What is shepard lemma?

Shepard's lemma is an economic principle that states that if the relative prices of goods remain constant, then the proportion of income spent on each good will remain constant as well. This principle is often used as a tool for analyzing consumer behavior in response to changes in prices or income.

The lemma is named after the economist Donald Shepard, who first proposed it in 1953. It is based on the assumption that consumers have fixed preferences for goods and that they allocate their income in such a way as to maximize their utility.

The Shepard lemma has important implications for the analysis of consumer behavior. It suggests that changes in income or prices will cause consumers to make adjustments in their consumption patterns, but the relative proportion of spending on each good will remain unchanged as long as relative prices are constant.

The Shepard lemma is used widely in the field of economics to analyze consumer behavior and market trends. It can help to identify which goods are substitutes for each other and which ones are complements. It is also useful for predicting changes in demand in response to changes in prices or income.