Roy's Identity

Roy's identity, named for the French economist Rene Roy, is a result in microeconomics with applications to consumer choice and the theory of the firm. It relates a good's ordinary, or Marshallian, demand function to the price and income derivatives of the indirect utility function, so a consumer's demand can be recovered directly from how that consumer's own maximized utility responds to changes in prices and wealth. The result holds for continuous utility functions representing locally non-satiated, strictly convex preferences on a convex consumption set, provided the indirect utility function is differentiable in every argument, and it does for indirect utility what the expenditure function's own derivatives do for recovering Hicksian demand.