Paret for

1

valuation

) based -

preference (

absolute

) 2 (

valuation

) based -

arbitrage (

relative

) 1 (

valuation

security

5.

option

mkt

the enrich that

schemes

4.

. structures

mkt different

w.r.t.

CME

in comparison

) welfare (

untility

3.

PE and

structures mkt

e alternativ

2.

) PE (

efficiency

Pareto

and

) CME (

. equil mkt

e Competitiv

1.

: objective

Learning

mkt structure

welfare comparison

CME PE

1 2

33

n Informatio

Fixed under

Analysis m

Equilibriu

General

3 Ch

. t improvemen

Paret for

y possibilit

no mean t

doesn'

"

pei Fixed

"

mkt

issuing

no

problem

decision

structure

capital

no

supplies

securities

) exogenous (

fixed

: economy

exchange

pure

welfare

and

economy

exchange

Pure

.

 一

3

. welfare s

everyone'

improve

and

) patterns n

consumptio or

(

securities

of allocation

sharing -

risk

efficient

more

make

y potentiall may

s individual

, securities

new

of supplies

no even

, ) omorrow pattern t

n consumptio

of exchange

means

implicitly

and

( securities

of exchange

pure By

設 S = 2

Z · A = ( W_{1 ,} W₂ )

Z z z

Z z z

2 22

12

1 21

11









Pareto improved allocations of

Endowed allocation

二 . Competitive Market Equilibrium Model

vecter

I ) 1 S

( a is ) ,

, ,

( s

allocation

) w

, , w , w ( w

) z

, , z , z ( z

individual

th i of pattern

n consumptio

choice

R R

) w , c ( ) A z , c (

individual

. economy

the in exist

s individual

I , , 2 , 1 i

notations

) (

I 2

1

iS i2

i1 i

iJ i2

i1 i

S 1

i i

i i

i





































 一

5

patterns

and

n consumptio

ZA

of supplies

total

fixed

) W , C ( )

A z , c (

sccurities

and

n consumptio

endowment

of supplies

total

fixed

) Z , C ( )

z , c (

social

preference

) a z w

, c ( U )

A z , c ( V ) (

V

endowments

initial

) A z w

, c ( or

R R

) z , c ( attributes

individual

th i of belief

s

' individual

ties probabili

state

0 )

, , ,

(

I i

i i

I i

i i

S s

s i is

i is

is i

i i

i i

i i

i i

J 1

i i

iS i2

i1 i



















































=

one least

at exists

there

risk

social

is there

If : 2 question

? riskless

are securities

all

risk

social

No : 1 question

. risk

) aggregate or

( social

is there

that

say we , W W

t and

s some least

at exist

there

If

. tomorrow

states

across

GNP

as regarded

be can

W

C c

c

W w

w

C c

c

Z z z

) . cond

cleaning

mkts (

condition

on conservati

C c

, Z z

, I

A z w

: )

A G(

A

w.r.t set

s allocation

feasible

t s

I

i i I

i i I

i i I

i i

I

i i I

i i I

i i I

i i

I i

i I

i

i i

i i























 





















      





 

 

 

 





 

 

 

 





7

（二） Competitive Market Equilibrium ( CME )

.

CME affect

will

} ) z , c ( {

allocation

endowments

also but

. ) Z , C ( total

social

only Not

: Note

: endogenous

: exogeneous

) Z , C ( ) z , c (

) 2 (

and

, I i SP s ' individual

th i the maximizes

) z , c ( ) 1 (

If . equil

exchange

pure

a is }

) z , c ( { allocation

and

P . }

) z , c ( {

endowments

and

} ) ( V { beliefs /

s preference

MISC

with

individual

I of set

a and

A structure mkt

given

economy

exchange

pure

in CME :

3.1 definition

I i i

i

I i

i i i i

I i i

I i i i

i

I i i





















CME

of definition

e alternativ

: definition

) 3.6c (

)

Z , C ( ) z , c (

) ii (

3.6b) (

I

i

P z c

P z c

3.6a) (

I

i and J

j P

) c

A z , c ( V

) z

A z , c ( V

) i (

I i

i i

i i i

i

j i

i i i

j i i

i i























 

 



9

 

Law

s Walra'

. too , hold must

one last

the then

, hold

) 3.6c (

and ) 3.6b (

in equations J

I

of set

any if is That

. redundent

is ) 3.6c (

and

) 3.6b (

of One

number

I ) 1 J ( : )

Z , C (

number

J with

P :

variables

endogenous

? nce inconsiste

equations

) 1 J ( ) 1 I ( , totally

equations

1 J has ) 3.6c (

equations

I has

) 3.6b (

equations J

I has ) 3.6a (

) 3.6b (

and

) 3.6a (

3.1 def.

in ) i ( then ,

i MISC

is ) ( V If : Note

I i i

i i











 



















     

   





) w , c (

) ii (

and

, I i , A

of span

the from

derived

being

B matrix

the

with

CCCP

s ' individual

th i the maximizes

) i (

if , CME

exchange

pure

a is

)

w , c (

allocation

and R

vector

price implicit

An .

