Week 2b Lecture_Demand

# Week 2b Lecture_Demand - Week 2 Part II Demand Budget...

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Week 2 – Part II Demand

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Budget Constraints Q: When is a bundle (x 1 , … , x n ) affordable at prices p 1 , … , p n ? A: When p 1 x 1 + … + p n x n m where m is the consumer’s (disposable) income.
Budget Constraints The consumer’s budget set is the set of all affordable bundles; B(p 1 , … , p n , m ) = { (x 1 , … , x n ) | x 1 0, … , x n 0 and p 1 x 1 + … + p n x n m } The budget constraint is the upper boundary of the budget set. { (x 1 ,…,x n ) | x 1 0, …, x n ≥ 0 and p 1 x 1 + … + p n x n = m }.

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Budget Set and Constraint for Two Commodities x 2 x 1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 Affordable Just affordable Not affordable m /p 2
Budget Set and Constraint for Two Commodities x 2 x 1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 Budget Set the collection of all affordable bundles. m /p 2

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Budget Set and Constraint for Two Commodities x 2 x 1 p 1 x 1 + p 2 x 2 = m is x 2 = -(p 1 /p 2 )x 1 + m /p 2 so slope is -p 1 /p 2 . m /p 1 Budget Set m /p 2
Budget Constraints If n = 3 what do the budget constraint and the budget set look like?

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Budget Constraint for Three Commodities x 2 x 1 x 3 m /p 2 m /p 1 m /p 3 p 1 x 1 + p 2 x 2 + p 3 x 3 = m
Budget Set for Three Commodities x 2 x 1 x 3 m /p 2 m /p 1 m /p 3 { (x 1 ,x 2 ,x 3 ) | x 1 0, x 2 0, x 3 0 and p 1 x 1 + p 2 x 2 + p 3 x 3 m }

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Budget Constraints For n = 2 and x 1 on the horizontal axis, the constraint’s slope is -p 1 /p 2 . What does it mean? Increasing x 1 by 1 must reduce x 2 by p 1 / p 2. 2 1 2 1 2 p m x p p x + - =
Budget Constraints x 2 x 1 +1 -p 1 /p 2 Opp. cost of an extra unit of commodity 1 is p 1 /p 2 units foregone of commodity 2.

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x 2 x 1 Opp. cost of an extra unit of commodity 1 is p 1 /p 2 units foregone of commodity 2. And the opp. cost of an extra unit of commodity 2 is p 2 /p 1 units foregone of commodity 1. -p
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Week 2b Lecture_Demand - Week 2 Part II Demand Budget...

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