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# Lecture 7 - Lecture 7 Income and Substitution II Beware...

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Lecture 7 Income and Substitution II Beware that thou forget not the L ORD thy God … lest when thou hast eaten and art full, and hast built goodly houses, and dwelt therein …thou say in thine heart, My power and the might of mine hand hath gotten me this wealth. Deuteronomy 8:11-14, 17 The Economics Outline 1. The Slutsky Equation The Mathematics Outline 1. The Envelope Theroem The Slutsky Equation The Slutsky Equation is the mathematical version of the income and substitution effects discussion that we developed graphically in the previous lecture. Remember, that we started this discussion because we are interested in how the quantity demanded changes as price changes, or the sign of i i P x * . Going back to the identity ) , ,..., ( , ,..., ( ) , ,..., ( 1 1 1 U P P E P P x U P P h n n i n i , if we differentiate both sides by P i we get: i i i i i i P E E x P x P h + = and rearranging terms we can write this term as: i i i i i i P E E x P h P x = Note: The i subscripts denote the i th good hence we are talking about taking the derivative of the price of good i . These are called “own price” derivatives. We will deal with “cross-price” derivatives later.

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