)

w , c ( and

) ( V and

A given

CCCP

of terms

in CME

Exchange

Pure

: 3.2 definition

i I

i

i i

I i i

I i i

i

I i i

I i i

I i i i





























 

 



11

 

     





statement

this about

careful

be

must

We

. principle

in , 3.2 . def CME

to ent

correspond

one -

to - one is 3.1 . def in CME

then

, hold

) 3 ( ~ ) 1 ( If

3.2 . def )

w , c ( , R

)

z , c ( , P 3.1

.

def  _{i i iI i i iI} 

R A

P ) 2 (

I i w A

z ) 1

( ^{i i}











S rank(B) rank(A)

and

0 B

A ) 3

( J S S K







 



(

I , , 3 , 2 i

v

) (

V

) Z , C ( ) z , c ( ,

I i

w

: A)

G(

s.t

only

not

) ( V max

) v , A ( g

solves it

if w.r.t A

CPE

a is

CPE

: 3.3 definition

i i

i

I i

i i

i

1 1

 











    

























A z_i

13

. inquality strict

one least at

with

and

I i ) ( V ) ( V

G(A)

no exists

there

if w.r.t A

CPE

a is

: c - 3.3 def.

i k

) (

V v

) ( V

G(A)

s.t.

) ( V max

problems

I , , 2 , 1 i following

solves it

if w.r.t A

CPE

a is

: b - 3.3 def.

I , , 3 , 2 i

v )

( V

G(A)

s.t.

) ( V max

) v , A g(

solves it

if w.r.t A

CPE

a is

: a - 3.3 def.

i i

i i

k k

k k

k

1 1

i i

i

1 1













































































Four alternations of CPE w.r.t. A above are equivalent ( c.f. appendix )

decreasing

(1) : proof

. V in concave

strictly

and V

in decreasing

is

)

V

,

A

(

g

§.

15

sets

factors

G(A) G

(A) CME

w.r.t. A ( C , Z )

 ^V

⁽

⁾ 

 ( c

, z

) 

< proposition 3.1> The First Fundamental Theorem of Welfare Economics

: Proof

A w.r.t.

CPE

a is

A w.r.t.

C.E.

a is If

  

17

< proposition 3.2> The Second Fundamental Theorem of Welfare Economics

  ^{ }

 

 

I

i and J

j u

u V

V Z

solve must

, problem

) V , A ( g of F.O.Cs

By

) z

, c ( V

-

) Z -

Z ( u )

c (

) z , c ( V

) Z , C , V , A

; , u , u , z , c ( L Define

: Proof

) z , (c )

z , c ( or

when

A w.r.t.

CPE

a is A w.r.t.

C.E.

a is If

0

j i

ij i

I

2 i

i i

i i

i

ij j

J

1 j

j i

0 i

i i

0

I i

i i I

i









 

 

































i

i i

i i

C

A V

C u















)

! yourself

by Derive (

   

  ^{ }

   

 































and

A w.r.t.

C.E

a is

, ,

P with

associates

means

(3) ~ (1)

(3)

Z , C z

, c

and

(2)

I

i P

z , c P z c

I i

z

, c z , c But

(1)

I i

and J

j P

C

) (

V

Z )

( V

A w.r.t.

C.E

in vector

prices

securities

be to ,

, ,

P ,

, P , P P

put

0 J1 0

1 0

J1 0

2 0

1

i

i i

i i

i i

i i i

i

j i

i

j i i

J 2

1































 

 



























i i

19

三﹑ Alternative Market Structure and Economic

Efficiency — Constrained v.s Full Pareto Efficiency

 

 

     

 



^{A , V}

^g

^{A , V}

^{g ( A , V ) g ( A , V)}

^{, OTBE .}

g

if , A than efficient

) more (

loss

no is A

that

say

We .

V , A g

affect

, OTBE

, structure mkt

different

how

te investinga

to want

we , section

this

In

W , C or

Z , C and

V V

, A

V , A g

utility

maximizing

s planner' affect

to Factors

I i i

i

 



 







