Shephard's Lemma

1
Shephard's Lemma

• Shephards lemma is a major result in
  microeconomics having applications in consumer
  choice and the theory of the firm.

2
Shephards Lemma

• Shephards lemma states that if indifference
  curves of the expenditure or cost function are
  convex, then the cost minimizing point of a given
  good (X) with price (PX) 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. It was named after Ronald
  Shephard who gave a proof using the distance
  formula in a paper published in 1953, although it
  was already used by John Hicks (1939) and Paul
  Samuelson (1947).
• Sources Wikipedia, http//dictionary.sensagent/sh
  ephardslemma/en-en/

3
Shephards Lemma

• Shephards lemma gives a precise formulation for
  the demand for each good in the market with
  respect to that level of utility and those
  prices the derivative of the expenditure
  function E(PX, PY, U) with respect to that price.