Chapter Nine Buying and Selling. u Trade involves exchange, so when something is bought something else must be sold. u What will be bought? What will.
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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
x2x2 x1x1 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.
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 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 *- 1 = 7-10 = -3, x 2 *- 2 = 4-2 = +2.
Net Demands p 1 =2, p 2 =3, x 1 *- 1 = -3 and x 2 *- 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 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.
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.
Net Demands x2x2 x1x1 x 2 *= x 1 *= At prices (p 1 ”,p 2 ”) the consumer consumes her endowment; net demands are all zero.
Net Demands x2x2 x1x1 Price-offer curve contains all the utility-maximizing buy-sell gross demands for which the endowment can be exchanged.
Net Demands x2x2 x1x1 Price-offer curve Sell good 1, buy good 2
Net Demands x2x2 x1x1 Price-offer curve Buy good 1, sell good 2
Labor Supply A worker is endowed with $m of nonlabor income and R hours of time which can be used for labor or leisure. = (R,m). u The price of the consumption good is p c. u Let w denote the wage rate.
Labor Supply u The worker’s budget constraint is where C, R denote the worker’s gross demands for the consumption good and for leisure. That is endowment value expenditure
Labor Supply C R R endowment m slope =, the ‘real wage rate’
Labor Supply C R R endowment m C* R* leisure demanded labor supplied
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 x1x1 22 11 x2x2 Pure substitution effect Ordinary income effect
Slutsky’s Equation Revisited x1x1 22 11 x2x2 Pure substitution effect Ordinary income effect Endowment income effect
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