What is Expenditure Function?

The Expenditure Function:

When preferences satisfy the local nonsatiation assumption, in that case v(p, m) will be strictly increasing into m. After that invert the function and resolve for m as a function of the level of utility; which is, given any level of utility, u, determine the minimal amount of income essential to attain utility u at prices p. The function which relates income and utility in this method the inverse of the indirect utility function is termed as the expenditure function and is denoted through e(p, u). Properly, the expenditure function is specified by the given problem:

e(p, u) = min px

that is u(x) > u.

The expenditure function specifies the minimum cost of getting a fixed level of utility.