)
:
1 30 , - 25 , , ...
)
)
)
)
(i) , (Y0 ), :
)
)
)
)
:
IS ( , IS ), LM ( LM)
8% 3%,
1. 6%
2. 3.67%
3. 11%
4. 3%
: + ( ) = 8 % + 3 % = 11 %
12% 3%,
1. 12%
2. 15%
3. 4%
4. 3%
, 2 300 . . . , 20% , ..
) 250 . . .
) 225 . . .
) 275 . .
) 300 . . .
: (.. 300 .) .
PV = FV: (1 + nr), n ( , = 1 , r , ()
Þ PV = 300: (1+ 20,2) = 214,28
, 225 . ., !
75 . , 5% , 1500 . ..
:
() = ( (R): %) 100 %; Þ (75 . . .: 5 %) 100 % = 1500 . . .
50 . . . , 5 % , _ 1000 _ . . .
:
() = ( (R): %) 100 %; Þ = (50 .: 5%) 100 %= 1000 .
, 4 24000 , , 12% ______
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1) 200000
2) 50000
3) 288000
4) 24000
:
() = ( (R): %) 100 %; Þ (24000: 12 %) 100 % = 200000
(MPC) 0,74,
) 3.85
) 3,24
) 4,19
) 2,67
:
k () = 1: MPS = 1:(1 MPC) = 1: (1 0,74) = 1: 0,26 = 3,84615.. 3,85
(MPC) 0,45,
) 1.45
) 1,82
) 2,36
) 2,95
: .
100. , 2000 ., - 10., 30
:
1. ATC = AFC + AVC; AVC = VC: Q = 2000: 100 = 20
2. ATC = AFC + AVC = 10 + 20 = 30.
4% 2%, ....
)
)
)
)
:
1. : 2 %: 4 % = 1:2 = 0,5
2. .. < 1,
1000 800 .., 780 680 . ., (MPS) 7
:
= 1000 680, .. (680: 1000) = 85 %; 15 % (100 % - 85 %); Þ)MPS = 15 %
.. MPS 15 % - 22 % = - 7 %
400 800 .., 240 . ., (MPS) ( ) 40
:
.. 1 = MPC + MPS; MPS = 1 MPC; MPC = Δ : Δ Y = 240: (800 400) = 0,6 Þ MPS = 1 0,6 = 0,4; : 0,4 x 100 % = 40 %
400 800 .., 360 680 . ., (APC) 5,55
: APC = : Y
1. APCo = 360: 400=0,9; APCt = 680: 800=0,85
2. : (APCt - APCo): APCo 100%= - 5,5555 %
400 800 .., 360 630 . ., (APC) 12,5
: .
1000 800 . ., 780 680 . ., (P) 8,97
1) APC = : Y
2) APCo = 780: 1000=0,78; APCt = 680: 800=0,85
3) : (APCt - APCo): APCo 100%= 8,97 %
400 800 . ., 300 600 . ., () ( ) 75
:
= (600 - 300): (800 400) = 3: 4 = 0,75; : 0,75 100 % = 75 %
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=200 . ., =7%, =2%, =2, 180 . .
:
1) = 7 % - 2 % = 5 %
2) (Y) (Yf) = 5 % 2 (. )= 10 %
3) Y=Yf 10 % Yf = 200 20 = 180
150 ., -160 ., 170 ., 15% ...
1. 363,16
2. 460,15
3. 453.37
4. 386.54
: ; - : PV = FV: (1 + r)n, n ( , = 1 , r , ()
1. PV1 = 150: (1+ 0,15)1 = 150:1,15 = 130,43
2. PV2 = 160: (1+ 0,15)2 = 150:1,152 = 121,03
3. PV3 = 170: (1+ 0,15)3 = 150:1,153 = 111,84
4. PV1 + PV2 + PV3 = 363,3, .. ~ 363,16!
$ 300, - $ 325, 10%,
1) $ 532,5
2) $ 541,3
3) $ 549,4
4) $ 556,1
: .
200 . ., 70 . ., , 35
:
APS = S: Y = 70: 200 = 0,35; Þ 0,35 100 %= 35 %
= 270 . ., = 5 %, = 2, 300 ..
:
1) (Y) (Yf) = 5 % 2 (. )= 10 %
2) Yf =[Y:(100 % Y Yf)] 100 % = [270:(100 % 10 %)] 100 % = 300
= 340 . ., = 5 %, = 3, 400 ..
