Handout%209 - Handout 9 Consumer Behavior 2 2 Notation R(R...

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Handout # 9 Consumer Behavior Notation : R + ( R ++ ) is the set of non-negative (positive) reals; R 2 + ( R 2 ++ ) is the set of all pairs of non-negative (positive) reals; for a real number x , its absolute value , denoted by ° x ° is de°ned as ° x ° = ° x if x > 0 ° x if x < 0 : ; (1) [ As an example, ° ° 5 ° = 5 ; we simply disregard the sign of the negative number, when we talk about its absolute value]. We come to the demand side of the market. The market demand (also called aggregate demand) is the sum of the individual demands over all consumer. Hence, we study the choice problem of a consumer who accepts prices p x > 0 and p y > 0 (2) of goods x and y as given. A consumer is described by its utility function u [representing its preferences] and its wealth or income _ m > 0 : In the model that we develop, a consumer chooses the best commodity bundle it can a/ord; more formally, t he consumer maximizes its utility function over the budget set determined by p x ; p y and _ m: The budget set is B ( p x ; p y ; _ m; ) = f ( x; y ) 2 R 2 + : p x x + p y y 5 m g : (3) The budget line is f ( x; y ) 2 R 2 + : p x x + p y y = m g ; (4) and its slope is ° p x =p y [ market rate of conversion between x and y ]. The absolute value of the slope of the budget line is p x =p y ; [ interpret ] m=p x and m=p y : How does the budget set change when p x ; p y and/or m change? The consumer is assumed to choose an element of the budget set; this is the set of all commodity bundles it can a/ord. The utility function u : R 2 + °! R (5) describes the consumer±s preferences. The inequality u ( x; y ) > u (^ x; ^ y ) is interpreted as " ( x; y ) is strictly preferred to ( ^ x; ^ y ) " and u ( x; y ) = 1
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u (^ x; ^ y ) is interpreted as " the consumer is indi/erent between the commodity bundles ( x; y ) and (^ x; ^ y ) " [ brie²y, ( x; y ) is indi/erent to (^ x; ^ y )] : For a given
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