chapter thirty exchange tausch 交换. hu jingbei’s declaration to copyright may 17, 2007 u this...
TRANSCRIPT
![Page 1: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/1.jpg)
Chapter Thirty
Exchange
Tausch
交换
![Page 2: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/2.jpg)
Hu Jingbei’s declaration to copyrightMay 17, 2007
This ppt-file may come from an American source which is not known to me at the moment. It based on Varian’s Intermediate Microeconomics, 5th ed. In many places of this file, I made changes for my lectures with Varian’s 6th ed. I will be grateful to persons who may show me the original sources of this file.
![Page 3: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/3.jpg)
Contents
The Edgeworth Box Pareto improving trade Pareto Efficient Allocation The Core (核 ) Trade in a competitive market Walras’ Law First Fundamental Theorem of Welfare
Economics (福利经济学第一定理 ) Second Fundamental Theorem of Welfare
Economics (福利经济学第二定理 )
![Page 4: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/4.jpg)
Exchange
Two consumers, A and B. Their endowments of goods 1 and 2
are
E.g. The total quantities available
A A A( , )1 2 B B B( , ).1 2and
A ( , )6 4 B ( , ).2 2and
1 1 6 2 8A B
2 2 4 2 6A B
units of good 1
units of good 2.and
are
![Page 5: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/5.jpg)
Exchange
The English economist Edgeworth devised a diagram, called an Edgeworth box (Edgeworth Diagramm) , to show all possible allocations of the available quantities of goods 1 and 2 between the two consumers.
![Page 6: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/6.jpg)
Starting an Edgeworth Box
Width = 1 1 6 2 8A B
Height = 2 2
4 2
6
A B
The dimensions ofthe box are thequantities availableof the goods.
![Page 7: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/7.jpg)
Feasible Allocations
What allocations of the 8 units of good 1 and the 6 units of good 2 are feasible?
How can all of the feasible allocations be depicted by the Edgeworth box diagram?
One feasible allocation is the before-trade allocation; i.e. the endowment allocation (urspaengliche Allokation).
![Page 8: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/8.jpg)
Width = 1 1 6 2 8A B
Height =
2 2
4 2
6
A B
The endowmentallocation is A ( , )6 4
B ( , ).2 2
and
The Endowment Allocation
![Page 9: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/9.jpg)
Width = 1 1 6 2 8A B
Height =
2 2
4 2
6
A B
A ( , )6 4B ( , )2 2
The Endowment Allocation
![Page 10: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/10.jpg)
A ( , )6 4OA
OB
6
8B ( , )2 2
The Endowment Allocation
![Page 11: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/11.jpg)
A ( , )6 4OA
OB
6
8
4
6
The Endowment Allocation
![Page 12: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/12.jpg)
B ( , )2 2
OA
OB
6
8
4
6
2
2
The Endowment Allocation
![Page 13: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/13.jpg)
A ( , )6 4B ( , )2 2
OA
OB
6
8
4
6
2
2
Theendowmentallocation
The Endowment Allocation
![Page 14: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/14.jpg)
More generally, …
The Endowment Allocation
![Page 15: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/15.jpg)
The Endowment Allocation
OA
OB
Theendowmentallocation
1 1A B
2A
2
2
A
B
1A
1B
2B
![Page 16: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/16.jpg)
Other Feasible Allocations
denotes an allocation to consumer A.
denotes an allocation to consumer B.
An allocation is feasible if and only if
( , )x xA A1 2
( , )x xB B1 2
x xA B A B1 1 1 1
x xA B A B2 2 2 2 .and
![Page 17: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/17.jpg)
Feasible Reallocations
OA
OB
1 1A B
xA2
2
2
A
B
xA1
xB1
xB2
![Page 18: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/18.jpg)
Feasible Reallocations
OA
OB
1 1A B
xA2
2
2
A
B
xA1
xB1
xB2
![Page 19: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/19.jpg)
Feasible Reallocations
All points in the box, including the boundary, represent feasible allocations of the combined endowments.
Which allocations will be blocked by one or both consumers?
Which allocations make both consumers better off?
![Page 20: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/20.jpg)
Adding Preferences to the Box
2A
1A
xA2
xA1
OA
For consumer A.
![Page 21: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/21.jpg)
Adding Preferences to the Box
2A
1A
xA2
xA1
More preferred
For consumer A.
OA
![Page 22: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/22.jpg)
Adding Preferences to the Box
2B
1B
xB2
xB1
For consumer B.
