lecture_1 - Budget Constraints Budgetary and Other...

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ECOS1001 L1 1 Budgetary and Other Constraints on Choice 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
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ECOS1001 L1 2 Budget Constraints A consumption bundle containing x1 units of commodity 1, x2 units of commodity 2 and so on up to xn units of commodity n is denoted by the vector (x1, x2, … , xn). Commodity prices are p1, p2, … , pn. Q: When is a consumption bundle (x1, … , xn) affordable at given prices p1, … , pn?
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ECOS1001 L1 3 When p 1 x 1 + … + p n x n m where m is the consumer’s (disposable) income. 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
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ECOS1001 L1 4 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. Budget Constraints
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ECOS1001 L1 5 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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ECOS1001 L1 6 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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ECOS1001 L1 7 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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ECOS1001 L1 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 Budget Set the collection of all affordable bundles. m /p 2
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ECOS1001 L1 9 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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ECOS1001 L1 10 Budget Constraints • For n = 2 and x 1 on the horizontal axis, the constraint’s slope is -p 1 /p 2 . What does it mean? 2 1 2 1 2 p m x p p x + =
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ECOS1001 L1 11 Budget Constraints • For n = 2 and x 1 on the horizontal axis, the constraint’s slope is -p 1 /p 2 . What does it mean? • Increasing x 1 by 1 must reduce x 2 by p 1 /p 2. 2 1 2 1 2 p m x p p x + =
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ECOS1001 L1 12 Budget Constraints x 2 x 1 Slope is -p 1 /p 2 +1 -p 1 /p 2
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ECOS1001 L1 13 Budget Constraints x 2 x 1 +1 -p 1 /p 2 Opp. cost of an extra unit of commodity 1 is p 1 /p 2 units foregone of commodity 2.
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ECOS1001 L1 14 Budget Constraints x 2 x 1 Opp. cost of an extra unit of commodity 1 is p 1 /p 2 units foregone of commodity 2. And the opp. cost of an extra unit of commodity 2 is p 2 /p 1 units foregone of commodity 1. -p 2 /p 1 +1
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ECOS1001 L1 15 Budget Sets & Constraints; Income and Price Changes • The budget constraint and budget set depend upon prices and income. What happens as prices or income change?
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ECOS1001 L1 16 How do the budget set and budget constraint change as income m increases?
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ECOS1001 L1 17 Higher income gives more choice Original budget set New affordable consumption choices x 2 x 1 Original and new budget constraints are parallel (same slope).
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ECOS1001 L1 18 Budget Constraints - Income
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This note was uploaded on 04/20/2010 for the course ECOS 2001 taught by Professor None during the One '09 term at University of Sydney.

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lecture_1 - Budget Constraints Budgetary and Other...

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