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116

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: (02)

2939-3091

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51548;

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: (02) 2939-0074; E-mail: klueng@nccu.edu.tw

b o / ( = O 3

2005

5

21

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(2)

! !

Kaplow

"

1992, AER

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,

c > ?

@ A - h i ' B | W % . C D % / * t E

,

F k ' G H W % . * % / I i

,

& ' J 0 * K * B | 1 2 3 4

Rothschild and Stiglitz

"

1976

# * %

/ 5 ) > ? ( 6 @ A h L 7 % / M N 8 9 W % . * F O P : Q w "

three-stage game

#

,

; < c > ? @ A - h i * J 0 = > 1 3 ? @ R A S +

,

:

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,

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Rothschild and Stiglitz

"

1976

# ( 3 ;

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:

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;

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;

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l ? m d k ] n 1

(3)

1.

1 2

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partial insurance

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tax benefit

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S 3 I A - .

,

9 : { y B 9 - .

,

Bittker

"

1967

#

Musgrave

"

1967

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? & : 9 S T "

ability to pay

#

,

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;

1

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,

Arrow

"

1963

#

Kaplow

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1991a, 1991b, 1992

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, Kaplow

"

1992

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& " D

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1 $ ! @ ! 2 $ ? 6 k : 1 & @ F "

,

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, Stiglitz

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1988, pp. 526–527

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:

1

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income concept

#

, Bittker

.

Haig-Simons

q

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comprehensive income tax base

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Musgrave

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Bittker

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Haig-Simons

&

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B A , J $ 5 R D b l J K @ !

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, Stiglitz

$ X @ & <

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;

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, Stiglitz

"

1988

# ' J $ ' @ l c m w - .

,

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, Kaplow

"

1992

# 1 , J $ % & @ $ f @ } ~ d t r s

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,

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2 _Kaplow

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first best

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q _ ! "

full insurance

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5 a &

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,

% & 4 I > 3 u I # 1 , , J $ D 7 !

F F z & 1

Kaplow

@ f " ] ! R T + , E 1 @ U V W - . "

adverse

selection problem

#

,

3

' ~

Rothschild and Stiglitz

"

1976

# @ f ) * b

J K ! 7 8 d | ! @ P " B - "

three-stage game

#

,

~ g

2

d ) ) " Q * +

,

5 i e , w | Z 8 b

3 Akerlof

"

1970

# v P

:

D W -

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3 X & Y Z

,

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:

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(5)

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:

k b

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Rothschild and Stiglitz

"

1976

# b & ~ + % 1 @ @ )

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;

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Kaplow

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1 = 4 "

graduated tax system

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e

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4

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(

Rothschild and Stiglitz

"

1976

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1992

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, Kaplow

"

1992

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a

Rothschild and Stiglitz

"

1976

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Rothschild and Stiglitz

"

1976

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Nash-type

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1 @ D ) 4

,

!

(6)

Spence

"

1978

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non-Nash-type

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@ E 1

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, Crocker and Snow

"

1985

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e q r 5 ! % 1 @ E 1 ! G 0 @

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-

Crocker and Snow

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1985

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& = & @ ! " ' $ < ! ' , J $ 5 , " % @ ! " !

4 , Dahlby

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1981

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Rothschild and Stiglitz

"

1976

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com-pulsory insurance

# , 5 C $ # ¨ 6 i j @ "

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4 / ! p U ; b 6 !

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o p # 7 F p @ ! ® "

cross-sub-sidy

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Eckstein et al.

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1985

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Rothschild and Stiglitz

"

1976

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Y A / } 9 ! , 5 C $ # ¨

6 i j @ " ! / } 9 P d % E 7 C t ) q !

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m @ J K 5 d o p ! ® @ q r . / E 7 C # # p @ 3 u

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Huang et al.

"

2004

#

|

Li et al.

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2005

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,

+ ~

Rothschild and Stiglitz

"

1976

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f

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certainty

equivalent

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Taylor expansion

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5 d

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, Huang et al.

"

2004

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quadratic utility

func-tion

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Huang et al.

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2004

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Li et al.

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2005

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(7)

M F = ! / . g I @ ) " Á

Varian, 1992, p. 189

# ! a r s c

? ]

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; @ @ | b ? m @ ; M F = ! / $ " 0 I #

p Â Ã F @ \ I 7 # e

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d ; ' ! % ¨ 6 . @ > " & i @ # D ,

; Li et al.

"

2005

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Kaplow

"

1992

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:

k b

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Kaplow

"

1992

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2. Kaplow

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Kaplow

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1992

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o 7 D C D & f 9 6 a 2 2

Kaplow

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p,

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7

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(w, w − d)

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α

₁

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premium

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payout

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d + α

2 ),

k "

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indemnity

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{w−α

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α

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t

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Stiglitz

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k "

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t(d − ˆα)

D 1 J K ! 4 = 0 @ !

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{ 5 R D 1 J K ! 4 0 ! @ ! ! d

{α

1 (p, t, τ), α

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§ A 1 C

p

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risk neutral

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:

π(p, t, τ ) = (1 − p)α

1 (p, t, τ) − pα

2 (p, t, τ).

(1)

F F 1 # _ 2 & Q b " f ! p @ & ) 4

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t

1 , α

t

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8

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q

(1)

r D >

;

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@ 2

:

max

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1 ,α

2 (1 − p)U(w

t

NA

) + pU(w

t

A

),

s

.t.

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1 − pα

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(2)

7

/ 3

w > d,

, 2 q Y 3 4 E F e : % Ô = M c b

8

H

t

I O D 3 4 X Y H [ \ J K b

9 Rothschild and Stiglitz

"

1976

# Z d L 1 4 5 .

Cournot-Nash

H + 1

,

z ] ) > [ \ O w ? Y e < Õ @ @ 9 M [ \ O w ? Y I ^ _ b U M 4 !

Gibbons (1992,

(9)

k "

,

w

NA

t

= w − α

t

₁

− τ,

§ , A P R 5 e / l F

;

w

t

A

=

w − d + α

t

2 − τ + t(d − α

t

1 − α

t

2 ),

§ A P h e / l F ! P B

,

1 y ! r e b " $ = c "

:

U

(w

t

_NA

)

U

(w

t

_A

)

=

1 − p − t

1 − p

.

(3)

1 2

(2)

|

(3)

r e " < q \ Ö

,

T 1 0 @ 9 7 $ % ® D

C ≡ {α

t

1 , α

t

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(3)

r 5 O

,

t > 0

h

,

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t

NA

> w

t

A

,

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(1 − t)(d − ˆα

t

_),

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6 0 # ! $ % D b } ~ ! $ % ! | - 1 G 1 , J $ 4

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,

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,

? # 4 I > @ 6 7 !

