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Chapter Nine Buying and Selling

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Endowments u The list of resource units with which a consumer starts is his endowment. u A consumer’s endowment will be denoted by the vector (omega).

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Endowments u E.g. states that the consumer is endowed with 10 units of good 1 and 2 units of good 2. u What is the endowment’s value? u For which consumption bundles may it be exchanged?

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Endowments u p 1 =2 and p 2 =3 so the value of the endowment is u Q: For which consumption bundles may the endowment be exchanged? u A: For any bundle costing no more than the endowment’s value.

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Budget Constraints Revisited u So, given p 1 and p 2, the budget constraint for a consumer with an endowment is u The budget set is

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Budget Constraints Revisited x2x2 x1x1

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x2x2 x1x1 Budget set

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Budget Constraints Revisited x2x2 x1x1

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x2x2 x1x1 Budget set

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Budget Constraints Revisited x2x2 x1x1 The endowment point is always on the budget constraint. So price changes pivot the constraint about the endowment point.

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Budget Constraints Revisited u The constraint is u That is, the sum of the values of a consumer’s net demands is zero.

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Net Demands u Suppose and p 1 =2, p 2 =3. Then the constraint is If the consumer demands (x 1 *,x 2 *) = (7,4), then 3 good 1 units exchange for 2 good 2 units. Net demands are x 1 *- 1 = 7-10 = -3 and x 2 *- 2 = 4 - 2 = +2.

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Net Demands p 1 =2, p 2 =3, x 1 *- 1 = -3 and x 2 *- 2 = +2 so The purchase of 2 extra good 2 units at $3 each is funded by giving up 3 good 1 units at $2 each.

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Net Demands x2x2 x1x1 x2*x2* x1*x1* 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 x2x2 x1x1 x2*x2* x1*x1* At prices (p 1 ’,p 2 ’) the consumer sells units of good 2 to acquire more of good 1.

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Net Demands x2x2 x1x1 x 2 *= x 1 *= At prices (p 1 ”,p 2 ”) the consumer consumes her endowment; net demands are all zero.

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Slutsky’s Equation Revisited u Slutsky: changes to demands caused by a price change are the sum of –a pure substitution effect, and –an income effect. u This assumed that income y did not change as prices changed. But does change with price. How does this modify Slutsky’s equation?

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Slutsky’s Equation Revisited u A change in p 1 or p 2 changes so there will be an additional income effect, called the endowment income effect. u Slutsky’s decomposition will thus have three components –a pure substitution effect –an (ordinary) income effect, and –an endowment income effect.

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Slutsky’s Equation Revisited x1x1 22 11 x2x2 x2’x2’ x1’x1’ Initial prices are (p 1 ’,p 2 ’).

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Slutsky’s Equation Revisited x1x1 22 11 x2x2 x2’x2’ x1”x1” x2”x2” Initial prices are (p 1 ’,p 2 ’). Final prices are (p 1 ”,p 2 ”). x1’x1’

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Slutsky’s Equation Revisited x1x1 22 11 x2x2 x2’x2’ x1”x1” x2”x2” Initial prices are (p 1 ’,p 2 ’). Final prices are (p 1 ”,p 2 ”). How is the change in demand from (x 1 ’,x 2 ’) to (x 1 ”,x 2 ”) explained? x1’x1’

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Slutsky’s Equation Revisited x1x1 22 11 x2x2 x2’x2’ x1’x1’ Initial prices are (p 1 ’,p 2 ’).

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Slutsky’s Equation Revisited x1x1 22 11 x2x2 x2’x2’ x1”x1” x2”x2” Initial prices are (p 1 ’,p 2 ’). Final prices are (p 1 ”,p 2 ”). x1’x1’

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Slutsky’s Equation Revisited x1x1 22 11 x2x2 Pure substitution effect

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Slutsky’s Equation Revisited x1x1 22 11 x2x2 Pure substitution effect Ordinary income effect

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Slutsky’s Equation Revisited x1x1 22 11 x2x2 Pure substitution effect Ordinary income effect

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Slutsky’s Equation Revisited x1x1 22 11 x2x2 Pure substitution effect Ordinary income effect Endowment income effect

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Slutsky’s Equation Revisited x1x1 22 11 x2x2 Pure substitution effect Ordinary income effect Endowment income effect

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Slutsky’s Equation Revisited Overall change in demand caused by a change in price is the sum of: (i) a pure substitution effect (ii) an ordinary income effect (iii) an endowment income effect

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