1

( ) 30 9 30 11 30

1. 2 A B 4 A, B, C, D2 A B 2 A B 4

10 2 3

[

2. 1 4 ([1] [2] ) 44 1 2

4 3

3. 4 1 24 4

4. ( A B ) ([1] [2] )

A (100 )

[ 1 ] [ 4 ]

[ 1 ] (25 ) 3× 3 M a, b

M =

⎡

⎢⎢⎣

1 b 3

a 3 6

3 6 9

⎤

⎥⎥⎦ .

(1) (3)

(1) a = 2, b = 0 M r M

r

(2) a, b M 1

(3) a = b M det(M) a

M a

[ 2 ] (25 ) n n Rn

W W W⊥

W⊥ = {y ∈ Rn | yTx = 0 (∀x ∈ W )}.

yTx x y (1) (2)

(1) W W⊥

(2) W W⊥ 1 W

x1,x2, . . . ,xr W⊥ y1,y2, . . . ,ys r, s

{x1,x2, . . . ,xr,y1,y2, . . . ,ys}

(1)

[ 3 ], [ 4 ]

2

[ 3 ] (25 ) (1) (2)

(1) f : Rn → R x̄ ∈ Rn d ∈ Rn

limt→+0

f(x̄+ td)− f(x̄)t

f : R2 → R

f(x1, x2) =

⎧⎨

⎩

(x1 + x2)(x1 − x2)2

(x1 + x2)4 + (x1 − x2)2((x1, x2) ̸= (0, 0)

),

0((x1, x2) = (0, 0)

),

(d1, d2)

(2) g : R → R 3∫ 2

0g(x) dx

g(0), g(1), g(2)

[ 4 ] (25 ) y x (A)

d2y

dx2+ 2

dy

dx+ y = 0

(1) (3)

(1) y = eαx (A) α

(2) y = xeβx (A) β

(3) (A)

3

B (100 )

[ 1 ], [ 2 ]

[ 1 ] (50 ) (1) (2)

(1) A B f A P f P

f(P ) = {b ∈ B | a ∈ P, f(a) = b}

{ }

a ∈ P f(a) ∈ f(P )

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

⎫⎪⎪⎪⎪⎬

⎪⎪⎪⎪⎭

(2) R f : R → R x, y ∈ R α ∈ [0, 1]

f((1− α)x+ αy) ≤ (1− α)f(x) + αf(y).

f x ∈ R

f(x) = x2 − 2x

f

[ 2 ]

4

[ 2 ] (50 ) (1) (2)

(1) X Y (a)

(c)

Y

X 1 2 3

0 1/8 0 0

1 0 2/8 1/8

2 0 2/8 1/8

3 1/8 0 0

(a) X Y

(b) X Y

(c) X Y

(2) X (Poisson)

P (x) =exp(−λ)λx

x!, x = 0, 1, 2, . . .

(a) (b)

(a) X ( )

(b) n (X1, X2, . . . , Xn)

λ

5

6

A 100 [ ] [ ]

[ ]

L x

2 21 1( , ) 2 ( ) 22 2

u R x R x x L L x x= + - = - + -

R L 3

(1) w x 1 2L =

2x wR w+ = 0 2R£ £ 0x ³

x ( )x w ( )R w

R x 4 1/2w = 1w = 2w =5

( )L w

4 4 [ 5

4 4

R x 4

[ ]

7

( ! "#, "% =min "#, "% "# "%

* = max - − /0, 0 0* - /

3 4(3)7# > 0 7% > 0

4

B (100 )

[ 1 ]

[ 1 ] (100 )

t(= 1, 2, . . .)

t

• iBct−1Mt −Mt−1 Bct −Bct−1 Bct Mt

t i > 0

• St iBct−1Bgt −B

gt−1 Gt iB

gt−1 B

gt

t

(1) (3)

(1) Bt ≡ Bgt − Bct2

Bt −Bt−1 +Mt −Mt−1 + St = iBt−1 +Gt.

