  Consider an agent taking two successive decisions to maximize his expected
utility under uncertainty. After his first decision, a signal is revealed that
provides information about the state of nature. The observation of the signal
allows the decision-maker to revise his prior and the second decision is taken
accordingly. Assuming that the first decision is a scalar representing
consumption, the \emph{precautionary effect} holds when initial consumption is
less in the prospect of future information than without (no signal).
\citeauthor{Epstein1980:decision} in \citep*{Epstein1980:decision} has provided
the most operative tool to exhibit the precautionary effect. Epstein's Theorem
holds true when the difference of two convex functions is either convex or
concave, which is not a straightforward property, and which is difficult to
connect to the primitives of the economic model. Our main contribution consists
in giving a geometric characterization of when the difference of two convex
functions is convex, then in relating this to the primitive utility model. With
this tool, we are able to study and unite a large body of the literature on the
precautionary effect.
