STOCHASTIC

where H > 0 is the determinant of the Hessian matrix of second-order partial derivatives
developed in (b).
(j) Show that the sign of Sa/dYi is, unfortunately, ambiguous for all a.
(k) Give an economic interpretation of why this ambiguity arises. [Hint: Note that
higher income increases both present consumption and planned future consumption via
present savings.]
(1) Suppose K(-) = v{Ci)+w(C2), where v is strictly concave. Show that Sa/SK, > 0
under the decreasing absolute risk-aversion assumption.
(m) Investigate alternative assumptions on u that lead to the result that the risky asset
is not an inferior good.
4. This problem concerns the development of relatively easily computable upper and lower
bounds on the value of information in uncertain decision problems, such as that illustrated
by Eq. (2.5) of the Dreze-Modigliani article.
Suppose that a decision maker must choose a decision vector x from a constraint set K.
A choice x will provide him with the payoff/(JC,