(i) Consider the general form of recursive preferences as defined in (9.16). Suppose that the functions \(v\) and \(\tilde{u}\) are of the following form:

Show that in this case the preference functional (9.16) reduces to the classical time additive utility.

(ii) Consider the recursive utility functional of the Epstein \& Zin [651] form given in (9.19). Show that, if \(\alpha=\varrho\), then the recursive preference functional reduces to the classical time additive expected utility with a power utility function.

Data From Equation (9.16)

Transcribed Image Text:

v(c,y) = u(c)+8y and u(x) = x.