11

3.

O P × E

Kaplow

"

1992

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,

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,

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w,

: R w 7

U (w), U

_{> 0, U}

_{< 0}

_a -9 9 :

,

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,

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d

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L G

L,

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p

H

> p

L

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< M G 9 G `

10 Kaplow

w

> ?

,

z ] ) c 9 -

t

_ 5 ^ _

,

R

t = 0

9 ! X a . 5 3 4 X Y

,

c >

, Kaplow

0 < t < 1

9 ! X a . 5 3 4 X Y H r I 5 x

,

t = 1

9 . Ø e r Ø @ "

tax credit

#

,

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,

B Z q D 3 4 6

,

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,

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Ù # X a E / b \

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M u M "

deductions and

credits

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b L M N 9 z Ú A

,

6 V 5

,

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,

, @

100

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100

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,

t = 0

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,

t = 1

M 9 X a T Z [ \ W - b

11

. U 9 : Û O r

Kaplow

"

1992

# Ü Ý ! I ( B h ;

,

M z \ Þ _ "

risk premium

# ~ P =

,

(1 − p)U(w − α

t

1 − τ) + pU[w − d + α

t

2 − τ + t(d − α

t

1 − α

t

2 )]

O r .

U (w − pd − ρ

t

),

9

,

α

t

₁

u

α

t

₂

I O [ 0 u ß 0 1 9

,

ρ

t

. z \ Þ _

;

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K F @

,

\ q M " % 3 4 X Y H r 2 q w 1 _ ` @ b

(10)

| E 9 9 ; q = G 9 G ` M 7 M a

2 2 > ? @

,

y u 7 9 A j + > à r

,

1

,

$ 9 +

,

$ W s 9 n : q

t

6

,

] b s : 4 m

,

C ] V W - 4 m

,

b

9 à r ^

Rothschild and Stiglitz

"

1976

# 9 P G

,

U b m * 9 C D &

f T ' 7

SW

0 ;

C ] V W 4 m

,

$ > ` q á " + G ` 9 A * 6

,

] V W I 2 9 s p :

τ

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,

U b 9 C D & f T ' 7

SW

t

_a w

,

$ v +

,

s

(t, τ),

` q á c : `

,

` 9 Q ) i

:

9 7 u "

separating contracts

#

,

# \ 5 m M G 7 N

C

i

_{≡ {α}

i

1 , α

i

2 }, i = L, H,

< 9 7 O B "

pooling contracts

#

,

# m M G 7 N 9 i

(α

1 , α

2 ),

{

,

$ j +

,

s

(t, τ)

" + G ` 6

,

G ` b s : L G `

,

" + V W C i a

3.1

e â ã ä å æ $ # w à r C R #

,

f ( ' "

backward induction

#

,

1 G ` 9 ç

,

N D ` q á 9 ç

,

" + ] * 4 m a 1

,

j + x : M 9 G ` b a

3.1.1

è é ê ë ì í î ï ð s ]

(t, τ)

" + `

{α

i

1 , α

i

2 }, i = L, H

a

12

,

F 1 y 1

, J $ 4 ! @ ! = 3 u "

reservation utility level

# 4

:

13 EU

it

0 = p

i

· U(w

A

it

0 ) + (1 − p

i

) · U(w

it

NA

0 ),

i = L, H.

(4)

k "

,

! /

t

0

§ !

i

1 , J $ 4 , U ! h @ D g

,

w

it

0 A

=

w − d − τ + t · d, w

it

0 NA

= w − τ

{ ~ § !

i

1 l 4 A P d | , A P @ l F ! & ) ! 7 8 Y Z ! $ %

{α

i

₁

, α

i

₂

}, i = L, H

Z ! V W

,

h ! U ! @ 3 u 4 &

:

12

D o /

t

. d _ W

,

τ

¹ ) U Y _ W b

13

9 5 ñ & )

,

3 4 X Y I ^ _ K [ q [ 9 w 1 _ `

,

D : % 3 4 X Y r +

,

K [ q [ 9 w 1 _ ` > 3

p

i

· U(w − d) + (1 − p

i

) · U(w), i = L, H

b

(11)

EU

it

= p

iU (w

_A

it

) + (1 − p

i

)U(w

it

NA

),

i = L, H.

(5)

k "

,

! /

t

§ , J $

,

w

it

A

= w−d+α

i

2 −τ +t(d− ˆα

i

), w

NA

it

= w−α

i

1 −τ

{ ~ § !

i

1 U ! / A P d | , A P @ / l F ! Q d

,

! ! / @ G ] 3 u 7 G k ! = 3 u h

,

! T I | !

,

] e

,

! V W U ! Q @ L z c " 4

:

EU

it

≥ EU

it

0 _,

_{i = L, H.}

₍₆₎

& ! T v e D | ° r "

participant constraints

# !

,

& d

w

NA

D ò ó

,

wA

D ó

,

{ ! @ $ 5 " e ¦ " C 4

:

dw

_A

i

dw

_NA

i

V

i

=constant

= −

(1 − pi)

p

i

U

(w

i

_NA

)

U

(w

i

_A

)

,

i = H, L.

(7)

k "

,

(1 − p

H

)/p

H

< (1 − pL

)/p

L

§ 0 # F p M 7 F p @ $ 5 " t 0 b

,

& $ 5 " @ C M B

p

i

? . ! ] e

,

# 7 g F " f @ ! @ $ 5 " v Q b ! "

single-crossing

# @ ) ! ! " 1 G e F " f @ ! M A P 1 d | , A P 1 @ l F D g @ Y I e

,

M 7 F p ? ]

,

# F p A P 1 @ H I # E

,

- # < R A P 1 h @ l F D g ! k i

,

1 y * : " B ! 7 8 * M @ - . !

3.2

e g h ô õ _ ö $ ' # V ) V W 9 C R ` . >

,

7 @ ) 9 A E = ? ?

,

" 6 i 1 # F r 9 G H a

3.2.1

è ÷ ø ù ú û ì î ü ý þ $ F r 9 G H 6

,

V ` q á V G ` M 9 G

,

v b D I - 9 G 9 G ` M

,

c : - 9 9 ` a 2 2 > 9 A > 9

i (i = H, L),

% 9 ; q 7

pi

a C "

C

i

∗

≡

{α

i

∗

1 , α

i

∗

2 }, i = H, L

C R 9

,

C

i

∗

7 J K Q

(8)

9 #

:

(12)

E

A

B

w

A

w

NA

U(CE

H*

₎

U(CE

L*

₎

w - d + td -œ

1 - p

L

- t

p

L

w - œ

C

L*

C

H*

-1 - p

H

- t

p

H

-45

ÿ

:

^ _ `

1

: j

1

k

max

α

i

1 ,α

i

2 (1 − pi)U(w

_NA

i

∗

) + piU (w

_A

i

∗

),

s

.t.

