# Lecture 9 - Lecture 9 Demand and Elasticity II John D...

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Lecture 9 Demand and Elasticity II John D. Rockefeller was once asked how much was enough. His answer? “Just a little bit more.” The Economics Outline 1. Market Demand 2. Own-Price Elasticity of Demand 3. Income Elasticity of Demand 4. Elasticity Relationships 4.1. From the Budget Constraint 4.1.1. Engel Aggregation 4.1.2. Cournot Aggregation 4.2. From the Slutsky Equation 4.3. From Homogeneity The Mathematics Outline 1. Euler’s Theorem Market Demand Let’s suppose there are n goods and m people in the economy and let: i = 1 to n (goods in the economy) j = 1 to m (individuals in the economy) (Marshallian demand for good i by individual j) ) , ,..., ( 1 j n j i j i I P P x x = Then market demand is characterized by the equation: = = = m j m n i j n j i i I I P P X I P P x X 1 1 1 1 ) ,..., , ,..., ( ) , ,..., ( Graphically, market demand is the horizontal summation of individual demand. Own-Price Elasticity of Demand Elasticity is a measure of responsiveness. In the setting of demand, we are interested in the response of demand to some change in the system. In order to get things into a unit- free measure, elasticity is calculated in percentages. With the Slutsky equation we looked at how changes as changes. However, if we find that the answer to this problem is –25 we need to put that in context. Is –25 a lot or a little. If you are currently consuming 30 units and your consumption changes by 25, then the change seems like a lot. If you are currently consuming 1,000 units, a change of 25 i x i P Dr. Steven Waters Econ 380 Page 1 of 8

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L9: Demand and Elasticity II doesn’t seem like much. If we put things in percentage terms the change is put in context. Own-price elasticity of demand is defined as: Arc Elasticity (Finite Changes): Q P P Q P P Q Q P P Q Q P Q x x x x x x P x x = = = = % % , ε Point Elasticity (Infinitely Small Changes): Q P P Q x P x = , Sometimes I may drop the subscripts on own-price elasticity (as I did here) and follow the convention in economics of denoting quantities with the letter Q. Up to this point in time, I have denoted quantities with letters like x and y , or . Don’t get confused
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Lecture 9 - Lecture 9 Demand and Elasticity II John D...

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