Comparative Statics of Information Acquisition and Risk Aversion

This paper studies how willingness to pay for information depends on risk aversion. We model a decision maker who faces background risk and can acquire information before choosing from a menu of assets. We show that the comparative statics depend on two factors. The first is whether available assets constitute an investment menu, whose payoffs are procyclical with background wealth, or an insurance menu, whose payoffs are countercyclical. The second factor is the tail geometry of background risk. We show that willingness to pay for information decreases with risk aversion for investment menus when the density of background risk is log-concave, and that it increases with risk aversion for insurance menus when background risk is downward-log-convex. The proofs compare the distributions of terminal wealth with and without information. They develop new aggregation arguments for state-dependent single-crossing comparisons. We also construct reversals under strictly log-convex tails for investment menus and super-exponential left tails for insurance menus.