(1 − p

i

)α

i

1 − p

iα

i

2 = 0.

(8)

2 2 `

,

w

i

∗

A

,

w

i

NA

∗

9 3 N <

,

\ < $ F r 6 G ` M

i

$ ` { | E s 7 " + / ) | E s 7 9 : { u a b 9 9 + , L 6

:

U

(w

i

_NA

∗

)

U

(w

_A

i

∗

)

=

1 − p

_i

− t

1 − pi

,

(9)

8

(8)

L

(9)

Q l # # n C R

,

{ 8 M 9 C R \ U 7

C

H

∗

L

C

L

∗

a 2 2 $ X M

,

2 : q

t

M ^ h i K

,

G ` M 8 - s `

,

b 1 v $ $ 6

,

G ` M L l M ` j m 9 ; D y - q ) 1 1 . `

,

k n p v @ X l M ` ; 4 . q . n : p

,

; b : p L : q r E

,

v b ` M 9 : q 8 D G ` M ` 9 ^

(13)

v a 8 b 9 : q 9 D s 7

¯t

i

,

i = L, H

a ` 7 @ b 9 : q 9 D

(¯t

i

),

$ ` q á \ f f 7 P 9 > c 6

,

8

EU

it

_m

_α

i

2

) w

,

$

α

i

2 = 0

,

y s 6

:

dEU

it

dα

i

2 α

i

2 =0

=

pi(1 − pi

− t)

1 − p

_i

U

_(w

it

0 A

) − piU

(w

NA

it

0 ),

i = L, H.

(10)

2 3 Q 7 P # % : q 9 D 6

:

14 ¯t

i

= (1 − p

i

)

1 −

U

_(w

it

0 NA

)

U

(w

it

0 A

)

,

i = L, H.

(11)

d ! @ ~ g

,

F 5 = & d 4 @ 2 t

:

! "

1

1 # _ 2 & ! $ % D h q 7 @ $ % 4

,

F p

i

k * M @ C # G ² v G

¯t

i

h

, ¯

ti

= (1 − pi){1 − [U

_(w

it

0 NA

)]/[U

(w

it

A

0 )]}, i = L, H,

{ # F p

i

T I | ! !

,

(11)

r 5 O

, ¯

tH

< ¯tL

! ! "

2 ¯

tH

< ¯tL

! # $

:

M

(11)

r > ; ' ~ 1

¯t

i

M

p

i

@ %

,

5 0 O

d¯t

i

/dp

i

= −(C/D)

< 0,

k "

,

C = 1 −

U

_(w

it

0 NA

)

U

(w

it

0 A

)

> 0,

D = 1 − (1 − pi)

U

(w

it

NA

0 )U

(w

A

it

0 ) · d

[U

_(w

it

0 A

)]

2 > 0,

0 ' !

14 (10)

\ 9 . `

,

, I O K [ q 4 u [ \ e w 1 _ ` P 3 ¾

,

- d D ] 8 \ . ¾ x 9 , . K [ q 4 u [ \ x r ; < 9 b

(14)

F F 5 O

,

A 1 H C | k C P @ o § G # E x

,

5 q # F p C P @ o § G # 7 ! b 2 t @ ³ ´ w 1 G

,

# F p - D k A P 1 @ H I # E

,

0 O J K ! @ H I # E

,

- k U v ! @ H I # z # # " ~ @ $ # µ #

,

d # F p C P C @ o § G T # 7 F p D 7 ! F F d ! @ 2 t 5 O

,

M B C @ !

,

v ! R T " @ ! " f 5 T , e ! C M # 7 "

t ≤ ¯tH

# h

,

v ! R T " T e h E 1 # 7 g " f @ !

;

m ?

,

C h G # 7 g " f @ C o § G e w h

,

5 q

, ¯

tH

< t < ¯tL

,

v ! R T ! T E 1 7 F p

;

C M # #

(t ≥ ¯t

L

)

h

,

v ! R T T ) E 1

,

! R T T % 4 , J $ Y Z @ J K ! ! ! "

3

1 # _ & # _ 2 @ ! R T 4

,

! $ % - C @ # 7 5 = ~ D P l % 1

:

t ≤ ¯t

H

,

v ! R T " T e h E 1 # 7 g " f @ !

;

¯t

H

< t < ¯tL

,

v ! R T ! T E 1 7 F p

;

t ≥ ¯tL

,

v ! R T T ) E 1

,

! R T T % 4 , $ Y Z @ J K ! ! F F d ! @ 2 t 5 O

:

, J $ @ h ] T s ) i C v @ ! R T @ % 1

,

# @ @

,

1 , , J $ 4 @ v ! R T "

,

# F p M 7 F p # , U v ! @ F

,

m ?

,

1 , J $ 4 @ v ! R T "

,

G # F p U v ! @ H I # z # #

,

- M 7 F p ? ]

,

k U v ! @ F # 7

,

$ - T & 6 v ! R T E 1 7 F p @ r ¶ !

3.2.2

& ' ( ) * + , - . / 0 1 ! R T E 1 U V W @ - . h

,

b ? ? ]

,

% 1 @ ! $ % 5 ~ D d 4 g

l

:

b D ~ + % 1 "

separating equilibrium

#

,

b { D N © % 1 "

pooling

equili-brium

# ! G z & " # 7 F " f @ ! @ $ 5 " ¡ m v Q b !

@ )

,

(

Rothschild and Stiglitz

"

1976

# @ ~ g

,

! $ % & E 1

,

$ m

N © % 1

,

5 a &

,

" % 1 E 1

,

{ $ D ~ + % 1 ! - & ! 7 8 Y Z N © $ %

,

1 ! @ $ 5 " v Q b ! ) @ 4

,

{ k ! 7 8 5 1 , , # F p t V @ 4

,

5 m c : 9 2 `

(15)

E

B

w

A

w

NA

w

w - d

U(CE

H0

)

U(CE

L0

)

-

1 - p

_p

H

-

1 - p

_p

L

C

H0

C

L0

45

j

2

k

,

b 8 O n 1 g 9 O B C R ^ 3 :

,

v ; O B 8 - | $ a V A v P

,

{ 8 5 m u C R 9 m } . a

15

3.2.3

& 4 5 6 7 0 1 - 8 9 Q d

,

6

1

5 L A # F I , N - : ; # 7 F p ? 6 0 ! 7 8 A r / @ p G > =

,

m 1 z & 4

{C

H

∗

, C

L

∗

}

' % 1 $ % ! " % 1 $ % ~ 5 2

?

d 4 T 1 2 b - . ! F F C @ # 7 I > ? ! U ! @ F

,

- d 4 T C ~ D «

t ≤ ¯t

H

;

¬

¯t

H

< t < ¯t

L

;

·

t ≥ ¯t

L

P l - e ! F F ,

,

- * b l

,

C M # 7 h

,

# 7 F p + , 5 C U v

!

