In this paper we will show that upper semicontinuity of the indirect utility function implies the upper semicontinuity of the direct utility function. By strengthening the assumptions, one can also deduce the continuity of the utility function. Based on indirect utility functions a model of...

It is shown that if a demand function with no inferior goods satisfies the Slutsky conditions and has a convex range, then it is generated by a continuous utility function. The same conclusion holds when the Slutsky conditions are replaced by the strong axiom of revealed preference.

It is shown that if a demand function with no inferior goods satisfies the Slutsky conditions and has a convex range, then it is generated by a continuous utility function. The same conclusion holds when the Slutsky conditions are replaced by the strong axiom of revealed preference.