A Note on the Continuous Differentiability of an Expected Utility Function: A Two Periods Consumer Decision Problems.

In the setting of a simple two-period model with money, the continuous differentiability of the expected utility function is shown to follow from the following assumptions provided the monotone von Neumann-Morgenstern utility function and the expectation function are sufficiently differentiable: (a) inelasticity of expectations: (b) risk aversion in future consumption. (Author)