,

h ! 7 8 * M @ - .

,

1 z ) ! |

Rothschild and Stiglitz

"

1976

#

b & %

,

k ! 4

:

! "

4

C 6 0 # 7 F p + F U v ! h

,

& d

{C

Ht

_{, C}

Lt

_}

§ # ~ + % 1 $ %

,

{

C

Ht

= C

H

∗

,

C

Lt

D s p

C

Ht

@ $ 5 " |

π

L

_{= 0}

@ !

;

&

w

Ht

NA

< w

Lt

NA

,

w

A

Ht

> w

Lt

A

!

15

. U " Q e p

,

8 H o / 3 d 1 9 e D b

(16)

F F ~ + $ % |

Rothschild and Stiglitz

"

1976

# b & @ % e ! 1 G

,

1 ~ + $ % 4

,

# F p @ $ % | # _ 2 4 @ $ % b &

,

1 h q 7 @ | { 4 2 E w k p G 3 u

;

m ? 7 F p @ $ % { I O k 7 ! = & # ! " @ | - 1 G # F p , N - V W M 7 F p ) 4 @ $ %

C

Lt

_,

- 1 ~ + % 1 @ $ % 4

,

, 9 ! 7 8 @ > = $ D > " G ! R T D # _ R T #

,

! 7 8 Y Z @ $ % I t 5 C ¹ # F p @ 3 u $ O 9 E ! 1 4

,

# F p @ $ % T | # _ 2 4 @ % 1 $ % = G b &

,

q

C

Ht

= C

H

∗

! m ?

,

G 7 F p , 5 C V W M # F p ) 4 @ $ %

,

-

C

Lt

_{≡ {α}

Lt

1 , α

Lt

2 }

@ 2 $ ? , d 4 @ c "

:

,

C

Lt

_$ 6 0 ! 7 8 @ p G > = D >

,

k i

,

C

Lt

_$ 6 0

(w

Lt

NA

, w

A

Lt

)

} G # F p s p

(w

Ht

NA

, w

A

Ht

)

e $ 5 " @ " ! ` k 4 q

,

d ? , N - ° r ! # F p : ; # 7 F p ! 9 /

,

&

(w

_NA

Lt

, w

Lt

_A

)

} G # F p s p

(w

Ht

_NA

, w

Ht

_A

)

e $ 5 " @ 4 q

,

{ F Q < O b ! $ % C ( e h ! 7 8 | ! p Ó I ! -

,

C

Lt

_{≡ {α}

Lt

1 , α

Lt

2 }

5 4 k g c q \ r " < 1 2 ? 0

:

p

H

U (w

Ht

A

) + (1 − p

H

)U(w

Ht

NA

) = p

H

U (w

Lt

A

) + (1 − p

H

)U(w

Lt

NA

),

(12)

(1 − pL)α

L

1 − pLα

L

2 = 0.

(13)

,

$ 5 " e ) 5 O

,

$ 5 " v Q ! @ )

,

# F p -D k A P 1 @ H I # E

,

d # < R A P 1 h @ l F D g

,

- 1 ~ + % 1 @ $ % 4

,

w

_NA

Ht

< w

_NA

Lt

,

w

_A

Ht

> w

_A

Lt

! ? |

Rothschild and Stiglitz

"

1976

#

b & @ 4 5 1 G

,

1 z & @ ~ + $ % 4

,

# F p @ ! $ % D } ~ !

,

m

?

Rothschild and Stiglitz

"

1976

# @ ~ + $ % 4

,

# F p @ ! $ % D _ !

! I E 1 4 5 @ | - 1 G

,

, J $ I ! @ 2 $

,

- I 6 0 # F p @ ! $ % # D } ~ !

,

? _ ! ! F F 2 t

4

5 O

,

0 C 6 0 # 7 F p + F U v ! h

,

, # F p 5 = & # _ 2 4 @ ! $ %

,

0 G 7 F p @ ! $ % { I O k 7

,

d & Y + 9 # _ 2 4 @ ! $ % ! G 0 @

,

1 ] , J $ e

,

1 $ % 4 ! @ | ° r $ m I # <

,

m ?

,

1 , J $ 4

,

p # @ C 4 T 5 C 6 0 ! F | !

,

#

,

G ` M 9 L Q _

(17)

E

A

B

w

A

w

NA

45 U(CE

Ht

₎

U(CE

Lt

₎

w - d + td -œ

1 - p

L

- t

p

L

w - œ

C

Lt

C

Ht

-1 - p

H

- t

p

H

-j

3

k Q ? D l a V = s =

1

N

,

$ 3 @ 9 G H 6

,

q R

t ≤ ¯t

H

,

M # D s & l M `

;

,

b < V = s =

2

N

,

$

t ≤ ¯t

H

9 G H 6

, ¯

t

H

≤ ¯t

L

,

v b

t ≤ ¯t

L

a : ` _ { | $ V W i j 9 G H 6

,

9 ` D ] ^ > ?

,

v b

t ≤ ¯t

L

: D ` 9 R , L ; = > , L

,

" b <

t ≤ ¯t

L

) & - s & `

,

$ { j 9 w @ A

2

`

,

i 8 i X b i G H - D | E

,

! : i

,

$

t ≤ ¯t

H

9 G H 6

,

C C R | $

,

7

{C

H

∗

, C

Lt

}

a 2 2 w

,

> v i G H

, ¯

t

H

< t < ¯t

L

a 2 : q d b v 3 4 D . g

,

$ X M

,

$ ! " q U " M 7 %

EA,

7 %

EB

#

,

= : q

t ≥ ¯t

H

9 G H 6

,

) ) l M ` 9 ^ v " X

4

# a ;

,

V 9 - F r

,

7 @ B G M O 7 7 N 9 ` A

,

` 9 c : C o ^ v 8 3 9 Q _ Q a - `

,

V X

4

N

,

m ) C o ! " q U = ) s 9 ; ? " h X

4

` %

EL

3 9 r C 9 . #

,

M ^ D ) s g i ` A " b { 8 D ` q á 9 D #

,

v b _ { 3 ' | $ 9 i O 7 c : 9 `

,

9 ` q á f - 7 | = C o M 9 ^ v 8 3 Q _ Q " X

4

#

,

v b l M ` _ { ' c : 9 i ) D g 9 ! " q U . ` a S

(18)

E

B

A

w

A

w

NA

U(CE

Lt

₎

U(CE

Ht

₎

w - d + td -œ

1 - p

L

- t

p

L

w - œ

L

-1 - p

H

- t

p

H

-45

j

4

k E F G N H I ? .

