Symmetry of net substitution effects is one of the principal conclusions of the theory of utility maximization.Which two mathematical theorems are used to prove this symmetry?

Question

Quizplus · Accepted Answer

The symmetry of net substitution effects is proven using the Envelope Theorem and Young's Theorem. The Envelope Theorem states that the marginal change in the value of the objective function due to a small change in an exogenous variable is equal to the partial derivative of the objective function with respect to that variable, evaluated at the optimum. Young's Theorem states that if two functions have the same first-order Taylor expansion at a given point, then their difference has a higher-order Taylor expansion that starts with at least a quadratic term. Together, these theorems are used to show that the net substitution effect of a price change on the demand for a good is the same, regardless of whether the price of the good itself changes or the price of another good changes. This result is known as the symmetry of net substitution effects.

Symmetry of Net Substitution Effects Is One of the Principal