(Alvarez and Jermann (2000)) For each $i \in I$ there is a constant $\xi_i$ such that for all $t, z^t$, $$|u(c_{i,t}(z^t))| \le \xi_i u'(c_{i,t}(z^t)) c_{i,t}(z^t).$$ $\cdots$. This condition holds if (i) $u(\cdot)$ has relative risk aversion different from one at zero consumption, i.e.: $$\lim_{c \to 0} - \frac{c u''(c)}{u'(c)} \not=1,$$ which can be verified by repeated application of L'Hopital's rule, or (ii) $u'(0) < + \infty$, or (iii) if consumption for an agent is uniformly bounded away from zero.

It is Remark 1 in page 21 of working paper version, and page 784-5 in Econometrica. I don't understand how either (i), (ii), or (iii) imply the inequality condition. I was thinking maybe it has something to do with the concavity of $u(\cdot)$; i.e., $u(\xi) \le u(c_{i,t}(z^t)) + u'(c_{i,t}(z^t))(\xi - c_{i,t}(z^t))$. But, not sure about the next step. If you have any idea, can you give some help?

source: Working paper version, JSTOR.



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.