An ordinal theorem of the maximum

This paper extends the notion of equivalent variation, Hicks (Value and capital, 1939) to an abstract decision problem. It also provides a modern, ordinal variant of the maximum theorem, Berge (Topological spaces: including a treatment of multi-valued functions, vector spaces, and convexity, Courier Corporation, Chelmsford, 1963) that formulates the assumptions in terms of underlying preferences and demonstrates the continuity of the classic preference-based welfare indices (i.e., the equivalent and compensating variations) as well as the upper hemicontinuity of the choice correspondence. We apply the theorem to relevant economic problems.