:
1) (Y) (Yf) = 5 % 3 (. )= 15 %
2) Yf =[Y:(100 % Y Yf)] 100 % = [340:(100 % 15 %)] 100 % = 400
=340 . ., =7%, =2%, =3, , 60 . .
:
1) = 7 % - 2 % = 5 %
2) , .. (Y) (Yf) = 5 % 3 (. )= 15 % ( 0,15, %)
3) Yf =[Y: (100 % Y Yf)] 100 % = [340:(100 % 15 %)] 100 % = 400
4) Y=15 % Yf = 400 0,15 = 60
10 150 . ., 8%, _____ . .
- 1725
- 1500
- 1875
- 1250
:
() = ( (R): %) 100 %; Þ = (150 .: 8%) 100 %= 1875 .
- Qd=40-P (Qd- , .P-.. .), AC(Q)=2Q+10( .), , , 35 .
:
1. P=MR=MC
2. MC= (Q)΄; TC= AC x Q = (2Q+10) x Q = 2Q2+10Q
3. .. TC= 2Q2+10Q Þ MC= 4Q + 10
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4. Qd= 40 P Þ P = 40 Q Þ MR= 40 2Q
5. . MR= MC Þ 40 2Q=4Q + 10; Q=5
6. Pmax (c.4)= 40 Q= 40-5=35
- Qd=106-P(Qd- ,., P- , . .), AC(Q)= 5Q+10 ( .), , , 94 .
:
1. P=MR=MC
2. MC= (Q)΄; TC= AC x Q = (5Q+10) x Q = 5Q2+10Q
3. .. TC= 5Q2+10Q Þ MC= 10Q + 10
4. Qd= 106 P Þ P = 106 Q Þ MR= 106 2Q
5. MR= MC Þ 106 2Q=10Q + 10; Q=12
6. Pmax (c.4)= 106 Q= 106 - 12=94
- Qd=40-P (Qd- , .P-.. .), AC(Q)=2Q+10( .), , , 5 .
:
1. P=MR=MC
2. MC= (Q)΄; TC= AC x Q = (2Q+10) x Q = 2Q2+10Q
3. .. TC= 2Q2+10Q Þ MC= 4Q + 10
4. Qd= 40 P Þ P = 40 Q Þ MR= 40 2Q
5. MR= MC Þ 40 2Q=4Q + 10; Q=5
5%, 400 .., 8000 . .
:
1) () = ( (R): %) 100 %;
2) = (400 . .: 5 %) 100 % = 8 000 . .
, , 1000 . 500 , 800 . , 100 . ,
.
2) 2 .
3) 5 .
4) 100 .
: R - ( ); Pr ; Pr ; FC ; VC .
1. Pr = Pr:Q; Pr = R = TR FC - VC
2. Pr = 1000 800 100 = 100
3. Pr = 100: 500 = 0,2
C=200+0,8Y (Y - ), Y = 2000 . . () 90 .
:
APC = C: Y = (200+0,8 2000): 2000 = 0,9; : 0,9 100 % = 90 %
S=(-20)+0,25 ( - ), =100 .. (APS) 5
:
APS = S: Y Þ APS = (- 20+ 0,25 100): 100=0,05; Þ 0,05 100 %= 5 %
S=(-40)+0,5 ( - ), =200 .. (APC) 70
:
1. APS + APC = 100 %; Þ APC = 100 % - APS;
. 2. APS = S: Y = [(-40) + 0,5 200]: 200 = 0,3; Þ 0,3 100 %= 30 %
3. APC = 100 % - 30 % = 70 %;
S = (-50)+0,5Y, (Y ), Y=100 (APC), 100
:
1. APS + APC = 100 %; Þ APC = 100 % - APS;
2. APS = S: Y = [(-50) + 0,5 100]: 100 = 0: 100 = 0. .. !
3. APC = 100 % - 0 % = 100 %;
12 59 . 1 , 6%, , 42,48 . . .
:
3) () = ( (R): %) 100 %; Þ R =( %): 100 %
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4) = 59 . . 12 = 708 . .
5) R = (708 6%): 100 % = 42,48 .
12 50 . , 6%, , 36 . . .
:
1) () = ( (R): %) 100 %; Þ R =( %): 100 %
2) = 50 . . 12 = 600 . .
3) R = (600 6%): 100 % = 36 .
10 8 . , 5%, , 4 . . .
: .
: Qd=11-P, Qs=-4+2P(Qd- , Qs- ,P-,. .), 6 . . 6 .
:
1. Pt. , . (Qd=11-P).
2. (P). Qd=Qs, .. 11-P =-4+2P Þ 3=15; (.. )= 5
3. (Pt)= + 6 = 11.