,

q R : q 2 ` b 9 3 4 D

,

l M 9 ` _ { 8 - w | $ a v b j i G H 8 : A - o | 9 i j

,

y T 8 L v i G H 9 #

,

l M 9 ` _ { 8 - | $ a 2 2 V " 3 9 x N

,

$ V ) V W 9 G H 6

,

6 & 9 u C R D : q 9 M 7 v i

,

2

t < ¯t

H

,

C l M ` _ { 9 C R | $

,

7

{C

H

∗

, C

Lt

};

2

t ≥ ¯t

H

,

l M ` _ { 9 C R 8 - | $ a J K

1

2 : q M 9 3 4 D

,

C l M ` _ { 9 C R | $

,

7

{C

H

∗

, C

Lt

};

2 : q M M 9 3 4 D

,

l M ` _ { 9 C R 8 - | $ a 2 2 & I b = j

,

" 6 9 } T 8 < t $

t < ¯t

H

9 G H

,

b l M ` _ { 8 9 | $ M a b 7

,

7 @ L # ]

(t, τ)

m G ` M G ` ' 7 9 U V

,

" 6 i

t,

" +

τ

m

α

Ht

1 , α

Ht

2 , α

Lt

1

L

α

₂

Lt

9 E = H x y s a

3.2.4

è M N O P Q 2 M G 9 G ` M ^ | $ l M 9 ` _ {

,

V " 3 x N

,

$ C

(19)

R 6

,

C

Ht

_{= C}

H

∗

7

(8)

L

(9)

Q . l #

,

C

Lt

₇

₍₁₂₎

_L

₍₁₃₎

Q . l # a = - < :

α

Ht

1 , α

Ht

2 ,

? :

α

Lt

1 , α

Lt

2

^ :

t, τ

9 R w

,

v b y q 8 \ m

t

" +

τ

. E = H x y s a D n _ s 9 :

,

t

9 U V u 7 9 i , : s

,

;

τ

9 U V u 7 9 i n : s a 2 2 m

(8)

L

(9)

Q r n

α

Ht

1 , α

Ht

2

. E = H x y s

:

16 ∂α

Ht

2 ∂t

= −

(1 − p

H

)[(1 − p

H

− t)(d − ˆα

Ht

)U

(w

Ht

A

) − U

(w

Ht

A

)]

(1 − p

H

− t)

2 U

(w

A

Ht

) + p

H

(1 − p

H

)U

(w

Ht

NA

)

< 0, (14)

∂α

Ht

1 ∂t

=

pH

(1 − p

H

)

∂α

Ht

2 ∂t

< 0,

(15)

∂α

Ht

2 ∂τ

=

(1 − pH

)

2 _U

_(w

Ht

NA

)[RA(w

Ht

NA

) − RA(w

A

Ht

)]

(1 − pH

− t)

2 _U

_(w

Ht

A

) + pH

(1 − pH

)U

(w

Ht

NA

)

> 0,

(16)

∂α

Ht

1 ∂τ

=

p

H

(1 − p

H

)

∂α

Ht

2 ∂τ

> 0.

(17)

k "

,

R

A

(·)

§ ; M @ F = ! / "

absolute risk aversion index

#

,

; M @ F = ! / D l F @ $ ; h

,

17 ₍₁₆₎

|

(17)

g r @ < D D 3

(

.

w

_A

Ht

<

w

_NA

Ht

),

§ 0 X Y @ 0 " 6 0 # F p @ ! º 1 . / ! k ³ ´ w 1 G

,

X Y 6 0 ! p @ 0 $ f

,

F @ C @ C 4

,

- M ! @ º 1 I . /

;

?

(14)

|

(15)

g r @ < D D / § 0 Z " 6 0 # F p @ ! º 1 $ f ! k ³ ´ w { 0 C Y # h

,

! | v ! @ H I # z T M e . /

,

18

- T 6 7 M ! @ º 1 ! G , J $ e h g \ "

,

- k 0 E " @ 3 / q . ' d !

,

T

(8)

|

(9)

g r 1 0 e " < 2

,

]

(12)

|

(13)

g r ' 1 k x # S g ~ g ! "

:

16

J K

,

D 9 M e R 1 H

,

# a 1 e 9 [ \ J K > 3 X & H 1 9 e

,

9 F @ \ F e p 3 | u d H )

,

S , 3 4 X Y n e 0 L w |

,

9 ( M 5 w | Q 5 $ z \ L K [ S T u

,

T I w | Q 5 $ z \ L K [ S T h i b

17

v x

Pratt

"

1964

# y

Arrow

"

1970, Ch. 3

#

Laffont

"

1989, Ch. 2

# V ;

,

U Y z \ ' W V h 3 < v o \ W 8 . J 6 ?

;

Y 3 < Y z \ ' W ) V y > f V h

,

D / " ] y i % < ^ = . b

18

# % r [ 0

,

( 0 1 - u * q [ \ f g ) [ r 3 4 X Y - \ r 5 M b

(20)

∂α

Lt

2 ∂t

= −

p

H

(1 − p

L

)[(d − ˆα

Ht

)U

(w

A

Ht

) − (d − ˆα

Lt

)U

(w

Lt

A

)]

(1 − p

H

)p

L

U

(w

NA

Lt

) − p

H

(1 − p

L

− t)U

(w

Lt

A

)

,

(18)

∂α

Lt

1 ∂t

=

pL

(1 − pL)

∂α

Lt

2 ∂t

,

(19)

∂α

Lt

2 ∂τ

= (1 − p

L

)

(1 − p

H

)[U

(w

Ht

NA

) − U

(w

Lt

NA

)] + p

H

[U

(w

A

Ht

) − U

(w

Lt

A

)]

(1 − p

H

)p

L

U

(w

NA

Lt

) − p

H

(1 − p

L

− t)U

(w

Lt

A

)

,

(20)

∂α

Lt

1 ∂τ

=

p

L

(1 − pL)

∂α

Lt

2 ∂τ

.

(21)

M G 7 F p @ ! $ % @ x # S g ~ g ! "

,

k 3 / < D @ q . ' $ <

,

$ ! " 5 C % - G 1 , U V W @ ! R T "

,

! 7 8 D 9 | # F p t U ] D 7 F p ) 4 @ ! $ %

,

$ % @ ) 4 I k 7 7 F p ! º 1 6 k ? , N - ° r

,

$ - T 6 0 x # S g ~ g ! " $ < ^ ! _ `

1

J K @ 2 $ & ) 4 I > ; D u Q * > H @ ; ! 1 & ) 4

,

, F T ! b " B " 1 0 @ % 1 $ % ] @ G ] ; "

,

d 1 y J K s » , J $ 4 @ 4 I > 3 u 4

:

SW

t

= λ

_H

· EU

Ht

+ λ

_L

· EU

Lt

,

(22)

k "

,

λH

D # F p @ x

,

λL

D 7 F p @ x

,

λH

+λL

= 1

!

