Integrability of demand

In microeconomic theory, the problem of the integrability of demand functions deals with recovering a utility function (that is, consumer preferences) from a given walrasian demand function. The "integrability" in the name comes from the fact that demand functions can be shown to satisfy a system of partial differential equations in prices, and solving (integrating) this system is a crucial step in recovering the underlying utility function generating demand.

The problem was considered by Paul Samuelson in his book Foundations of Economic Analysis, and conditions for its solution were given by him in a 1950 article. More general conditions for a solution were later given by Leonid Hurwicz and Hirofumi Uzawa.