# Lecture 8 - Lecture 8 Demand and Elasticity I Can God be...

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Dr. Steven Waters Econ 380 Page 1 of 6 Lecture 8 Demand and Elasticity I Can God be pleased by the vast and increasing inequities among us? Is he not grieved by our arrogant accumulation? Foster, Richard J. Freedom of Simplicity , 1981, Harper & Row, Publishers, p. 32 The Economics Outline 1. Consumer Surplus 2. Cross-Price Effects 3. Substitutes (Gross & Net) 4. Complements (Gross & Net) The Mathematics Outline 1. More Slutsky Equation! 2. Young’s Theorem Consumer Surplus Consumer surplus is a measure of the value that consumers receive above and beyond what they pay for. How much a person is willing to pay for a good is different from what she has to pay for a good. In this graph, the shaded area is the consumer surplus. There is a direct relationship between consumer surplus and expenditure functions. Suppose we are thinking about a situation where the price of good x increases. With the increase in price, we are worse off because our real income goes down. However, in the compensated demand world (Hicksian demand) we have the situation that income is compensated to assure that the same level of utility is attained. How much income has to be compensated is exactly what the expenditure function measures.

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L8: Demand and Elasticity I Dr. Steven Waters Econ 380 Page 2 of 6 Suppose price increases from 0 x P to 1 x P (i.e., 0 1 x x P P > ): Expenditures when price is 0 x P : ) , , ( 0 0 0 U P P E E y x = Expenditures when price is 1 x P : ) , , ( 0 1 1 U P P E E y x = The loss in welfare (consumer surplus) is measured as the increase in needed expenditures. Thus: welfare change = 1 0 E E Since 0 1 E E > , the welfare change is negative (i.e., the person is worse off). It turns out that this change in expenditures can be written: 1 0 E E = = 1 0 1 0 ) , , ( 0 x x x x P P x y x x P P dP U P P h dE In other words, it is just the area under the Hicksian demand curve. What happens if we look at the area under the Marshallian demand curve? 1.
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Lecture 8 - Lecture 8 Demand and Elasticity I Can God be...

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