EU

Ht

, EU

Lt

{

(5)

r !

,

D 9 , b x # L n

,

a

Kaplow

"

1992

# @ &

,

, J $ % & % 4 f @ } ~ d r s

,

- d 4 @ r b $ # <

:

τ = λ

H

p

H

t(d − ˆα

Ht

) + λ

L

p

L

t(d − ˆα

Lt

),

(23)

k "

,

! r : 7 @ \ W "

,

t(d − ˆα

Ht

_{), t(d − ˆα}

Lt

₎

_~ _§ _# ₇ _F _p _e ₅ 8 @

,

Ò ! A P 1 @ H C { D p G e 5 8 ! 6 7 { § 0 M # 7

(21)

F p X Y @ ! r 5 2 0

τ

D 0 C

t

@ ; ! T ! " c * : " B " @ ~ + $ % @ 2

,

o p ; t

,

T , P C + § D

t

@ ;

,

- 4 I > 3 u 5 D

t

@ ; !

,

D 9 ~ 2 , J $ e > "

,

d 4 T ! @ G ] 3 u § D @ " r 4

:

19 SW

t

= λ

_H

U (CE

Ht

) + λ

L

U (CE

Lt

),

(24)

k "

, CE

Ht

= pH

w

Ht

A

+ (1 − pH

)w

NA

Ht

− ρ

H

t

= w − pH

d − [τ − pH

t(d − ˆα

Ht

)] − ρ

H

t

,

CE

Lt

= p

_L

w

Lt

_A

+(1−p

L

)w

NA

Lt

−ρ

t

L

= w−p

L

d−[τ −p

L

t(d− ˆα

Lt

)]−ρ

L

t

! !

ρ

H

t

|

ρ

L

_t

§ # 7 F p 1 J K s » , J $ 4 $ u A e F ® 3

,

q

Yitzhaki

"

1987

# v @ e f @ & / "

the excess burden of tax evasion

#

" n

Yitzhaki, 1987; Ueng and Yang, 2000, 2001

#

,

1 ! { § 1 , J

$ 4 # 7 F p 1 F " 4 C @ ! b § $ q r @ I !

,

5 F ® 3 @ " { t & d , J $ M F " # @ > ? ! D 9 u w < D

,

T

w − p

H

d, w − p

L

d

~ ® D

y

H

_|

_y

L

_,

_k _"

_y

H

_{< y}

L

_! _' _T

τ −pH

t(d− ˆα

Ht

), τ −pLt(d− ˆα

Lt

)

~ ® D

τ

H

|

τ

L

;

- ?

CE

Ht

= y

H

−τ

H

−ρ

H

t

,

CE

Lt

= y

L

− τ

L

− ρ

L

_t

!

,

τ

H

_|

_τ

L

_~ _§ _g _" _f _@ _! _u _A _@ /

;

&

τ

H

E " # G >

,

{

τ

L

_" _E _# _G >

,

§ 0 J K M # F p X " ® #

,

M 7 F p ® " X #

,

0 ' . { # " 7 # F p ' . 7 " # # F p ! F F G 0 b Y @

,

t = 0

h

,

z f q @ w D J K s » , J $ @

,

4 I > 3 u

SW

0

5 § D 4

:

SW

0 = λH

U (CE

H0

) + λLU (CE

L0

),

(25)

k "

, CE

H0

= y

H

−ρ

H

₀

, CE

L0

=y

L

−ρ

L

₀

;

e t

,

ρ

H

₀

,

ρ

L

₀

~ § # 7 F p $ u A @ F ® 3 ! k "

ρ

H

0 = 0, ρ

L

0 > 0,

§ 0 1 s » , J $ @ % 1 $ % 4

,

# F p , - F ? # C ! @

,

7 F p { , !

19

v x

Jehle and Reny

"

2000, p. 107

# 1 $ d Y u z \ Þ _

:

= w 1 _ ` M > 3 E F H 5 4 h w 1

,

} .

CE,

,

U (CE) ≡ pU(W

A

) + (1 −

p)U(W

NA

), p

. P * x

,

CE

= EM − ρ, EM

. 4 h k O

, EM

= p × W

A

+ (1 − p) × W

NA

,

ρ

. z \ Þ _ b

(22)

3.3

e g h i j k r x 9 & f : s E =

SW

t

_L

_SW

0

. g 9 S X a 8

SW

t

₋

SW

0 ≡ SW,

2

SW > 0

< A c l C D 9 & f T '

,

A .

,

2

SW < 0

< A A ; D C D 9 & m a V y k s 2 9 Y J Q

,

i $ 3 n N

,

2 G ` M ) A 9 G

, SW

t

₌

U (y − ρ

t

), SW

0 = U(y),

20

-

SW = U(y − ρ

t

) − U(y) < 0,

§ 0

, J $ I 6 7 4 I @ ¥

,

q

Kaplow

"

1992

# = & @ ! ! 1 ! R T , U V W @ 4

,

D 9 b ~ 2 , J $ @ > "

,

1

τ

i

_,

_ρ

i

t

d |

ρ

i

₀

@ 4

,

5 T

U (CE

it

)

d |

U (CE

i0

)

1

y

i

J b " ´ µ : r 5 0

:

U (CE

it

) ≈ U(y

i

− τ

i

− ρ

i

_t

) = U(y

i

) − (τ

i

+ ρ

i

_t

)U

(y

i

),

i = H, L. (26)

U (CE

i0

) ≈ U(y

i

− ρ

i

0 ) = U(y

i

) − ρ

i

0 U

(y

i

),

i = H, L.

(27)

- ?

,

21 SW ≈ −λH

τ

H

[U

(y

H

) − U

(y

L

)] − λH

U

(y

H

)ρ

H

_t

− λLU

(y

L

)ρ

L

.

(28)

k "

,

ρ

H

₀

= 0, ρ

L

₀

> 0, ρ

L

= ρ

L

t

− ρ

₀

L

! o p $ X @ ! t

, (28)

r @ : 7 5 ~ D P \ > "

:

22

F F ,

,

* b \ 5 v e D 0 < ~ "

,

k | - 1 G

:

1 ! F " f D # _ 2 "

complete information

# @ 4

,

* b ( @ ! "

,

! J $ 6 0 H " f @ ! * M @ F G >

,

5 q

ρ

H

t

= ρ

L

t

= 0,

h # 7

20

9

y = w − pd

b

21 (23)

\ M "

λ

H

τ

H

_{+ λ}

L

τ

L

= 0,

-

λ

L

τ

L

= −λ

H

τ

H

,

- d

,

M - > @ R !

