, . , , . ,
. , , .
. . , , . .
, , , . , , , , 300 / 10 //, 700 / 8 , / 5 //7. 1 / 750 95 ., 750 ( ) 58 . 750 86 .//, 750 50 ./ /.
8.12 (Q). Q k k () : Q k =∑ q k, q k -
. q1 , 1. q2 2 q3 - 3. , :
1 = P(Q1), 2 = P(Q2) = P(q1 + q2), 3 = P(Q3) = P(q1 + q2 + q3).
- , TS (TS = FAE). , pc, ( pc), ( FpcE). , , . , , . , , ( + + 8.12), -.
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pc E
F
D
Q1 Q2 Q3 Qc Q
q1 q2 q3
. 8.12.
.
- P = P(Q), TC = TC(Q). q1 , q2 - , q i - i - , k . 1 = (q1). q2 q1 : p2 = P(q1 + q2). 3 q3 q2 q1: p3 = P(q1 + q2 + q3). , :
1(q1) = (Q1), Q1 = q1,
2(q2) = (Q2), Q2 = q1 + q2,
(8.6)
i (qi) = (Q i), Q i = q1 + q2 + + q i,
k(qk) = (Qk), Qk = q1 + q2 + + q i + qk.
.
(Qk)={TR(q1) + TR(q2) ++ TR(q i) ++ TR(qk)} - TC(q1 + q2 ++ q i ++qk) max (8.7)
(Qk) = {q1(Q1) + q2 (Q2) ++ q i (Q i) ++ qk (Qk)} - TC(Qk) max (8.8)
k :
(8.6), , d Qj/ d q j = 1 (i, j = 1,2, , k). , ,
, (8.10), (8.9.1) - (8.9. k) :
MR1 + MR2 - P2 + + MR i - p i + + MRk - pk - MC = 0 (8.11.1)
MR2 + MR3 - P3 + + MR i - p i + + MRk - pk - MC = 0 (8.11.2)
MR i + MR i+1 - p i+1 + + MRk - pk - MC = 0 (8.11. i)
MRk - MC = 0 (8.11.k)
(8.11.1) (8.11.2), (8.11.2) (8.11.3) .. (8.11.i) 8.11. i +1), , , (8.11.k-1) (8.11.k), q i (i = 1,2, , k), , (8.7) - (8.8) .
MR(q1) = p2,
MR(q2) = p3,
(8.12)
MR(q i) = p i,
MR(qk) = MC(Qk).
, (8.12), . , , , i .
. 8.13 P = 100 - Q, C(Q) -.
100 P(Q)
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pm g
p3 = 40
pc h
20 g MC
e d
F
MR3 100 Q
Q m MR1 MR2
. 8.13.
, , k = 3, , 20 . Q = ∑q , q - - .
:
1 = (Q1) = P(q1) = 100 - q1 = 100 - 20 = 80, (8.13)
2 = (Q2) = P(q1 + q2) = (100 - q1) - q2 = 80 - q2 q > q1 = 20. (8.14)
, (8.12). MR1(q1). (8.13) MR1 = 100 - 2q1 = 100 - 40 = 60. 2 = 60, q2 = 20.
3. (8.12) 3 = MR2 (q2) = 80 - 2q2 = 80 40 = 40.
3 = P(Q3) = 100 - (q1 + q2 + q3) = (100 - 40) - q3 = 60 - q3 q > (q1 + q2) = 40, q3 = 60 - 3 = 20. (8.12), ,
(Q3) = MC(q1 + q2 + q3) = (60).
(q3) = MR3 (q3) = 60 - 2q3 = 60 40 = 20.
8.13 , , (MR1 = MC), , (p = MC = pc). , , , F,pc,h,d . , ( F,pm,m,e).
F,pc,g, . pc,100,g. 8.13 , . + + , .
, . , P = a b Q (a > 0, b > 0), TC(Q) (Q = q1 + q2 + + q i + qk, k = 2, , n). (8.6), pk .