OB
![Page 23: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/23.jpg)
Adding Preferences to the BoxxB2
xB1
More preferred
For consumer B.
OB
2B
1B
![Page 24: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/24.jpg)
Adding Preferences to the Box
2B
1B
xB1
xB2
More preferred
For consumer B. OB
![Page 25: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/25.jpg)
Adding Preferences to the Box
2A
1A
xA2
xA1
OA
For consumer A.
![Page 26: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/26.jpg)
Adding Preferences to the Box
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
![Page 27: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/27.jpg)
Edgeworth’s Box
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
![Page 28: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/28.jpg)
Pareto-Improvement
An allocation of the endowment that improves the welfare of at least a consumer without reducing the welfare of another is a Pareto-improving allocation (Allokation der Pareto-Verbesserung)
Where are the Pareto-improving allocations?
![Page 29: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/29.jpg)
Edgeworth’s Box
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
![Page 30: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/30.jpg)
Pareto-Improvements
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
The set of Pareto-improving allocations
![Page 31: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/31.jpg)
Pareto-Improvements
Since each consumer can refuse to trade, the only possible outcomes from exchange are Pareto-improving allocations (Allokationen der Pareto-Verbessrung).
But which particular Pareto-improving allocation will be the outcome of trade?
![Page 32: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/32.jpg)
Pareto-Improvements
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
The set of Pareto-improving reallocations
![Page 33: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/33.jpg)
Pareto-Improvements
![Page 34: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/34.jpg)
Pareto-Improvements
![Page 35: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/35.jpg)
Pareto-Improvements
Tradeimproves bothA’s and B’s welfares.This is a Pareto-improvementover the endowment allocation.
![Page 36: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/36.jpg)
Pareto-ImprovementsNew mutual gains-to-trade region is the set of all further Pareto- improving reallocations.
Tradeimproves bothA’s and B’s welfares.This is a Pareto-improvement(帕累托改进 )over the endowment allocation.
![Page 37: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/37.jpg)
Pareto-ImprovementsFurther trade cannot improve both A and B’s welfares.
![Page 38: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/38.jpg)
Pareto-Optimality (Pareto-Optimum,帕累托最优 )
Better forconsumer B
Better forconsumer A
![Page 39: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/39.jpg)
Pareto-OptimalityA is strictly better off but B is strictly worse off
B is strictly betteroff but A is strictlyworse off
![Page 40: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/40.jpg)
Pareto-OptimalityA is strictly better off but B is strictly worse off
B is strictly betteroff but A is strictlyworse off
Both Aand B are worse off
Both A andB are worseoff
![Page 41: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/41.jpg)
Pareto-Optimality
The allocation isPareto-optimal since theonly way one consumer’swelfare can be increased is todecrease the welfare of the otherconsumer.
![Page 42: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/42.jpg)
Pareto-Optimality
The allocation isPareto-optimal since theonly way one consumer’swelfare can be increased is todecrease the welfare of the otherconsumer.
At the Pareto-optimality both of the Marginal Rates of Substitution must be equal.
![Page 43: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/43.jpg)
Pareto-Optimality
Where are all of the Pareto-optimal allocations of the endowment?
![Page 44: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/44.jpg)
Pareto-Optimality
Condition of the Pareto-Optimality: MRSA = MRSB
To explain the condition, we can assume one consumer’s utility constant and see how to maximize another’s utility. With both the budget constraints, a Lagrange method can be used to show the condition.
![Page 45: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/45.jpg)
Pareto-Optimality
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
![Page 46: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/46.jpg)
Pareto-Optimality
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
All the allocations marked bya are Pareto-optimal.
![Page 47: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/47.jpg)
Pareto-Optimality
The contract curve (契约线 ) is the set of all Pareto-optimal allocations.
![Page 48: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/48.jpg)
Pareto-Optimality
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
All the allocations marked bya are Pareto-optimal.
The contract curve
![Page 49: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/49.jpg)
Pareto-Optimality
But to which of the many allocations on the contract curve will consumers trade?
That depends upon how trade is conducted.
In perfectly competitive markets? By one-on-one bargaining?
![Page 50: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/50.jpg)
The Core (Kore, 核 )
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
The set of Pareto-improving reallocations
![Page 51: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/51.jpg)
The Core
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
![Page 52: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/52.jpg)
The Core
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Pareto-optimal trades blocked by B
Pareto-optimal trades blocked by A
![Page 53: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/53.jpg)
The Core
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Pareto-optimal trades not blocked by A or B are the core.
