02. Budgets and Preferences 1.19.10

# 02. Budgets and Preferences 1.19.10 - The Budget Set and...

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The Budget Set and Consumer Preferences Professor John W. Diamond ECON 370: Microeconomic Theory Lecture 2

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2 Consumption Choice (Budget) Sets Consumption choice (or budget) set All consumption choices available to consumer “Available” – subject to constraints Constraints on consumption choice Income (budget) Time Other resource limitations (fixed wealth)
3 Budget Sets and Constraints Consumption bundle: (x 1 , x 2 , … , x n ) Commodity prices: p 1 , p 2 , … , p n Budget set defined by income constraint: x 1 0, …, x n p 1 x 1 + … + p n x n m m = consumer’s (disposable or after -tax) income Budget constraint assumes all income is spent p 1 x 1 + … + p n x n = m Is thus upper boundary of budget set

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4 Budget Set, Constraint for Two Goods x 2 x 1 Budget constraint is p 1 x 1 + p 2 x 2 = m Intercepts are m/p 1 and m/p 2 m /p 1 m /p 2
5 Budget Set, Constraint for Two Goods 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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6 Budget Set, Constraint for Two Goods x 2 x 1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 Just affordable m /p 2
7 Budget Set, Constraint for Two Goods 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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8 Budget Set, Constraint for Two Goods x 2 x 1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 Affordable with cash left Just affordable Not affordable m /p 2
9 Budget Set, Constraint for Two Goods x 2 x 1 Budget constraint is p 1 x 1 + p 2 x 2 = m m /p 1 Budget Set Collection of all affordable bundles m /p 2

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10 Budget Set, Constraint for Two Goods x 2 x 1 Solve p 1 x 1 + p 2 x 2 = m for x 2 : x 2 = m /p 2 - (p 1 /p 2 )x 1 m /p 1 Budget Set m /p 2
11 Budget Constraint for Three Goods 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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12 Slope of Budget Constraint (2 Goods) x 2 = m/p 2 - (p 1 /p 2 )x 1 Along budget constraint dm=0 dp 1 =dp 2 =0
13 Slope of Budget Constraint (2 Goods) dx 2 = - (p 1 /p 2 )dx 1 Since constraint linear, true for finite changes x 1 =1 x 2 = - (p 1 /p 2 ) Opportunity Cost of x 1 =1 is x 2 = - (p 1 /p 2 )

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14 Budget Constraint (2 Goods) x 2 x 1 Slope is - p 1 /p 2 +1 -p 1 /p 2
15 Effects of increase in income m Original budget set x 2 x 1

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16 Effects of increase in income m Original budget set New affordable consumption choices – budget set expands x 2 x 1 Original and new budget constraints are parallel (same slope).
17 Effects of decrease in income m Original budget set x 2 x 1

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Effects of decrease in income m x 2 x 1 New, smaller budget set Consumption bundles that are no longer affordable. Old and new
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02. Budgets and Preferences 1.19.10 - The Budget Set and...

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