1 = P(q1) = a - b q1,
2 = P(q1 + q2) = a - b (q1 + q2) = (a - b q1) - b q2 ,
(8.15)
i = P(q1 + q2 ++ q i ) = a - b (q1 + q2 ++ q i) = [ a - b (q1 + q2 ++ q i-1)] - b q i,
k = P(q1 + q2 ++ q i + + qk) = a - b (q1 + q2 ++ q i ++ qk) =
= [ a - b (q1 + q2 ++ q k-1)] - b qk.
.
(q1 + q2 ++ q i ++ qk) = q1p1 + q2p2 ++ q i p i ++ qkpk = q1(a - b q1) + q2[(a - b q1) - b q2] + + q i [ a - b (q1 + q2 ++ q i-1) - b q i ] + + qk [ a - b (q1 + q2 ++ q k-1) - b qk ] -
- TC (q1 + q2 ++ q i ++ qk) max (8.16)
k (8.16), :
a 2 b q1 b q2 - - b q i - - b qk - MC(Q) = 0 (8.17.1)
a b q1 2 b q2 - - b q i - - b qk - MC(Q) = 0 (8.17.2)
a b q1 b q2 - - 2 b q i - - b qk - MC (Q) = 0 (8.17. i)
a b q1 b q2 - - b q i - - 2 b qk - MC (Q) = 0 (8.17.k)
(8.17.1) - (8.17.k), :
, , :
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q1 = q2 = = q i = = qk, (8.19)
. q i (i = 2, , k). (8.18.1) (8.18.k) (8.19), , :
8.1. , : k = 3. - P = 100 - Q, Q = (q1 + q2 + q3 ). TC(Q) = 0,1Q2 + 8Q.
:
1) ,
;
2) ;
3) ?
. 8.13.
1) (8.19) . Q = 3q i. = 0,2Q + 8 = 0,2(3q i) + 8 = 0,6q i + 8. (8.20), ,
, q i = 20. , . (8.15), 1 = 100 20 = 80, 2 = (100 20) - 20 = 60
3 = (100 20 - 20) - 20 = 40.
2) .
= TR(q1) + TR(q2) + TR(q3) - TC(q1 + q2 + q3 ) = 80×20 + 60×20 + 40×20 - 0,1(60)2 8×60 =
180×20 360 480 = 2760.
, , . . , p = 100 Q = 0,2Q + 8 = . 1,2Q = 92 Qc 76,7, p 100 76,6 = 23,4. , + + = (80 23,4)20 + (60 23,4)20 + (40 23,4)20 = 1132 + 732 + 332 = 2196. , 2760:
( + + )/ = 2196 / 2760 0,796.
. , .
1. 8.
. 8.14.1 (LAC) (LMC) . . p, qc, , - 8.14.1. 1 , q1. . , . , , , : , . , .
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LAC 1) LAC 2)
pm LMC
pc pc
qm MR q1 qc q1 q2 qc
. 8.14.
8.14.2 . , , 1, 2 pc,
LMC. q1, (q2 - q1), (q - q2). q, L 2 . , , , , , . , . , , .
, , . , , , , , , , .
2. .
. 13.08.02 ., 1 2002 .
, (.)
60 240
20 100
10 50
5 30
2 14
1 7
,
70 250 .
. , , 8.15. . = . 1 . 2 7., 1,
2 1 7. (14 - 7 = 7).
5: 2 = 14 ., 5 2 = 30 14 = 16 ., 16/3 .
1 | = | |||||||||||||||||
2 | = | |||||||||||||||||
5 | = | 16/3 | 16/3 | 16/3 | ||||||||||||||
10 | = | 16/3 | 16/3 | 16/3 | ||||||||||||||
20 | = | 16/3 | 16/3 | 16/3 | ||||||||||||||
60 | = | 16/3 | 16/3 | 16/3 | 3,5 | 3,5 | ||||||||||||
. 8.15.
10: 14 ., 16 ., , 20 . 4 . 20 50 ., 5 . , 60 140 ., 3,5 .
, :
7 .
5,3 (16/3) .
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4 .
5 .
3,5 .
70 = 250, , 1 .
8.16 , .
8.16 : . 10 20 .
. 8.1 .
8.1
1 | 2 | 5 | 10 | 20 | 60 | 70 | |
3,6 |
( 1)
( . 8.15 8.16) , , .
.
, 4 . ( = 4) , = 2, .