中级微观经济学 第六讲
合集下载
相关主题
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
2
Budget set
' ' ' p' x p x p p 1 1 2 2 1 1 2 2
1
x1
Budget Constraints Revisited
x2 The endowment point is always on the budget constraint.
p 1 x 1 p 2 x 2 p 1 1 p 2 2
x1*=1
x1
Net Demands
x2
p1(x1 1 ) p 2 (x 2 2 ) 0
Price-offer curve contains all the utility-maximizing gross demands for which the endowment can be exchanged.
Net Demands
x2 x 2*
p1(x1 1 ) p 2 (x 2 2 ) 0
At prices (p1,p2) the consumer sells units of good 1 to acquire more units of good 2.
2
x 1* 1
endowment
m/pc
R
R
Labor Supply
m wR pc
C
w m wR C R pc pc
C*
m/pc
endowment
R* leisure demanded labor supplied
R
R
Slutsky’s Equation Revisited
We
Price-offer curve Buy good 1, sell good 2
2
1
x1
19
20
Some Results about Price Change
If
a consumer is a net seller of a good, when the price of that good decreases, if she remains a seller then the consumer is worse off. However, if she switches to a net buyer, then she may be better off. If a consumer is a net buyer of a good, when the price decreases, the consumer will remain a buyer and be better off.
A
Labor Supply
The
worker’s budget constraint is pcC = wL + m
p c C w (R R ) m
where C, R denote gross demands for the consumption good and for leisure.
used to assume that income y did not change as prices changed But y p 1 1 p 2 2 so there will be an additional income effect, called the endowment income effect.
北京大学国家发展研究院2014年秋季学期 本科双学位课程 中级微观经济学(2班)
第六讲： 购买和销售
任课教师：李力行
第9章 购买和销售
（禀赋） Budget constraints with endowments Net demands - Price offer curve Example: Labor supply - Comparative statics Slutsky equation revisited
x1
Net Demands
x2
p1(x1 1 ) p 2 (x 2 2 ) 0
At prices (p1”,p2”) the consumer consumes her endowment; net demands are all zero.
x2*=2
" " " p" x p x p p 1 1 2 2 1 1 2 2
Suppose
p 1 x 1 p 2 x 2 p 1 1 p 2 2 2 6 .
If
p1=2, p2=3. Then the constraint is
( 1 , 2 ) ( 1 0 , 2 ) and
the consumer demands (x1*,x2*) = (7,4), then 3 units of good 1 exchange for 2 units of good 2. Net demands are x1*- 1 = 7-10 = -3 and x2*- 2 = 4 - 2 = +2.
2
1
x1
Net Demands
x2
p1(x1 1 ) p 2 (x 2 2 ) 0
Price-offer curve Sell good 1, buy good 2
2
1
x1
Net Demands
x2
p1(x1 1 ) p 2 (x 2 2 ) 0
Endowments
Buying and Selling
How
is income generated? When something is bought something else must be sold. What will be bought? What will be sold? Who will be a buyer? Who will be a seller? How does the value of income depend upon commodity prices?
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?
Budget Constraints Revisited
So,
given p1 and p2, the budget constraint for a consumer with an endowment ( 1 , 2 ) is
p 1 x 1 p 2 x 2 p 1 1 p 2 2 .
2
So price changes pivot the constraint around the endowment point. ' ' ' p' x p x p p 1 1 2 2 1 1 2 2
1
x1
Budget Constraints Revisited
The
constraint
21
A net seller facing falling price
22
A net buyer facing falling price
23
Labor Supply
worker’s non-labor income endowment is m, and time endowment is R hours of time, which can be used for labor or leisure. = (R,m). Consumption good C, price is pc. w is the wage rate.
Endowments
p1=2
p 1 1 p 2 2 2 1 0 3 2 2 6
Q:
and p2=3 so the value of the endowment ( 1 , 2 ) ( 1 0 , 2 ) is
For which consumption bundles may the endowment be exchanged? A: For any bundle costing no more than the endowment’s value.
budget set is
( x 1 , x 2 ) p1 x 1 p 2x 2 p1 1 p 2 2 ,
x 1 0 , x 2 0 .
The
Budget Constraints Revisited
x2
p 1 x 1 p 2 x 2 p 1 1 p 2 2
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
expenditure
pcC w R w R m
endowment value
Labor Supply
p c C w (R R ) m
rearranges to
w m wR C R . pc pc
Labor Supply
m wR pc
C
w m wR C R pc pc w slope = , the ‘real wage rate’ pc
2
Budget set ( x 1 , x 2 ) p1 x 1 p 2x 2 p1 1 p 2 2 , x 1 0 , x 2 0
1
x1
Budget Constraints Revisited
x2
p 1 x 1 p 2 x 2 p 1 1 p 2 2
p 1 x 1 p 2 x 2 p 1 1 p 2 2
is
p1(x1 1 ) p 2 (x 2 2 ) 0.
That
is, the sum of the values of a consumer’s net demand is zero.
Net Demands
Net Demands
p1=2, p2=3, x1*-1 = -3 and x2*-2 = +2 so p1 ( x 1 1 ) p 2 ( x 2 2 )
2 ( 3)
3 2
0.
The purchase of 2 extra units of good 2 at $3 each is funded by giving up 3 units of good 1 at $2 each.
Endowments
The
list of resource with which a consumer starts is his endowment. A consumer’s endowment will be denoted by the vector . E.g. ( 1 , 2 ) ( 1 0 , 2 ) 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?
x1
Net Demands
x2 At prices (p1’,p2’) the consumer sells units of good 2 to acquire more of good 1.