4. Q ( Qd) =11-P=11 5=6.
5. Qt ( Qd) =11-P= 0.
6. Qt Q: Qgt Q=0-6= - 6.
: Qd=11-P, Qs= - 4+2P(Qd- , Qs- ,P-,. .), , 3 . . 2 .
:
1. ( Pg) Qg. , .. (- 4+2P).
2. Qg ( Qs) =- 4+2P = - 4+2 3= - 4 + 6=2
: Qd=11-P, Qs= - 4+2P(Qd- , Qs- ,P-,. .), 6 . ., 18 .
:
1. , . , , D D1. , (Qs= - 4+2P), .
2. (P). Qd=Qs, .. 11-P =-4+2P Þ 3=15; (.. )= 5
3. 1 = + 6= 5 + 6= 11.
4. Q1 ( Qs) =- 4+2P = - 4+2 11= - 4 + 22=18
: Qd=11-P, Qs= - 4+2P(Qd- , Qs- ,P-,. .), , 10 ., 10 .
1. .
2. , Pg= 10, . =: Qd=Qs, .. 11-P =-4+2P Þ 3=15; (.. )= 5. Þ Pg> Þ Qg Qd=11-P
3. Qg =11 -P = 11 10=1
4. : Pg Qg = 10 1 = 10
: Qd=11-P, Qs= - 4+2P(Qd- , Qs- ,P-,. .), 30 .
1. .
2. =: Qd=Qs, .. 11-P =-4+2P Þ 3=15; (.. )= 5.
3. , Qd=11-P
4. Q =11 -P = 11 5=6
5. : P Q = 5 6 = 30
P=20-Q, TC=2+4Q+Q2, , , 16
:
1. Pmax MR= MC
2. P = 20 Q Þ MR= 20 2Q; Pmax P = 20 Q
3. C(Q)=2 + 4Q+ Q2 Þ MC=4 + 2 Q
4. MR= MC Þ 20 2Q = 4 + 2Q Þ 16 = 4 Q; Q=4
5. Pmax (c..2)= 20 Q= 20-4=16
P=16-Q, TC=2+4Q+Q2, , , 13
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:
1) Pmax MR= MC
2) P = 16 Q Þ MR= 16 2Q; Pmax P = 16 Q
3) C(Q)=2 + 4Q+ Q2 Þ MC=4 + 2 Q
4) MR= MC Þ 16 2Q = 4 + 2Q Þ 12 = 4 Q; Q=3
5) Pmax (c..2)= 16 Q= 16 - 3=13
QD=20-2P, , 3, 49.
:
1) = D = 0,5 D. =3
2) 0D; QD=20-2P; QD = 0; Þ 20-2P = 0; = 10 =0D
3) D; 0D = 10 3= 7
4) 0Q QD=20-2P =3: 0Q = 20 2 3 =14
5) D= 7 14=98.
6) D = 0,5 98= 49
QD=12-3P, , 2, 6
: . .
QD=16-4P, , 2, : 8
: . .
QD=45-3, Qs= 2 + 10,
1. 110
2. 83
3. 96
4. 124
:
1. Pe 45-3 = 2 + 10; Pe = 7
2. P 45-3 0 = 45-3P; 45 = 3 P; P= 15 =P
3. Qe 45-3 45 3 7 = 24
4. = 24 (15 7) = 192
5. = 192: 2 = 96
P=60-Q, TC=10+Q2,
15
2) 43 17
3) 44 16
4) 46 14
:
1. Pmax MR= MC
2. P = 60 Q; Þ MR= 60 2Q;
3. C(Q) = 10 + Q 2; Þ MC= 2 Q
4. Q: MR= MC; Þ 60 2Q = 2Q; Þ 60 = 4 Q; Q= 15
5. P (c..2)= 60 Q = 60 - 15= 45
P=80-5Q, TC=50+20Q,
1) 45 7
6
3) 40 8
4) 55 5
:
1. Pmax MR= MC
2. P = 80 5 Q; Þ MR= 80 10 Q;
3. C(Q)= 50 + 20 Q; Þ MC= 20
4. Q: MR= MC; Þ 80 10Q = 20; Þ 60 = 10Q;; Q= 6
5. P (c..2)= 80 5Q = 80 - 30= 50
)
)
)
)
:
: MPL: PL = MPK: PK
.. 2: 1 > 5: 20 Þ , .. MPL: PL,
. .
)
)
)
)
:
Y