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04. Consumer Demand

# 04. Consumer Demand - Consumer Demand Professor John...

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Consumer Demand Professor John Diamond ECON 370: Microeconomic Theory Lecture 4

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Properties of Demand Functions Comparative statics analysis of demand How do ordinary demands x 1 *(p 1 , p 2 , m) and x 2 *(p 1 , p 2 , m) change w/exogenous variables? Exogenous: prices p 1 , p 2 and income m (and tastes) Example: Own-price increase Suppose p 1 increases, from p 1 ’ to p 1 ’’, and to p 1 ’’’ Hold p 2 and m constant
x 1 x 2 p 1 =p 1 p 1 x 1 + p 2 x 2 = m Own Price Changes

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Own Price Increase p 1 = p 1 ’’ x 1 x 2 p 1 = p 1 p 1 x 1 + p 2 x 2 = m
Own Price Increases x 2 x 1 p 1 = p 1 ’’ p 1 = p 1 ’’’ p 1 = p 1 p 1 x 1 + p 2 x 2 = m

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x 2 x 1 x 1 *(p 1 ’) p 1 = p 1 Own Price Changes
x 2 x 1 x 1 *(p 1 ’) p 1 x 1 *(p 1 ’) p 1 x 1 * p 1 = p 1 Own Price Changes

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p 1 Own Price Changes x 1 *(p 1 ’) x 1 *(p 1 ’’) x 1 *(p 1 ’) p 1 p 1 = p 1 ’’ x 1 * 2 x 1 x
x 2 x 1 x 1 *(p 1 ’) x 1 *(p 1 ’’) p 1 x 1 *(p 1 ’) x 1 *(p 1 ’’) p 1 p 1 ’’ x 1 * Own Price Changes

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Own Price Changes x 2 x 1 x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) p 1 x 1 *(p 1 ’) x 1 *(p 1 ’’) p 1 p 1 ’’ p 1 = p 1 ’’’ x 1 * 2 x 1 x
Own Price Changes x 2 x 1 x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) p 1 x 1 *(p 1 ’) x 1 *(p 1 ’’’) x 1 *(p 1 ’’) p 1 p 1 ’’ p 1 ’’’ x 1 * x 1 x 2

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Own Price Changes x 2 x 1 x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) p 1 x 1 *(p 1 ’) x 1 *(p 1 ’’’) x 1 *(p 1 ’’) p 1 p 1 ’’ p 1 ’’’ x 1 * demand curve x 1 x 2
p 1 Own Price Changes x 1 *(p 1 ’) x 1 *(p 1 ’’’) x 1 *(p 1 ’’) p 1 p 1 ’’ p 1 ’’’ x 1 * demand curve x 1 x 2 x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’)

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p 1 x 1 *(p 1 ’) x 1 *(p 1 ’’’) x 1 *(p 1 ’’) p 1 p 1 ’’ p 1 ’’’ x 1 * demand curve p 1 -Price Offer Curve Own Price Changes x 1 x 2 x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’)
Summary: Own Price Changes p 1 - price offer curve: contains all utility-maximizing bundles traced out as p 1 changes p 2 and m constant Ordinary demand curve for commodity 1: Plot of demand function for each value of p 1 holding p 2 and m constant Reflects optimal consumption of x 1 at each p 1

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Example: Cobb-Douglas Utility Assume Cobb-Douglas Utility function Ordinary demand functions are Consider a change in p 1 x 2 * is constant (flat) not a function of p 1 x 1 * demand is rectangular hyperbola (px=k) 2 2 1 * 2 1 2 1 * 1 ) , , ( , ) , , ( p m b a b m p p x p m b a a m p p x b a x x x x U 2 1 2 1 ) , (
Example: Cobb-Douglas Utility x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) x 2 x 1 2 * 2 1 * 1 ) ( ) ( p b a bm x p b a am x x 1 x 2 p 1 price-offer curve

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x 2 x 1 p 1 x 1 * demand curve 1 * 1 ) ( p b a am x Example: Cobb-Douglas Utility x 1 x 2 x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) price offer curve
Example: Perfect Complements Utility function

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