Stabilization and the timing of consumption decisions. Suppose that the consumer must decide on the consumption of good 1 before the state and its price are known. Her direct utility function, income...

Stabilization and the timing of consumption decisions. Suppose that the consumer must decide on the consumption of good 1 before the state and its price are known. Her direct utility function, income and all other prices do not vary across states. Thus when state s occurs the consumer has y ps1 xs1 to spend on all goods. Show that the consumer is made better off by a mean preserving contraction in the distribution of ps1 if she is averse to income risks. (Hint: derive her indirect utility function and show that it is concave in ps1 if it is concave in y.)