Chapter Nine Buying and Selling
Buying and Selling u Trade involves exchange, so when something is bought something else must be sold. u What will be bought? What will be sold?
Buying and Selling u And how are incomes generated? u How does the value of income depend upon the prices of commodities? u How can we put all this together to explain better how price changes affect demands?
Endowments u The list of resource units with which a consumer starts is called his endowment. u A consumer’s endowment will be denoted by the vector (omega).
Endowments u For example means 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?
Endowments u Given prices p 1=2 and p 2=3 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 market value.
Budget Constraints Revisited u So, given prices p 1 and p 2, the budget constraint for a consumer with an endowment is u The budget set is
Budget Constraints Revisited x 2 w 1 x 1
Budget Constraints Revisited x 2 w 1 x 1
Budget Constraints Revisited x 2 Notice that the endowment point is always on the budget constraint. So relative price changes cause the budget constraint to pivot about the endowment point. w 2 w 1 x 1
Budget Constraints Revisited u The budget constraint can be rewritten as u This says that the sum of the values of a consumer’s net demands is zero.
Net Demands u Suppose and that p 1=2, p 2=3. Then the budget constraint is u Suppose the consumer demands (x 1*, x 2*) = (7, 4), so the consumer exchanges 3 units of good 1 for 2 units of good 2. Net demands are x 1* - w 1 = 7 -10 = -3, x 2*- w 2 = 4 -2 = +2.
Net Demands p 1=2, p 2=3, x 1*-w 1 = -3 and x 2*-w 2 = +2 so The purchase of the 2 extra units of good 2 at $3 each is funded by giving up 3 units of good 1 at $2 each.
Net Demands x 2 At prices (p 1, p 2) the consumer sells units of good 1 to acquire more units of good 2. x 2* w 2 x 1 * w 1 x 1
Net Demands x 2 At prices (p 1’, p 2’) the consumer sells units of good 2 to acquire more of good 1. w 2 x 2* w 1 x 1* x 1
Net Demands x 2 At prices (p 1”, p 2”) the consumer consumes her endowment; net demands are all zero. x 2*=w 2 x 1*=w 1 x 1
Net Demands x 2 Price-offer curve contains all the utility-maximizing buy-sell gross demands for which the endowment can be exchanged. w 2 w 1 x 1
Net Demands x 2 Price-offer curve Sell good 1, buy good 2 w 1 x 1
Net Demands x 2 Price-offer curve Buy good 1, sell good 2 w 1 x 1
Labor Supply u. A worker is endowed with $m of ¾ nonlabor income and R hours of time which can be used for labor or ¾ leisure. w = (R, m). u The price of the consumption good is pc. u Let w denote the wage rate.
Labor Supply u The worker’s budget constraint is ¾ where C, R denote the worker’s gross demands for the consumption good and for leisure. That is expenditure { { ¾ endowment value
Labor Supply ¾ rearranges to ¾
C ¾ Labor Supply slope = ¾ , the ‘real wage rate’ endowment m ¾ R R
C ¾ Labor Supply ¾ C* endowment m ¾ R* leisure demanded R labor supplied R
Slutsky’s Equation Revisited u Slutsky explained that changes to demands caused by a price change can always be decomposed into – 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. What does this do to Slutsky’s equation?
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.
Slutsky’s Equation Revisited x 2 Initial prices are (p 1’, p 2’). x 2’ w 2 x 1’ w 1 x 1
Slutsky’s Equation Revisited x 2 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? x 2’ w 2 x 2” x 1’ w 1 x 1” x 1
Slutsky’s Equation Revisited Þ x 2 Pure substitution effect w 2 w 1 x 1
Slutsky’s Equation Revisited Þ Þ x 2 Pure substitution effect Ordinary income effect w 2 w 1 x 1
Slutsky’s Equation Revisited Þ Þ Þ x 2 Pure substitution effect Ordinary income effect Endowment income effect w 2 w 1 x 1
Slutsky’s Equation Revisited Overall change in demand caused by a change in relative price is the sum of: (i) a pure substitution effect (ii) an ordinary income effect (iii) an endowment income effect
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