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Notes 2-Demand

Notes 2-Demand - 2 Preferences and Demand Microeconomic...

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2. Preferences and Demand Microeconomic Analysis, Chapters 7-9 Intermediate Microeconomics, Chapter 3-5; 8-9 I. Preference Orderings A. Bundles 1. Our main goal with this section is to model how people choose between consumption options. 2. We call these options bundles . 3. A bundle is represented as a vector x with a dimension equal to the number of goods. 4. If consumers only make choices between two goods (1 and 2), we could represent this as a vector x = ( x 1 , x 2 ) 1 a. x = (7 , 4) represents a bundle consisting of 7 units of good 1 and 4 units of good 2. b. For simplicity we’ll assume there are only two goods through most of this section c. These results, however, extend to an arbitrarily large number of goods. Ex: Bundles in a 2-dimensional consumption space. B. Preferences Over Bundles 1. We assume that people can compare any two bundles. 2. We call this comparison a preference . 3. In other words, a preference is really a relation(ship) between between two bundles. 4. We assume that for any two bundles x and y one of these preference relations is true: a. Indifference : x y The consumer is indifferent between x and y . The consumer is just as happy with x as she is with y . b. Strict Preference : x y or x y The consumer either prefers x to y or prefers y to x . The consumer is happier with x than y or is happier with y than x . Given the choice, the consumer would always choose one to the other. c. Weak Preference : x y or x y The consumer prefers x to y (alternatively prefers y to x ). The consumer is not happier with y than x (alternatively is not happier with x than y ). The consumer is either indifferent between x and y or prefers x to y (alternatively the consumer is either indifferent between y and x or prefers y to x ). Ex: Indifference curves and better sets in a 2-dimensional consumption space. C. Preferences are always assumed to satisfy three main properties: 1. Complete: Either x y , y x or both (in which case x y ). 2. Reflexive: x x 3. Transitive: If x y and y z then x z . Ex: Preference no-nos D. Preferences are often assumed to have two extra properties (when someone talks about well behaved preferences this is what they mean). 1. Strong Monotonicity: More is better. 1 In this section a bold variable will denote a vector like this. 1
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2. Convexity: If x y then for any 0 α 1, ( αx 1 + (1 - αy 1 ) , αx 2 + (1 - αy 2 )) ( x 1 , x 2 ) Ex: Not well behaved preferences II. Utility Functions A. It seems pretty hard to model decision making using the preference theory we just talked about because we’d have to specify the preference relations between every pair of bundles.
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