2
x 2*
' ' ' p' x p x p p 1 1 2 2 1 1 2 2
1
x 1*Baidu Nhomakorabea
Budget set
' ' ' p' x p x p p 1 1 2 2 1 1 2 2
1
x1
Budget Constraints Revisited
x2 The endowment point is always on the budget constraint.
p 1 x 1 p 2 x 2 p 1 1 p 2 2
x1*=1
x1
Net Demands
x2
p1(x1 1 ) p 2 (x 2 2 ) 0
Price-offer curve contains all the utility-maximizing gross demands for which the endowment can be exchanged.
Net Demands
x2 x 2*
p1(x1 1 ) p 2 (x 2 2 ) 0
At prices (p1,p2) the consumer sells units of good 1 to acquire more units of good 2.
2
x 1* 1
endowment
m/pc
R
R
Labor Supply
m wR pc
C
w m wR C R pc pc
C*
m/pc
endowment
R* leisure demanded labor supplied
R
R
Slutsky’s Equation Revisited
We
Price-offer curve Buy good 1, sell good 2
2
1
x1
19
20
Some Results about Price Change
If
a consumer is a net seller of a good, when the price of that good decreases, if she remains a seller then the consumer is worse off. However, if she switches to a net buyer, then she may be better off. If a consumer is a net buyer of a good, when the price decreases, the consumer will remain a buyer and be better off.
A
Labor Supply
The
worker’s budget constraint is pcC = wL + m
p c C w (R R ) m
where C, R denote gross demands for the consumption good and for leisure.
used to assume that income y did not change as prices changed But y p 1 1 p 2 2 so there will be an additional income effect, called the endowment income effect.
北京大学国家发展研究院2014年秋季学期 本科双学位课程 中级微观经济学(2班)
第六讲： 购买和销售
任课教师：李力行
第9章 购买和销售
（禀赋） Budget constraints with endowments Net demands - Price offer curve Example: Labor supply - Comparative statics Slutsky equation revisited
x1
Net Demands
x2
p1(x1 1 ) p 2 (x 2 2 ) 0
At prices (p1”,p2”) the consumer consumes her endowment; net demands are all zero.
x2*=2
" " " p" x p x p p 1 1 2 2 1 1 2 2
Suppose
p 1 x 1 p 2 x 2 p 1 1 p 2 2 2 6 .
If
p1=2, p2=3. Then the constraint is
( 1 , 2 ) ( 1 0 , 2 ) and
the consumer demands (x1*,x2*) = (7,4), then 3 units of good 1 exchange for 2 units of good 2. Net demands are x1*- 1 = 7-10 = -3 and x2*- 2 = 4 - 2 = +2.
2
1
x1
Net Demands
x2
p1(x1 1 ) p 2 (x 2 2 ) 0
Price-offer curve Sell good 1, buy good 2
2
1
x1
Net Demands
x2
p1(x1 1 ) p 2 (x 2 2 ) 0
Endowments
Buying and Selling
How
is income generated? When something is bought something else must be sold. What will be bought? What will be sold? Who will be a buyer? Who will be a seller? How does the value of income depend upon commodity prices?
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?
Budget Constraints Revisited
So,
given p1 and p2, the budget constraint for a consumer with an endowment ( 1 , 2 ) is
p 1 x 1 p 2 x 2 p 1 1 p 2 2 .
2
So price changes pivot the constraint around the endowment point. ' ' ' p' x p x p p 1 1 2 2 1 1 2 2
1
x1
Budget Constraints Revisited
The
constraint
21
A net seller facing falling price
22
A net buyer facing falling price
23
Labor Supply
worker’s non-labor income endowment is m, and time endowment is R hours of time, which can be used for labor or leisure. = (R,m). Consumption good C, price is pc. w is the wage rate.
Endowments
p1=2
p 1 1 p 2 2 2 1 0 3 2 2 6
Q:
and p2=3 so the value of the endowment ( 1 , 2 ) ( 1 0 , 2 ) is
For which consumption bundles may the endowment be exchanged? A: For any bundle costing no more than the endowment’s value.
budget set is
( x 1 , x 2 ) p1 x 1 p 2x 2 p1 1 p 2 2 ,
x 1 0 , x 2 0 .
The
Budget Constraints Revisited
x2
p 1 x 1 p 2 x 2 p 1 1 p 2 2
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
expenditure
pcC w R w R m
endowment value
Labor Supply
p c C w (R R ) m
rearranges to
w m wR C R . pc pc
Labor Supply
m wR pc
C
w m wR C R pc pc w slope = , the ‘real wage rate’ pc
2
Budget set ( x 1 , x 2 ) p1 x 1 p 2x 2 p1 1 p 2 2 , x 1 0 , x 2 0
1
x1
Budget Constraints Revisited
x2
p 1 x 1 p 2 x 2 p 1 1 p 2 2
p 1 x 1 p 2 x 2 p 1 1 p 2 2
is
p1(x1 1 ) p 2 (x 2 2 ) 0.
That
is, the sum of the values of a consumer’s net demand is zero.
Net Demands
Net Demands
p1=2, p2=3, x1*-1 = -3 and x2*-2 = +2 so p1 ( x 1 1 ) p 2 ( x 2 2 )
2 ( 3)
3 2
0.
The purchase of 2 extra units of good 2 at $3 each is funded by giving up 3 units of good 1 at $2 each.
Endowments
The
list of resource with which a consumer starts is his endowment. A consumer’s endowment will be denoted by the vector . E.g. ( 1 , 2 ) ( 1 0 , 2 ) 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?
x1
Net Demands
x2 At prices (p1’,p2’) the consumer sells units of good 2 to acquire more of good 1.
2
x 2*
' ' ' p' x p x p p 1 1 2 2 1 1 2 2
1
x 1*Baidu Nhomakorabea