Chapter 2

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

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Unformatted text preview: Chapter Two Budgetary and Other Constraints on Choice 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 ¡ « ¡ [ n ). ¡ Commodity prices are p 1 , p 2 ¡ « ¡ S n . Budget Constraints ¡ Q: When is a consumption bundle (x 1 ¡ « ¡ [ n ) affordable at given prices p 1 ¡ « ¡ S n ? Budget Constraints ¡ Q: When is a bundle (x 1 ¡ « ¡ [ n ) affordable at prices p 1 ¡ « ¡ S n ? ¡ A: When p 1 x 1 ¢ « ¢ S n x n d m where m LV WKH FRQVXPHU¶V (disposable) income. 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 ¡ «¡ [ n t ¡ and p 1 x 1 ¢ « ¢ S n x n m }. 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 ¡ « ¡ [ n t 0 and p 1 x 1 ¢ « ¢ S n x n d m } ¡ The budget constraint is the upper boundary of the budget set. 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 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 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 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? 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 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 } Budget Constraints ¡ For n = 2 and x 1 on the horizontal D[LV¡ WKH FRQVWUDLQW¶V VORSH LV-p 1 /p 2 ....
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This note was uploaded on 04/18/2011 for the course ECON 1110 taught by Professor Mehta during the Spring '08 term at Brown.

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

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