Consider the standard two-period maximization problem for investor j over s states of nature: Subject to...

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Consider the standard two-period maximization problem for investor j over s states of nature: Subject to S max u(c) + (s)u(c;}(s)) S=1 Cjo + q(s) C; (s) = Wjo +244) S=1 where all terms are as defined in Campbell 4.1.8. ;(s) is investor j's subjective probability of state s occurring, which may be different from the true probability (s). Furthermore, subjective probabilities can differ across investors so that (s) (s). Assume two investors both of whom are characterized by log utility u = In(co) + BE [In(c)]. Assume that there are two investors i and j both of whom have the same but ; > i. In other words, investor j believes state s is more likely to occur than i does. Show that investor j experiences a higher level of consumption growth in states than investor i. Consider the standard two-period maximization problem for investor j over s states of nature: Subject to S max u(c) + (s)u(c;}(s)) S=1 Cjo + q(s) C; (s) = Wjo +244) S=1 where all terms are as defined in Campbell 4.1.8. ;(s) is investor j's subjective probability of state s occurring, which may be different from the true probability (s). Furthermore, subjective probabilities can differ across investors so that (s) (s). Assume two investors both of whom are characterized by log utility u = In(co) + BE [In(c)]. Assume that there are two investors i and j both of whom have the same but ; > i. In other words, investor j believes state s is more likely to occur than i does. Show that investor j experiences a higher level of consumption growth in states than investor i.