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### Chapter Nine

Buying and Selling

Buying and Selling

- Trade involves exchange, so when something is bought something else must be sold.
- What will be bought? What will be sold?

Buying and Selling

- And how are incomes generated?
- How does the value of income depend upon the prices of commodities?
- How can we put all this together to explain better how price changes affect demands?

Endowments

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

Endowments

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

Endowments

- Given prices p1=2 and p2=3 the value of the endowmentis
- Q: For which consumption bundles may the endowment be exchanged?
- A: For any bundle costing no more than the endowment’s market value.

Budget Constraints Revisited

- So, given prices p1 and p2, the budget constraint for a consumer with an endowment is
- The budget set is

Budget Constraints Revisited

Notice that the endowment point isalways on the budget constraint.

x2

So relative price changes cause thebudget constraint to pivot about the endowment point.

w2

w1

x1

Budget Constraints Revisited

- The budget constraintcan be rewritten as
- This says that the sum of the values of a consumer’s net demands is zero.

Net Demands

- Suppose and that p1=2, p2=3. Then the budget constraint is
- Suppose the consumer demands (x1*,x2*) = (7,4), so the consumer exchanges 3 units of good 1 for 2 units of good 2. Net demands are x1*- w1 = 7-10 = -3, x2*- w2 = 4-2 = +2.

Net Demands

p1=2, p2=3, x1*-w1 = -3 and x2*-w2 = +2 so

The purchase of the 2 extra units of good 2 at $3 each is funded by giving up3 units of good 1 at $2 each.

Net Demands

x2

At prices (p1,p2) the consumersells units of good 1 to acquiremore units of good 2.

x2*

w2

x1*

w1

x1

Net Demands

x2

At prices (p1’,p2’) the consumersells units of good 2 to acquiremore of good 1.

w2

x2*

w1

x1*

x1

Net Demands

x2

At prices (p1”,p2”) the consumerconsumes her endowment; netdemands are all zero.

x2*=w2

x1*=w1

x1

Net Demands

x2

Price-offer curve contains all theutility-maximizing buy-sell grossdemands for which the endowment can be exchanged.

w2

w1

x1

Labor Supply

- A worker is endowed with $m of nonlabor income and R hours of time which can be used for labor or leisure. w = (R,m).
- The price of the consumption good is pc.
- Let w denote the wage rate.

¾

¾

Labor Supply

- The worker’s budget constraint iswhere C, R denote the worker’s gross demands for the consumption good and for leisure. That is

¾

¾

{

{

expenditure

endowment value

Slutsky’s Equation Revisited

- Slutsky explained that changes to demands caused by a price change can always be decomposed into
- a pure substitution effect, and
- an income effect.
- 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

- A change in p1 or p2 changes so there will bean additional income effect, called the endowment income effect.
- 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

x2

Initial prices are (p1’,p2’).Final prices are (p1”,p2”).

How is the change in demandfrom (x1’,x2’) to (x1”,x2”) explained?

x2’

w2

x2”

w1

x1

x1’

x1”

Slutsky’s Equation Revisited

Þ

x2

Pure substitution effect

Þ

Ordinary income effect

Þ

Endowment income effect

w2

w1

x1

Slutsky’s Equation Revisited

Overall change in demand caused by achange 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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