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Intertemporal Elasticity of Substitution

4. More on the Intertemporal Elasticity of Substitution. Suppose that the individual’a lifetime utility is given by:u = u(c) + 515(6)where again the utility from consumption in a. given period is given by 4214-1a“): 1-0- The intertemporal budget on straint is given by f I C _ y1+r_y+1+r’ (a) What is implicitly being assumed, in the intertemporal budget constraint, about opportunities to borrow and save? (b) Derive the consumption Euler Equation. (G) Take natural logs of both sides of the Euler equation. Use (i) the approximation ln(1 + :r} H 2:, and (ii)the fact that ? = 1/(1+p), to derive the relationship between the growth rate of consumption (lnc’ wine)and the parameters 7′, p and o. (:1) Explain, based on your derivation, the role that 0′ plays in determining the consumption growth rate and provide the intuition. C+

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