Shephard's lemma
Shephard's lemma is a major result in microeconomics having applications in the theory of the firm and in consumer choice.
The lemma states that if indifference curves of the expenditure or cost function are convex, then the cost minimizing point of a given good () with price is unique. The idea is that a consumer will buy a unique ideal amount of each item to minimize the price for obtaining a certain level of utility given the price of goods in the market.
The lemma is named after Ronald Shephard who gave a proof using the distance formula in his book Theory of Cost and Production Functions (Princeton University Press, 1953).
The equivalent result in the context of consumer theory was first derived by Lionel W. McKenzie in 1957. It states that the partial derivatives of the expenditure function with respect to the prices of goods equal the Hicksian demand functions for the relevant goods. Similar results had already been derived by John Hicks (1939) and Paul Samuelson (1947).
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