Insuring and u (y)

We establish that an agent increases (decreases) her savings when insurance becomes unavailable when her marginal utility of consumption is convex (concave) in income. A mean neutral (not preserving) spread figures in the analysis. When the odds are actuarially unfair, increasing (decreasing) absolute risk aversion is necessary and sufficient for an agent to increase (decrease) her holding of insurance in response to an increase in her wealth. Increasing absolute risk aversion is sufficient for insurance being purchased to decline in response to a higher price (less fair odds).