Lecture 9 and 10 Exchange Economy (10:4, 10:9).ppt

Lecture 9 and 10 Exchange Economy (10:4, 10:9).ppt -...

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Lectures 9 and 10: Endowment, Exchange Economy, General Equilibrium & Welfare Theorems (Varian: Ch. 31)
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Buying and Selling How are incomes generated? How does the value of income depend upon commodity prices? How can we put all this together to explain better how price changes affect demands?
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Endowments The list of resource units with which a consumer starts is his endowment. A consumer’s endowment will be denoted by the vector (omega).
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Endowments E.g. p 1 =2 and p 2 =3 so the value of a endowment is Q: For which consumption bundles may the endowment be exchanged? A: For any bundle costing no more than the endowment’s value. ) 2 , 10 ( ) , ( 2 1 26 2 3 10 2 2 2 1 1 p p
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Budget Constraints Revisited So, given p 1 and p 2 , the budget constraint for a consumer with an endowment is The budget set is ) , ( 2 1 . 2 2 1 1 2 2 1 1 p p x p x p . 0 , 0 , ) , ( 2 1 2 2 1 1 2 2 1 1 2 1 x x p p x p x p x x
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Budget Constraints Revisited x 2 x 1 2 2 1 1 2 2 1 1 p p x p x p Budget set 0 , 0 , ) , ( 2 1 2 2 1 1 2 2 1 1 2 1 x x p p x p x p x x
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Budget Constraints Revisited - suppose p 1 changes - slope changes (p 1 /p 2 becomes p 1 ’/p 2 ) - budget line still has to intersect the endowment point x 2 x 1 2 2 1 1 2 2 1 1 p p x p x p pxpxpp 11221122 ''''  
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Budget Constraints Revisited p 1 changes to p 1 x 2 as a function of x 1: (slope of budget line) x 2 x 1 2 2 1 1 2 2 1 1 p p x p x p pxpxpp 11221122 ''''   Budget set
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Budget Constraints Revisited x 2 x 1 2 2 1 1 2 2 1 1 p p x p x p The endowment point is always on the budget constraint. pxpxpp 11221122 ''''  
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Budget Constraints Revisited x 2 x 1 pxpxpp 11221122   The endowment point is always on the budget constraint. pxpxpp 11221122 ''''   So price changes pivot the constraint about the endowment point.
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Budget Constraints Revisited The constraint is That is, the sum of the values of a consumer’s net demands is zero. . 0 ) ( ) ( 2 2 2 1 1 1 x p x p 2 2 1 1 2 2 1 1 p p x p x p
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Net Demands x 2 x 1 0 ) ( ) ( 2 2 2 1 1 1 x p x p x 2 * x 1 * At prices (p 1 ,p 2 ) the consumer sells units of good 1 to acquire more units of good 2.
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Net Demands x 2 x 1 pxpxpp 11221122 ''''   x 2 * x 1 * At prices (p 1 ’,p 2 ’) the consumer sells units of good 2 to acquire more of good 1.
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