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 . Discount factor (0, 1). Since future income is uncertain, future consumption is also uncertain. . ) ( = t t t C u E ECN/APEC 7240 III - 3 Notes on Preferences The discount factor is where > 0 is the discount rate. There is risk in this model, so strictly speaking the fact that 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 is that - 1 is the elasticity of intertemporal substitution. , 1 1 + = 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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