(28)

\ . / ( > L b

22

\ + d 3 ! m F G H

,

d & L ( B w | M # % < n S o } ~ . A

,

8 ; " t : Û f p m Z e . & L

,

\ / , / " Q e p

,

M 8 c 9 3 4 X Y # % q ( B w | b

(23)

F p ! / @ l F q G k p G l F

,

e / 0 < ~ 6 k / @ l F ! ] e

,

U

_(y

H

_{) − U}

_(y

L

_{) = 0}

_h

_,

₀ _~ _' _r _G ₉ ₇ _@

,

- 7 @ 0 < ~ T 5 . 4 I @ ¥

,

d F 5 T * b \ v e D 0 < ~ " ! 1 z & "

U

_(y

H

_{) − U}

_(y

L

_{) > 0,}

23

-

τ

H

_D _/ h

,

# \ @ > " D 3 ! , ¡ @

,

B (

Edgeworth

"

1897

# = & @ ! "

,

1 \ @ 0 D # _ 2 " E 1 l F @ - T #

,

9 7 ~ 6 0 \ / @ 7 @ 3 u

,

1 ; e h

,

k / @ 0 3

u 5 T = G b &

,

q & ! v 7 8 9 | { "

marginal equal sacrifice

principle

# ! m ?

,

1 z & @ f * 4

,

9 7 0 < ~ @ J $ { ~ 6 0 \

/ p G @ 7 3 u

,

1 ; e h

,

# p G l F 3 u 5

T = G b &

,

$ ! " 5 R D

Edgeworth

"

1897

# b & @ L 3 ` ¥ : ! - D 1

z & @ ) 4

,

v # 7 F p k l F + e

,

&

Edgeworth

"

1897

# @ ! % W , 0 < ~ @ $ =

,

m ? G z & " # 7 F p @ p G l F ' e "

y

H

< y

L

#

,

- 7 @ T l F 7 F p _ # F p T 5 Y 4 I @ > 3 u ! B ( z & @ ~ g

,

1 , J $ 4

τ

H

@ 3 / ' d

,

&

τ

H

< 0,

§ 0 # F p @ / G >

,

0 ' . 7 F p ' . # F p

,

- 0 < ~ " D 3

,

E e

,

0 < ~ " D / ! F F k i

,

* : \ § # F p @ F "

,

k "

ρ

H

t

> 0,

- # \ @ > " D /

,

- 1 , , J $ @ 4

,

v ! $ % I # F p @ 2 $

,

- k F D >

,

m ? 1 , J $ 4

,

# F p @ ! 2 $ I O

,

- I # C ! @ ! F F 9 /

,

* P \ § 7 F p @ F "

,

k "

ρ

L

_@ ₃ _/ < D ' d

,

- 7 F p 1 , , J $ @ 4 @ ! 2 $ q O

,

- & 1 , J $ 4 @ 6 7 " q

ρ

L

_{< 0}

_#

_,

_{ _# _\ _@ _> " D 3

,

E e

,

{ D / !

24

F F G 0 @

,

4 I ! , b l " f @ h

,

* b \ 0 < ~ " d | * P \ 7 F p @ F " % T + n

,

% 4 @ * : \ # F

23 .

.

U

< 0

y

H

< y

L

b

24

3 x R 3 $ z \ L r x ; < 9 F G

,

t > ¯t

H

F G

,

d e [ \ W - - 3 4 X Y . 5 X a [ \ y

,

9 ( B w | e 9 ` n 8 e p * \

,

# , d e $ z \ L z \ v a w | t f . `

,

ρ

H

t

t f R 3 ¾ b

(24)

p e F "

,

m ? # \ " D /

,

- 5 0 s » , J $ T

% & C @

,

b ! " q

Kaplow

"

1992

# = & @ ! !

F F ¨ © ] e

,

s » , J $ I a P P \ > "

,

b D 0 < ~ "

,

k M 4 I > 3 u @ " ' d

,

: D # F p e F "

,

k M 4 I > 3 u @ " D /

,

P D 7 F p e F "

,

k M 4 I > 3 u @ " ' d ! Æ & ! % P \ @ 0 " D 3

,

{ , J $ T 6 0 4 I > 3 u = 0 i j !

3.4

e s t u v i 4 * " 9 A @ A z ! g P 4 m k 4 ) & Y ^ C D & f > 9 : s a $ i 9 z ! 2 `

,

: R w ? 7 7

U (w) =

√

w,

M 9 1 W n L 7

100,

d

7

50,

M 9 % ; q 7

0 .5,

9 % ; q 7

0 .05,

M 9 M w E z 7

λ

H

,

9 M w E z 7

λ

L

= 1 − λ

H

a i D \ i G H g % w D x

,

9 7 | $ b # 9 G H

,

# $ h 9 n : q 6

,

M ^ D L G `

;

v

,

| $ " # 9 G H

,

# $ h 9 n : q 6

,

M ^ - D L G ` a 2 2 D I = j

1,

N

t < ¯t

H

,

7 b # 9 G H

;

t ≥ ¯t

H

,

7 " # 9 G H a ; D ` w D P 9 J Q

,

i | ]

¯t

H

S 7

15%

a 1

,

$ b # 9 G H V W $

t = 5%

L

t = 10%

9 ' s n : q 6

,

f

(8)

(9)

(12)

(13)

+

(23)

p Q

,

25

N 1 A

α

Ht

2 α

Lt

₂

|

τ

G ! ? d

(28)

r x # s » | s » , J $ e 4 I > 3 u

,

§

1

0 ! §

1

F A r C $ O ¨ 6 i j " @ { # F @ x

,

- D # F @ x I e h > ? 0 < ~ " # F p e F " d | 7 F p e F "

,

# F @ x . / h

,

l m J K M # F @ ®

(τ

H

₎

_$ _f

_,

_¿ À £ ? ]

,

0 < ~ @ 3 . " Y # 9

;

k i

,

w x y z ( & R { | } & ~

25

w T 9 _ B M

(α

Ht

2 , α

Lt

2 )

F @

,

f g x /

Mathematica

r ) b y ? B z B T 9

,

T 9 @ { ` H

:

F T 9

(8)

y

(9)

\ r I m g * 8 T C

(α

Ht

1 , α

Ht

2 )

b , T

(α

Ht

1 , α

Ht

2 )

I Z

(12)

y

(13)

\ T 5

(α

Lt

1 , α

Lt

2 )

b 9

,

α

Ht

₂

= (6.25 − 56.25t + 100t

2

|

−50t

3 + 0.5tτ − 0.5t

2 τ )/(0.25 − 0.75t + 0.5t

2 )

b - T I Z

(23)

\ D E b \

:

τ = λ

H

p

H

t(d − ˆα

Ht

_{) + λ}

L

p

L

t(d − ˆα

Lt

),

5 P

τ

9 b G 5 P

τ

9

,

d e : I Z

α

Ht

2

u

α

Lt

₂

5 P 8 W 9 b

(25)

1

} ~ J

tλ

H

α

Ht 2

α

Lt 2

ττ

H

τ

L

ρ

H t

ρ

L t

ρ

L 0

−

λ

H

τ

H

[U

(y

H

)

−

U

(y

L

)]

−

λ

H

U

(y

H

)ρ

H t

−

λ

L

U

(y

L

)

ρ

L

SW

0.01

17 .2

3

0

1 .8

030

0.123 −

0.

