562_lecture2_consumer_theory_demand

562_lecture2_consumer_theory_demand - SI 562 Lecture 2...

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1 Page 1 SI 562 Lecture 2 1 Consumer Theory & Demand Analysis Professor Yan Chen Fall 2009 AGENDA MODULE 1: Review MODULE 2: Consumer Theory 2 MODULE 3: Individual consumer demand Consumer surplus Market demand Elasticity MODULE 1 3 Review
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2 Page 2 Concept Review and Reflection Math concepts Why derivative = 0 at local min and local max? Sufficient condition: 2 nd derivative Economics concept 4 Economics concepts Marginal revenue Marginal cost Sufficient condition for multivariable optimization MODULE 2 5 Consumer Theory Consumer Theory I. Motivating Example Cell phone developed What are they worth? To an individual: individual demand 6 – To an individual: individual demand • an individual’s willingness-to-pay (WTP) • might change with what? job change, income change… – On a market: how do you price it? Market demand
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3 Page 3 II. Consumer Preferences A. Rational choice: assumption 1. What is it? (A1) Completeness: for all x, y X, we have that x y or y x (or both). (A2) Transitivity For all x, y, z X, if x y and y z, then x z. at least as good as… 7 2. Why assume rationality? (1) Need a model to predict behavior (2) A useful approximation B. Utility maximization Theorem (loose) If an agent makes choices consistent with A1 and A2, then it is as if she is maximizing a utility function u(x 1 ,…, x n ). Q: How many CDs would I give up for one more book and be just as happy ? (indifferent) Books CDs 5 5 10 (7,6) (10,5) Books CDs u 2 u 1 8 The set of combinations that all yield the same level of utility is the level set or indifference set or curves More Assumptions: (A3) Monotonicity: Prefer more to less (A4) Diminishing marginal returns: 0 > dx du 0 < dx du dx d (A3) Utility increasing to the northeast x 1 x 2 (A4) Indifference curves are convex to the origin (A2) Transitivity: indifference curves don’t i B 9 intersect. A~C A~B B~C Violates transitivity OTHER ASSUMPTIONS: U(•) is continuous and twice differentiable. A C
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4 Page 4 Indifference Curves Indifference curves are contour sets of the utility function Convex preferences means if 10 Convex preferences means if consumer indifferent between two points, prefers points on the line segment connecting them. Convex Preferences 0.6 0.8 1 y 11 0.2 0.4 1 x Perfect substitutes vs. perfect complements Perfect substitutes Dimes and nickels Apples and pears 12 Perfect complements Left shoe and right shoe Coffee and cream
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5 Page 5 III. Budget Constraints Scarcity implies that utility maximization is constrained: i i i I x P Books Q b I Q P Q P c c b b = + b P I 13 CDs Q c 0 b c P P Slope = ~ rate of possible tradeoffs If you give up $P c in CDs, you can get P c / P b more books The The budget budget constraint: constraint: An example Suppose Jeff’s weekly income is M=$100 Food costs P f =$10/lb Sh lt t P $5/ d 14 Shelter costs P s =$5/sq yd What are his options?
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This note was uploaded on 12/16/2009 for the course SI 562 taught by Professor Chen during the Fall '08 term at University of Michigan.

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562_lecture2_consumer_theory_demand - SI 562 Lecture 2...

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