Chapter Nine
Buying and Selling
What Are We Doing in this
Chapter?
? We expand our basic consumer
choice framework to include the
possibility that consumers can sell
something to generate income.
? Again,in terms of theoretical
framework,nothing is new.
Endowments 禀赋
?The list of resource units with which
a consumer starts is his endowment.
?A consumer’s endowment will be
denoted by the vector (omega).?
Endowments
?E.g.
states 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?
? ? ?? ?(,) (,)1 2 10 2
Budget Constraints Revisited
?So,given p1 and p2,the budget
constraint for a consumer with an
endowment is
?The budget set is
(,)? ?1 2
p x p x p p1 1 2 2 1 1 2 2? ? ?? ?,
?
?
(,),
,.
x x p x p x p p
x x
1 2 1 1 2 2 1 1 2 2
1 20 0
? ? ?
? ?
? ?
Budget Constraints Revisited
x2
x1?1
?2
p x p x p p1 1 2 2 1 1 2 2? ? ?? ?
Budget set?
?
(,),
,
x x p x p x p p
x x
1 2 1 1 2 2 1 1 2 2
1 20 0
? ? ?
? ?
? ?
Budget Constraints Revisited
x2
x1?1
?2
p x p x p p1 1 2 2 1 1 2 2? ? ?? ?
p x p x p p1 1 2 2 1 1 2 2' ' ' '? ? ?? ?
Budget set
Budget Constraints Revisited
x2
x1?1
?2
p x p x p p1 1 2 2 1 1 2 2? ? ?? ?
The endowment point is always on
the budget constraint.
p x p x p p1 1 2 2 1 1 2 2' ' ' '? ? ?? ?
So price changes pivot the
constraint about the
endowment point.
Budget Constraints Revisited
?The constraint
is
?That is,the sum of the values of a
consumer’s net demands is zero.
p x p x1 1 1 2 2 2 0( ) ( ),? ? ? ?? ?
p x p x p p1 1 2 2 1 1 2 2? ? ?? ?
Net Demands
x2
x1?1
?2
p x p x1 1 1 2 2 2 0( ) ( )? ? ? ?? ?
x2*
x1*
At prices (p1,p2) the consumer
sells units of good 1 to acquire
more units of good 2.
Net Demands
x2
x1
p x p x1 1 1 2 2 2 0( ) ( )? ? ? ?? ?
x2*=?2
x1*=?1
At prices (p1”,p2”) the consumer
consumes her endowment; net
demands are all zero.
p x p x p p1 1 2 2 1 1 2 2" " " "? ? ?? ?
Net Demands
x2
x1?1
?2
p x p x1 1 1 2 2 2 0( ) ( )? ? ? ?? ?
Price-offer curve contains all the
utility-maximizing gross demands
for which the endowment can be
exchanged.
A Variation of the Theme,
Income from Labor
?A worker is endowed with $m of
nonlabor income and R hours of time
which can be used for labor or
leisure,? = (R,m).
?Consumption good’s price is pc.
?w is the wage rate.
?
?
Labor Supply
?The worker’s budget constraint is
where C,R denote gross demands
for the consumption good and for
leisure,That is
p C w R R mc ? ? ?( )?
p C wR wR mc ? ? ?? ??
endowment
value
expenditure
Labor Supply
C
RR?
endowmentm
($)
Labor Supply
C
RR?
endowment
C wp R m wRp
c c
? ? ? ?m wR
p c
?
?
?
m
Labor Supply
C
RR?
endowment
C wp R m wRp
c c
? ? ? ?m wR
p c
?
?
?
m
slope =,the ‘real wage rate’?
w
pc
Labor Supply
C
RR?
endowment
C wp R m wRp
c c
? ? ? ?m wR
p c
?
?
?
m
C*
R*
leisure
demanded
labor
supplied
The Morale of the Story,Limited
Possibility of Market Transactions
?There are some cases in which a
good cannot be sold or bought in
any amount!
Slutsky’s Equation Revisited
? Slutsky,changes to demands caused by a
price change are the sum of
– a pure substitution effect,and
– an income effect.
? This assumed that income y did not
change as prices changed,But
does change with price,How does this
modify Slutsky’s equation?
y p p? ?1 1 2 2? ?
Slutsky’s Equation Revisited
?A change in p1 or p2 changes
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.
y p p? ?1 1 2 2? ?
Slutsky’s Equation Revisited
x1
?2
?1
x2
x2’
x1’
Initial prices are (p1’,p2’).
Slutsky’s Equation Revisited
x1
?2
?1
x2
x2’
x1”
x2”
Initial prices are (p1’,p2’).
Final prices are (p1”,p2”).
How is the change in demand
from (x1’,x2’) to (x1”,x2”) explained?
x1’
Slutsky’s Equation Revisited
x1
?2
?1
x2
x2’
x1’
Initial prices are (p1’,p2’).
Slutsky’s Equation Revisited
x1
?2
?1
x2
x2’
x1”
x2”
Initial prices are (p1’,p2’).
Final prices are (p1”,p2”).
x1’
Slutsky’s Equation Revisited
x1
?2
?1
x2 Pure substitution effect?
Slutsky’s Equation Revisited
x1
?2
?1
x2 Pure substitution effect?
Slutsky’s Equation Revisited
x1
?2
?1
x2 Pure substitution effect?
Ordinary income effect?
Slutsky’s Equation Revisited
x1
?2
?1
x2 Pure substitution effect?
Ordinary income effect?
Slutsky’s Equation Revisited
x1
?2
?1
x2 Pure substitution effect?
Ordinary income effect?
Endowment income effect?
Slutsky’s Equation Revisited
x1
?2
?1
x2 Pure substitution effect?
Ordinary income effect?
Endowment income effect?
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
一个经典例子
白居易《卖炭翁》
……
可怜身上衣正单，
心忧炭贱愿天寒。
……