Question

Could someone please explain the concept of "shepherd's lema" in a clear way? Also, could you provide an example to further illustrate what it is? Also, please write legibly. I don't mean to be rude, but part of the reason why I'm asking this is the last person who answered my question did so through handwriting I couldn't clearly read, so I didn't actually understand the answer. If you write down the answer please be sure your writing is very readable

Answer 1

Shephard's lemma is a main outcome in microeconomics having applications in the firm’s theory & in consumer choice. The lemma says that if indifference curves of the cost function are convex, then the expenses minimizing point of a particular product (i) with price pi is exclusive. The idea is that a customer will purchase a unique ideal quantity of every item to minimize the price for obtaining a particular utility level given the price of products in the market.

Shephard's lemma provides a relation between cost functions & Hicksian demand. It can be re- articulated as Roy's identity, which provides a relation between an indirect function of utility & a corresponding Marshallian function of demand.