(2) t GDP yt pt

ytyt−1

= γ,ptpt−1

= π.

γ > 1 GDP π π > 1

π < 1

r

r =1 + i

π− 1

π < 1 + i r > 0

8

bt ≡Btptyt

, mt ≡Mtptyt

, gt ≡Gtptyt

, st ≡Stptyt

.

(1)

bt +mt =1 + r

γbt−1 +

1

πγmt−1 + gt − st.

(3)

t g < s+ b+m

(g − s > 0) m > 0

g − s > 0 b

9

C (100 )

[ 1 ], [ 2 ]

[ 1 ] (50 )

Yi = α+ βXi + ϵi, i = 1, 2, . . . , n

Xi E(ϵi) = 0, V ar(ϵi) = σ2, Cov(ϵi, ϵj) = 0 (i ̸= j)(1) (4)

(1) β β̂ = c0 +∑n

i=1 ciYi

c0, c1, . . . , cn β̂

(2) β̂

(3) wi =Xi−X̄∑n

j=1(Xj−X̄)2β b b =

∑ni=1wiYi

X̄ = 1n∑n

i=1Xi c0, c1, . . . , cn (1)

di = ci − win∑

i=1

diwi = 0

(4) β b

[ 2 ]

10

[ 2 ] (50 )

Y = X1β1 +X2β2 + ϵ, E[ϵ] = 0, E[ϵϵ′] = σ2In

Y n× 1 X1 n× k1 X2 n× k2β1 k1 × 1 β2 k2 × 1 ϵ n× 1In n× n (1) (4)

(1) X2 Y X1

β1 β1

(2) Y X1 β1 b1 b1

(3) b1 β1

(4) β2 = 0 Y X1 X2 β1

11

12

D 100 [ ] [ ]

[ ] 50

(1) (4)

X Y

X 2, a 3, b

Y 0, c 4, d

(1) a, b, c, d (2) 4 4

(1) 4 [

(3) 3 9 β 3 9 :3 ; 0 < ; < ; ;

3 1 − ; > 9, 9 + ;> 9, : > 1 − ; > :, 9 + ;>(:, :)

> 9, : 9 :9 β 3

3 (9, 9) 3 > 9, 9 = > :, 9 : > 9, : > > :, :

(4) (2) [ 4 4 4 β

3 (3) 4

[ ]

13

[ ] 50 3 1 2 3, ,r r r4 E 4 4

( ) max{ ,0}ii N Sv S E rÎ -= -å ( , )S N SÍ ¹Æ ( ) 0v Æ = {1,2,3}N = 3 4

i 0ix ³

1 2 310, 20, 30r r r= = =

(1) 10E = 1 2 3, ,x x x 103

1x 2x

3x 4 3

(2) 20E = 1 2 3, ,x x x 203

(3) 45E = 1 2 3, ,x x x 453

(4) 10E = 20E = 45E = (1), (2), (3) 4

(5) 10E = 20E = 45E = (1), (2), (3) 4

14

A 100 [ ] [ ]

[ ] 50 X 4 1 1

5 4 1

D B 1 6

(1) (4)

1 X

1 2 3 4 5 6 7 8 9 10

200 100 200 300 400 250 100 100 250 100

1 X

1 2 4 X MRP X

500 2 ]

4

2 MRP

1 2 3 4 5 6 7 8 9 10

]

X(1)

C(2)

C(3) B(2) A(1)

D(6)

15

2 A X C X 3

A 3 2 4 A

C MRP A 300

100 1 ] 4

C 1500 2 ]

600 300

2

3 4 X 4 3

200 1 50,000

1 1 3 125 3

4

4 MRP JIT MRP

4 [

[ ]

16

[ ] 25 3 42 4 3

4 4 (1) (3)

2

3

4

4

(1) 17 17

4 4 4

{

4

}

17

(2) (3) (2) 5

β 4 4

[ ] 25 3 ATM 4(1) (3)

