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
example   ( 1 ,  2 )  (10, 2)
means 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?
 For
Endowments
 Given
prices p1=2 and p2=3 the value
of the endowment ( 1 ,  2 )  (10, 2)
is
p1 1  p2 2  2  10  3  2  26
 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 ( 1 ,  2 ) is
p1x1  p2x 2  p1 1  p2 2 .
 The
budget set is
( x1 , x 2 ) p1 x1  p2x 2  p11  p2 2 ,
x1  0, x 2  0.
Budget Constraints Revisited
x2
p1x1  p2x 2  p11  p2 2
2
1
x1
Budget Constraints Revisited
x2
p1x1  p2x 2  p11  p2 2
2
p'1x1  p'2x 2  p'1 1  p'2 2
1
x1
Budget Constraints Revisited
x2
Notice that the endowment point is
always on the budget constraint.
p1x1  p2x 2  p11  p2 2
So relative price changes cause the
budget constraint to pivot about the
endowment point.
p'1x1  p'2x 2  p'1 1  p'2 2
2
1
x1
Budget Constraints Revisited
 The
budget constraint
p1x1  p2x 2  p11  p2 2
can be rewritten as
p1 ( x1   1 )  p2 ( x 2   2 )  0.
 This
says that the sum of the values
of a consumer’s net demands is zero.
Net Demands
 Suppose
( 1 ,  2 )  (10, 2) and that
p1=2, p2=3. Then the budget
constraint is
p1x1  p2x 2  p1 1  p2 2  26.
 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*- 1 = 7-10 = -3, x2*- 2 = 4-2 = +2.
Net Demands
p1=2, p2=3, x1*-1 = -3 and x2*-2 = +2 so
p1 ( x1   1 )  p 2 ( x 2   2 ) 
2  ( 3 )

3 2
 0.
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
x2
p1 ( x1   1 )  p2 ( x 2   2 )  0
At prices (p1,p2) the consumer
sells units of good 1 to acquire
more units of good 2.
x 2*
2
x1* 1
x1
Net Demands
x2
At prices (p1’,p2’) the consumer
sells units of good 2 to acquire
more of good 1.
2
p'1x1  p'2x 2  p'1 1  p'2 2
x 2*
1
x 1*
x1
Net Demands
x2
p1 ( x1   1 )  p2 ( x 2   2 )  0
At prices (p1”,p2”) the consumer
consumes her endowment; net
demands are all zero.
x2*=2
p"1x1  p"2x 2  p"1 1  p"2 2
x1*=1
x1
Net Demands
x2
p1 ( x1   1 )  p2 ( x 2   2 )  0
Price-offer curve contains all the
utility-maximizing buy-sell gross
demands for which the endowment
can be exchanged.
2
1
x1
Net Demands
x2
p1 ( x1   1 )  p2 ( x 2   2 )  0
Price-offer curve
Sell good 1, buy good 2
2
1
x1
Net Demands
x2
p1 ( x1   1 )  p2 ( x 2   2 )  0
Price-offer curve
Buy good 1, sell good 2
2
1
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.  = (R,m).
 The price of the consumption good is
pc.
 Let w denote the wage rate.
Labor Supply
 The
worker’s budget constraint is

pcC  w (R  R )  m
where C, R denote the worker’s
gross demands for the consumption
good and for leisure. That is

expenditure


pcC  wR  wR  m
endowment
value
Labor Supply

pcC  w (R  R )  m
rearranges to

w
m  wR
C  R
.
pc
pc
Labor Supply
C

m  wR
pc

w
m  wR
C  R
pc
pc
w
slope = 
, the ‘real wage rate’
pc
endowment
m

R
R
Labor Supply

w
m  wR
C  R
pc
pc
C

m  wR
pc
C*
endowment
m

R*
leisure
demanded
R
labor
supplied
R
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
y  p1 1  p2 2
does change with price. What does
this do to Slutsky’s equation?
Slutsky’s Equation Revisited
A
change in p1 or p2 changes
y  p1 1  p2 2 so there will be
an 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’).
x 2’
2
x 1’
1
x1
Slutsky’s Equation Revisited
x2
Initial prices are (p1’,p2’).
Final prices are (p1”,p2”).
How is the change in demand
from (x1’,x2’) to (x1”,x2”) explained?
x 2’
2
x 2”
x 1’
1
x 1”
x1
Slutsky’s Equation Revisited

x2
Pure substitution effect
2
1
x1
Slutsky’s Equation Revisited


x2
Pure substitution effect
Ordinary income effect
2
1
x1
Slutsky’s Equation Revisited



x2
Pure substitution effect
Ordinary income effect
Endowment income effect
2
1
x1
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