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Chapter 2 3

# Chapter 2 3 - Chapter Two Budgetary and Other Constraints...

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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, and x 2 units of commodity 2 is denoted by the vector (x 1 , x 2 ). Commodity prices are p 1 , p 2

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Budget Constraints Q: When is a consumption bundle (x 1 , x 2 ) affordable at given prices p 1 , p 2 ? When p 1 x 1 + p 2 x 2 m where m is the consumer’s (disposable) income.
Budget Constraints The bundles that are only just affordable form the consumer’s budget constraint. This is the set { (x 1 , x 2 ) | such that p 1 x 1 + p 2 x 2 = 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 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

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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
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
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 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. 1 2 1 2 2 p m x x p p =- +
Budget Constraints x 2 x 1 Slope is -p 1 /p 2 +1 -p 1 /p 2

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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.
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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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?
How do the budget set and budget constraint change as income m increases? Original budget set x 2 x 1

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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).
How do the budget set and budget constraint change as income m decreases?

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