# 02s - 2 2010 W. W. Norton & Company, Inc. Budgetary and...

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2 Budgetary and Other Constraints on Choice

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2 Consumption Choice Sets A consumption choice set is the collection of all consumption choices available to the consumer. What constrains consumption choice? Budgetary, time and other resource limitations.
3 Budget Constraints A consumption bundle containing x 1 units of commodity 1, x 2 units of commodity 2 and so on up to x n units of commodity n is denoted by the vector (x 1 , x 2 , … , x n ). Commodity prices are p 1 , p 2 , … , p n .

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4 Budget Constraints Q: When is a consumption bundle (x 1 , … , x n ) affordable at given prices p 1 , … , p n ?
5 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.

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6 Budget Constraints The bundles that are only just affordable form the consumer’s budget constraint. This is the set { (x 1 ,…,x n ) | x 1 0, …, x n ≥0 and p 1 x 1 + … + p n x n = m }.
7 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.

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8 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
9 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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10 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
11 Budget Constraints If n = 3 what do the budget constraint and the budget set look like?

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12 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
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## This note was uploaded on 06/12/2011 for the course ECON 101 taught by Professor Dee during the Spring '10 term at Andhra University.

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02s - 2 2010 W. W. Norton & Company, Inc. Budgetary and...

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