2

655

0.002

7

0 .1

9439

0.35

38

0 .3

574

0.

0

000

2 −

0.000

12

0.00

019

0 .0

0009

*

0.10

17 .2

3

8

1 .8

040

0.147 −

0.

2

411

0.026

7

0 .1

9406

0.35

39

0 .3

574

0.

0

001

9 −

0.001

16

0.00

016 −

0 .0

0081

0.20

17 .2

4

0

1 .8

050

0.173 −

0.

2

150

0.527

5

0 .1

9403

0.35

41

0 .3

574

0.

0

003

3 −

0.002

32

0.00

014 −

0 .0

0184

0 .0

5

0.30

17 .2

4

1 .8

066

0.200 −

0.

1

878

0.079

7

0 .1

9391

0.35

42

0 .3

574

0.

0

004

4 −

0.003

48

0.00

012 −

0 .0

0292

0.40

17 .2

4

7

1 .8

078

0.227 −

0.

1

606

0.106

7

0 .1

9383

0.35

43

0 .3

574

0.

0

005

0 −

0.004

63

0.00

010 −

0 .0

0404

0.50

17 .2

5

0

1 .8

090

0.253 −

0.

1

345

0.132

7

0 .1

9375

0.35

44

0 .3

574

0.

0

005

2 −

0.005

79

0.00

008 −

0 .0

0519

0.01

8 .81

0

0.47

8

0.260 −

1.35

9

0.012

5

0.809

7

0.35

95

0 .3

795

0.

0

001

2 −

0.000

50

0.00

106

0 .0

0068

*

0.10

8 .84

6

0.48

2

0.384 −

1.23

1

0.136

5

0.807

7

0.36

01

0 .3

795

0.

0

010

5 −

0.005

01

0.00

094 −

0 .0

0302

0.20

8 .88

0

0.48

7

0.520 −

1.09

2

0.272

5

0.806

0

0.36

08

0 .3

795

0.

0

018

7 −

0.010

00

0.00

080 −

0 .0

0732

0 .1

0

0.30

8 .91

0

0.49

1

0.650 −

0.95

9

0.402

5

0.804

6

0.36

14

0 .3

795

0.

0

024

6 −

0.014

97

0.00

068 −

0 .0

1183

0.40

8 .94

7

0.49

6

0.790 −

0.81

5

0.542

6

0.802

6

0.36

21

0 .3

795

0.

0

027

9 −

0.019

91

0.00

056 −

0 .0

1656

0.50

8 .98

0

0.50

0

0.920 −

0.68

2

0.672

6

0.801

0

0.36

28

0 .3

795

0.

0

029

2 −

0.024

84

0.00

045 −

0 .0

2147

(26)

,

A w x y & x y Z

,

w x y ¡ Q x y & ? ¢ £ ¤ w ¥

;

¦ §

,

w x y z ( & R { | }

,

® ¯ ° ± ¥ « x y ¡ Q x y & ' ¢ £ G ² ³ ´ = µ ¶ & § · ¢ £

,

¸ ¹ w x y z ( & R { | }

,

w x y ¡ Q x y & ? ¢ £ º $ @ A » ! ¼ ¢ £ } ½ « x y ¡ Q x y & ' ¢ £

,

® ¯

,

¸ ¹ w x y z ( & R { | }

,

¾ ¿ À Á Â Ã ´ = µ ¶ & ¢ £ Ä Å Æ Ç G È A É Ê & ª

,

Ë w x y ¡ z ( & R { Ì «

,

- Í Î Ï Ð µ ¶ ¢ £

,

ª ¢ £ ¨ ª Ñ Ò #

(9 × 10

−5

_),

,

Ë × > S «

,

Ø Ù Ú & Û £ º Ü ! S 3 Ý

Kaplow

"

1992

# @ Þ ß & Û £ G H H à ¹ á â ã ä & å æ

,

, ç è é w ê « x y ¡ ë +

t = 35%

ì

t = 45%

í î @ A × > Z

,

ï Ö ð w ê « x y ¡ ë + w @ A × > Z ñ ò B ó & å æ Z

,

ô õ ö Â ÷ + ¾ ¿ Ü ! ¤ ø Ü ! y

,

ª ù S ñ ú û ¾ ¿ À Á Â Ã Z Q ´ = ü M ï A w

?

ý (

2

@ ) G ö (

2

X þ ÿ ¡

,

( ) L ú û P ¾ ¿ À Á Â Ã ¤ ´ = ü M

,

w ê « x y ¡ & ¢ ü M / ¤ w

,

Ë @ A × > S w

,

¾ ¿ À Á Â Ã ñ X | & ´

,

I X Î Ï Ð | & ¢ £ G

4.

$ > j 9 x 2 `

,

7 @ L

Kaplow

"

1992

# % 9 E = " + @ d x

,

y 8 -9 G 9 G ` M . u n

w

? 7 7 8 9 9 G H

,

/ : $ 4 * 9 C D `

,

G ` M 9 u n 8 D ) - 9 a 2 i 8 G ` M u n 9 X [ > x >

,

8 D m 9 & f : s U V a $ | : _ 6

,

V ) * : q L n r 8 1 . 9

,

$ 8 9 9

d

. 6

,

n 8 m M v n ^ 9 J b 8 D M n 8 m

,

/ C H u n 8 m M Z Z D @ = M 9 G J " # j m = S

d

# a V b u

,

C > G ` M u n 9 X [

,

8 D j

(28)

Q ` n t 9 : s

,

v b 9 y s 8 / X <

Kaplow

"

1992

# 9 y T

,

! : i

,

# O | $ V W i j 9 ` _ {

,

A m C D 9 & m - f a b 7

,

@ 9 . 7

,

4 * 3 ` % 9 7 N ) 9 : s

,

ó y ý

Kaplow

"

1992

#