Budget Constraint

# Budget Constraint - Chapter Two Budgetary and Other...

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Chapter Two Budgetary and Other Constraints on Choice

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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.
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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Budget Constraints Q: When is a consumption bundle (x 1 , … , x n ) affordable at given prices p 1 , … , p n ?
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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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 }.
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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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 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 2 m /p 1

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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 Just 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 Just affordable Not affordable m /p 2

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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
For n = 2 and x 1 on the horizontal axis, the constraint’s slope is -p 1 /p 2 . What does it mean?

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Budget Constraint - Chapter Two Budgetary and Other...

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