![Page 54: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/54.jpg)
The Core The core is the set of all Pareto-
optimal allocations that are welfare-improving for both consumers relative to their own endowments.
Rational trade should achieve a core allocation.
![Page 55: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/55.jpg)
The Core
But which core allocation? Again, that depends upon the
manner in which trade is conducted.
![Page 56: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/56.jpg)
Trade in Competitive Markets
Consider trade in perfectly competitive markets.
Each consumer is a price-taker trying to maximize her own utility given p1, p2 and her own endowment. That is, ...
![Page 57: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/57.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
consumer A’s budget line:
p x p x p pA A A A1 1 2 2 1 1 2 2
x A2*
x A1*
![Page 58: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/58.jpg)
Trade in Competitive Markets
So given p1 and p2, consumer A’s net demands for commodities 1 and 2 are
x A A1 1* x A A
2 2* . and
![Page 59: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/59.jpg)
Trade in Competitive Markets
And, similarly, for consumer B …
![Page 60: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/60.jpg)
Trade in Competitive Markets
2B
1B
xB2
xB1
consumer B’s budget line:
OB x B1*
x B2*
p x p x p pB B B B1 1 2 2 1 1 2 2
![Page 61: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/61.jpg)
Trade in Competitive Markets
So given p1 and p2, consumer B’s net demands for commodities 1 and 2 are
x B B1 1* x B B
2 2* . and
![Page 62: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/62.jpg)
Trade in Competitive Markets A general equilibrium (Allgemeines
Gleichgewicht, 一般均衡 ) occurs when prices p1 and p2 cause both the markets for commodities 1 and 2 to clear; i.e.
x xA B A B1 1 1 1* *
x xA B A B2 2 2 2* * . and
![Page 63: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/63.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
![Page 64: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/64.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Can this PO allocation beachieved?
![Page 65: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/65.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer A
![Page 66: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/66.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer A
x A2*
x A1*
![Page 67: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/67.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer B
x A2*
x A1*
![Page 68: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/68.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer B
x A2*
x A1*
x B1*
x B2*
![Page 69: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/69.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
x A2*
x A1*
x B1*
x B2*
But x xA B A B1 1 1 1* *
![Page 70: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/70.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
x A2*
x A1*
x B1*
x B2*
and x xA B A B2 2 2 2* *
![Page 71: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/71.jpg)
Trade in Competitive Markets
So at the given prices p1 and p2 there is an
– excess supply of commodity 1
– excess demand for commodity 2. Neither market clears so the prices p1
and p2 do not cause a general equilibrium.
![Page 72: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/72.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
So this PO allocation cannot beachieved by the given prices.
![Page 73: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/73.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
How can PO allocations beachieved by competitive trading?
![Page 74: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/74.jpg)
Trade in Competitive Markets
Since there is an excess demand for commodity 2, p2 will rise.
Since there is an excess supply of commodity 1, p1 will fall.
The slope of the budget constraints is - p1/p2 so the budget constraints will pivot about the endowment point and become less steep.
![Page 75: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/75.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Which PO allocations can beachieved by competitive trading?
![Page 76: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/76.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Which PO allocations can beachieved by competitive trading?
![Page 77: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/77.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Which PO allocations can beachieved by competitive trading?
![Page 78: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/78.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer A
![Page 79: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/79.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer A
x A2*
x A1*
![Page 80: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/80.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer B
x A2*
x A1*
![Page 81: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/81.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Budget constraint for consumer B
x A2*
x A1*
x B1*
x B2*
![Page 82: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/82.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
x A2*
x A1*
x B1*
x B2*
So x xA B A B1 1 1 1* *
![Page 83: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/83.jpg)
Trade in Competitive Markets
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
x A2*
x A1*
x B1*
x B2*
and x xA B A B2 2 2 2* *
![Page 84: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/84.jpg)
Trade in Competitive Markets
At the new prices p1 and p2 both markets clear; there is a general equilibrium.
Question 1: Are prices p1 and p2 determined independently at equilibrium?
Question 2: Does the equilibrium exist?
![Page 85: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/85.jpg)
Walras’ Law Walras’sches Gesetz瓦尔拉斯法则
Walras’ Law is an identity; i.e. a statement that is true for any positive prices (p1,p2), whether these are equilibrium prices or not.
