption levels in part (c)(i) or in (c)(ii).

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Intertemporal Consumption Problem with Borrowing Constraint a Budget Constraints Period 1 c1 s1 y1 r ... View the full answer