(1) 4

{

}

(2) ATM [ 54 5 ATM 4

5 [

[

(3) 4 ATM4 4

4 [

4

ATM

4

5

B (100 )

[ 1 ], [ 2 ]

[ 1 ] (50 ) n c,a ∈ Rn+ b ∈ R+

P: max. c⊤x s. t. a⊤x ≤ b, 0 ≤ x ≤ 1

. λ ,

P(λ): max. c⊤x+ λ(b− a⊤x) s. t. 0 ≤ x ≤ 1

, f(λ) . (1) (5) .

(1) n = 3, c⊤ = (3, 4, 6), a⊤ = (2, 5, 10), b = 10 P

. ( ) ,

.

(2) n = 3, c⊤ = (3, 4, 6), a⊤ = (2, 5, 10), b = 10 P(1)

f(1) . ( ) ,

.

(3) n = 3, c⊤ = (3, 4, 6), a⊤ = (2, 5, 10), b = 10 y = f(λ)

, λ ∈ [0, 2](4) λ , f(λ) P .

(5) λ , f(λ) .

[ 2 ]

18

[ 2 ] (50 ) 70

86.0 146.3 106.9 147.2 107.9 62.1 147.4 52.0 122.9 83.3

104.9 68.8 87.0 117.0 69.5 185.0 45.2 105.8 108.8 60.9

83.2 47.5 156.4 136.3 95.8 112.1 32.8 37.1 94.1 78.1

20.6 135.2 80.8 119.1 55.8 76.3 58.3 98.9 146.4 135.0

160.4 99.1 114.2 66.9 64.5 87.4 56.1 90.3 59.5 118.2

50.4 87.6 54.6 87.1 78.0 47.1 81.5 36.9 114.6 152.4

95.7 44.6 86.1 63.1 149.5 110.0 89.2 47.2 90.0 93.1

( 100 )

19

20

A 100 [ ] [ ]

[ ] 40 PPM5 45

3 (1) (4) (1) PPM 4 3 1BCG

2 0

4 (2) 5 4

[ 4 4 [ (3) 5

4 [ 4 4

[ (4) 5

4 (1) 53 3

5 [

[ ] 30 (1) (2) (1)

3 4(a) (b) (a) 4 (b) (a) [

4 4 4

4 4

(2) 4 4(a) (c)

(a) 4 (b) 4

[ (c)

4 [

[ ]

21

[ ] 30 ] 3 ]5 3

] a h 8

8 ] 5

a f b 3 a c e 4

3 b d g 3 4 a f 3 f 3 a b C c d S e O f A g h I 3

(1) (3)

(1) a h ] 43 [

5 [ 4 4 (2) 4 4 ] 3 5

0 4 [ (3) O A I e f g h

5 ]

] 4 4

22

B 100 [ ] [ ]

[ ] 50 TOKO TOKO 20X5 , 20X6 , 20X7

4 4 , (1)

(5) , 4 4

4 4

TOKO

20X5 20X6 20X7

1,000 800 1,100

400 320 440

200 160 220

320 320 320

40 40 40

(1) 20X5 (%) (2) 20X5 20X6 , 20X7 500

460 , 540 3 20X7 (%)

(3) TOKO (4) TOKO

5

(5) (4) 3 [,

[ ],[ ]

23

[ ] 20 (1) (2) 4

2

(1) 3

100

2% 1 4

4

2

4%

(2) 1 3% 2

4% 1 2 %

5 4

[ ] 20 CAPM 4 (1) (2)

4

2

(1) 20XX 1% TOPIX

6% 20%

A TOPIX 0.05 B TOPIX

0.03 A B Y

X ) A B

Y (%)

(2) 4 C ]

) 0.8 C 5

30% ) 0.05

C 30% )

[ ]

24

[ ] 10 D D

4 D 4 MBO (Management Buyout)

5 4 M&A