![Page 86: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/86.jpg)
Terms of demand
w: goods in initial endowment allocation x: goods in the final allocation x: gross demand (Bruttonachfrage) for the good x (x – w): net demand (Nettonachfrage) for the good x, excess demand (Ueberschussnachfrage) (xA + xB): aggregate demand (aggregierte Nachfrage)
![Page 87: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/87.jpg)
Walras’ Law Every consumer’s preferences are
well-behaved so, for any positive prices (p1,p2), each consumer spends all of his budget.
For consumer A (budget constraint):
For consumer B:p x p x p pA A A A1 1 2 2 1 1 2 2* *
p x p x p pB B B B1 1 2 2 1 1 2 2* *
![Page 88: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/88.jpg)
Walras’ Law
p x p x p pA A A A1 1 2 2 1 1 2 2* *
p x p x p pB B B B1 1 2 2 1 1 2 2* *
p x x p x x
p p
A B A B
A B B B1 1 1 2 2 2
1 1 1 2 2 2
( ) ( )
( ) ( ).
* * * *
Summing gives
![Page 89: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/89.jpg)
Walras’ Law
Rearranged,
p x x
p x x
A B A B
A B A B1 1 1 1 1
2 2 2 2 2 0
( )
( ) .
* *
* *
The first parenthesis can be seen as the excess demand for good1 and the second one as the excess demand for good2.
![Page 90: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/90.jpg)
Walras’ Law
.0
)xx(p
)xx(pB2
A2
B*2
A*22
B1
A1
B*1
A*11
This says that the summed marketvalue of excess demands is zero forany positive prices p1 and p2 -- this is Walras’ Law.
![Page 91: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/91.jpg)
Walras’ Law We often name z the excess demand
function and, because x is a demand function with p, we get
It stands for any p(p1, p2) > 0. It is the Walras’ law.
* *1 1 2 1 1 2 1 1 2 1 1
* *2 1 2 2 1 2 2 1 2 2 2
1 1 1 2 2 2 1 2
( , ) ( ( , ) ( , ) )
( , ) ( ( , ) ( , ) )
( , ) ( , ) 0.
A B A B
A B A B
z p p x p p x p p
z p p x p p x p p
thenp z p p p z p p
![Page 92: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/92.jpg)
Implications of Walras’ Law
0)xx(p
)xx(pB2
A2
B*2
A*22
B1
A1
B*1
A*11
Suppose the market for commodity Ais in equilibrium; that is,
.0xx B1
A1
B*1
A*1
Then
implies
.0xx B2
A2
B*2
A*2
![Page 93: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/93.jpg)
So one implication of Walras’ Law for a two-commodity exchange economy is that if one market is in equilibrium then the other market must also be in equilibrium.
In general, if there are k markets, then only k-1 prices are determined at equilibrium.
I.e., the general equilibrium determines only relative prices.
Implications of Walras’ Law
![Page 94: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/94.jpg)
Implications of Walras’ Law
What if, for some positive prices p1 andp2, there is an excess quantity suppliedof commodity 1? That is,
.0xx B1
A1
B*1
A*1
0)xx(p
)xx(pB2
A2
B*2
A*22
B1
A1
B*1
A*11
Then
implies
.0xx B2
A2
B*2
A*2
![Page 95: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/95.jpg)
Implications of Walras’ Law
So a second implication of Walras’ Lawfor a two-commodity exchange economyis that an excess supply in one marketimplies an excess demand in the othermarket.It also means that not any p(p1, p2) > 0 can ensure z1 = 0 and z2 = 0 at the same time, even if any p(p1, p2) > 0 can ensure p1z1+p2z2 =0
![Page 96: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/96.jpg)
Implications of Walras’ Law
Because the equilibrium prices are prices which lead demand for and supply of every good to be equal at the same time, the Walras’ law does not mean there must be at least a set of prices pE(pE
1, pE2) > 0
which could result in z1 = 0 and z2 = 0 simultaneously.
Therefore: We must find the equilibrium prices pE(pE
1, pE2) > 0 if it/they would exist.
![Page 97: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/97.jpg)
Relative Prices Walras’ law means there are only k-1
prices that can be determined independently in an economy with k goods. That means also, we can only get pi for good i that
pi = pi(pj) i=1,2,…,k, i≠j Only after pj is determined, can we get all
pi. pj is called a numeraire price. Good j is the
numeraire.
![Page 98: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/98.jpg)
Relative prices All prices except the numeraire price are prices
relative to the numeraire price. Making it as 1, all prices are relative to the numeraire.
That is: All prices are relative prices. There are no absolute prices.
Changing pj from being 1 to being 2, all other prices will be double. But the exchange relations between each pair of all kinds of goods remain the same.
