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Unformatted text preview: Chapter Two Budgetary and Other Constraints on Choice Consumption Choice Sets Â¡ A consumption choice set is the collection of all consumption choices available to the consumer. Â¡ What constrains consumption choice? Â± Budgetary, time and other resource limitations. Budget Constraints Â¡ 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 Â¡ Â« Â¡ [ n ). Â¡ Commodity prices are p 1 , p 2 Â¡ Â« Â¡ S n . Budget Constraints Â¡ Q: When is a consumption bundle (x 1 Â¡ Â« Â¡ [ n ) affordable at given prices p 1 Â¡ Â« Â¡ S n ? Budget Constraints Â¡ Q: When is a bundle (x 1 Â¡ Â« Â¡ [ n ) affordable at prices p 1 Â¡ Â« Â¡ S n ? Â¡ A: When p 1 x 1 Â¢ Â« Â¢ S n x n d m where m LV WKH FRQVXPHUÂ¶V (disposable) income. Budget Constraints Â¡ The bundles that are only just DIIRUGDEOH IRUP WKH FRQVXPHUÂ¶V budget constraint . This is the set { (x 1 Â¡Â«Â¡[ n )  x 1 t Â¡ Â«Â¡ [ n t Â¡ and p 1 x 1 Â¢ Â« Â¢ S n x n m }. Budget Constraints Â¡ 7KH FRQVXPHUÂ¶V budget set is the set of all affordable bundles; B(p 1 Â¡ Â« Â¡ S n , m ) = { (x 1 Â¡ Â« Â¡ [ n )  x 1 t Â¡ Â« Â¡ [ n t 0 and p 1 x 1 Â¢ Â« Â¢ S n x n d m } Â¡ 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 Â¡ 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 Â¡ For n = 2 and x 1 on the horizontal D[LVÂ¡ WKH FRQVWUDLQWÂ¶V VORSH LVp 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.
 Spring '08
 Mehta

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