Chapter 2 - Chapter Two Budgetary and Other Constraints on...

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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.
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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 ± « ± [ n ). Commodity prices are p 1 , p 2 ± « ± S n .
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Budget Constraints Q: When is a consumption bundle (x 1 ± « ± [ n ) affordable at given prices p 1 ± « ± S n ?
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Budget Constraints Q: When is a bundle (x 1 ± « ± [ n ) affordable at prices p 1 ± « ± S n ? A: When p 1 x 1 ² « ² S n x n d m where m LV WKH FRQVXPHU¶V (disposable) income.
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Budget Constraints The bundles that are only just DIIRUGDEOH IRUP WKH FRQVXPHU¶V budget constraint . This is the set { (x 1 ±«±[ n ) | x 1 t 0 ± «± [ n t ± and p 1 x 1 ² « ² S n x n m }.
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Budget Constraints 7KH FRQVXPHU¶V budget set is the set of all affordable bundles; B(p 1 ± « ± S n , m ) = { (x 1 ± « ± [ n ) | x 1 t 0 ± « ± [ n t 0 and p 1 x 1 ² « ² S n x n d 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
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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 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
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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 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
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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 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
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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
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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 t 0, x 2 t 0, x 3 t 0 and p 1 x 1 + p 2 x 2 + p 3 x 3 d m }
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Budget Constraints For n = 2 and x 1 on the horizontal D[LV± WKH FRQVWUDLQW¶V VORSH LV -p 1 /p 2 . What does it mean?
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