# lecture3 - Lecture 3 Technology Shocks and Consumption...

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Unformatted text preview: Lecture 3 Technology Shocks and Consumption ECN/APEC 7240 III - 2 The Household • There is a representative household that lives forever. • The household maximizes – Utility is CRRA with risk aversion θ . – Discount factor β ∈ (0, 1). – Since future income is uncertain, future consumption is also uncertain. . ) ( ∑ ∞ = t t t C u E β ECN/APEC 7240 III - 3 Notes on Preferences • The discount factor is where ρ > 0 is the discount rate. • There is risk in this model, so strictly speaking the fact that θ is risk aversion should matter. – However, in the linear approximation that we focus on, the effects of risk will be neglected. – As before, the primary role of θ is that θ- 1 is the elasticity of intertemporal substitution. , 1 1 ρ β + = ECN/APEC 7240 III - 4 Budget Constraint • As in the CKR model, the household sells its labor for the real wage W t . • The household saves by investing in capital, which earns the gross return R t . • The household budget constraint is . 1 t t t t t K R W K C + = + + ECN/APEC 7240 III - 5 No-Ponzi Condition • The equation for capital will again be second- order, although now a difference equation. • We need a terminal condition for K t . • Define the gross interest compounded from t- s to t as • The generalized no-Ponzi condition is that with probability 1, ∏- =- = 1 s i i t s t R R . lim ≥ ∞ → t t t t R K ECN/APEC 7240 III - 6 Future Consumption and Capital • In the CKR model, we solved for C t and K t +1 for all t , given K ....
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lecture3 - Lecture 3 Technology Shocks and Consumption...

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