In the economy with paper money, governments can multiply the numeraire price. We refer it to change in price level or in absolute price level.
![Page 99: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/99.jpg)
Solve for General Equilibrium
Individual optimization problem Xi
j=Xij (P1, P2, Mj), i=1, 2; j=A, B
Mj=Mj (P1, P2, j1, j
2)
Xij=Xi
j (P1, P2 ) Market clearing for market 1:
X1A (P1,P2)+ X1
B (P1,P2) = 1A + 1
B
Can solve for equilibrium P1/P2? Can solve for demand at equilibrium?
![Page 100: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/100.jpg)
Existence of Equilibrium
Require that the aggregate excess demand functions be a continuous function, which in turn require that– Each individual’s demand function be
continuous, or– Each consumer is small relative to the
market.The second requirement is just one of
conditions for perfectly competitive makerts. Therefore: Competitive markets will necessarily reach equilibriums.
![Page 101: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/101.jpg)
Existence of Equilibrium
Example: The endowment allocation Apple Orange (good 1) (good 2) A wa
1 wa2
B wb1 wb
2 (The whole example will come…)
![Page 102: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/102.jpg)
Trade in Competitive Markets Trading in competitive markets
achieves a particular Pareto-optimal allocation of the endowments.
This is an example of the First Fundamental Theorem of Welfare Economics.
![Page 103: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/103.jpg)
First Fundamental Theorem of Welfare Economics
Given that consumers’ preferences are well-behaved, trading in perfectly competitive markets implements a Pareto-optimal allocation of the economy’s endowment.
It means that competitive equilibrium will necessarily be Pareto efficient.
![Page 104: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/104.jpg)
The Equilibrium with Monopoly
Figure 30.5 in textbook.
It was taken off to reduce the size of this ppt.
![Page 105: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/105.jpg)
The Equilibrium with Monopoly
Figure 30.6 in textbook.
It was taken off to reduce the size of this ppt.
![Page 106: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/106.jpg)
Implicit Assumptions
No consumption externality (外部效应 ) Agents behave competitively Equilibrium exists
This theorem gives a general mechanism—the competitive market—to ensure Pareto efficiency or Pareto optimality.
![Page 107: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/107.jpg)
Market Socialism: The Debate
Lange vs. Hayek Socialism with economic planning
– State-ownership
– Government chooses prices to clear markets
Advantage of competitive markets
– Information
![Page 108: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/108.jpg)
Second Fundamental Theorem of Welfare Economics
The First Theorem is followed by a second that states that any Pareto-optimal allocation (i.e. any point on the contract curve) can be achieved by trading in competitive markets provided that endowments are first appropriately rearranged amongst the consumers.
![Page 109: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/109.jpg)
Given that consumers’ preferences are well-behaved, for any Pareto-optimal allocation there are prices and an allocation of the total endowment that makes the Pareto-optimal allocation implementable by trading in competitive markets.
That means any Pareto efficient or optimal allocation is the competitive equilibrium allocation.
Second Fundamental Theorem of Welfare Economics
![Page 110: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/110.jpg)
Second Fundamental Theorem
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
The contract curve
![Page 111: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/111.jpg)
Second Fundamental Theorem
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
A*2x B*
2x
A*1x
B*1x
![Page 112: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/112.jpg)
Second Fundamental Theorem
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
A*2x B*
2x
A*1x
B*1x
Implemented by competitivetrading from the endowment .
![Page 113: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/113.jpg)
Second Fundamental Theorem
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Can this allocation be implementedby competitive trading from ?
![Page 114: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/114.jpg)
Second Fundamental Theorem
2A
1A
xA2
xA1
OA
2B
1B
xB1
xB2
OB
Can this allocation be implementedby competitive trading from ? No.
![Page 115: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/115.jpg)
Second Fundamental TheoremxA2
xA1
OA
xB1
xB2
OB
But this allocation is implementedby competitive trading from .
A1
B2
B1
A2
![Page 116: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/116.jpg)
The Assumption about Convexity
![Page 117: Chapter Thirty Exchange Tausch 交换. Hu Jingbei’s declaration to copyright May 17, 2007 u This ppt-file may come from an American source which is not known](https://reader034.vdocument.in/reader034/viewer/2022051621/56649e6c5503460f94b6a6c6/html5/thumbnails/117.jpg)
Implications of the 2nd Theorem
Market equilibrium is distributionally neutral.
Redistribution can be carried out for endowments.
The market plays only the allocation role.