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(R=0.5700) (2.6)
Y =723. 71+ I, 557N+ O. 029N2+0,426p+5,447yp(R=O.5304) (2.7)
Y =654. 99-5.41N+22.86Y'N+ 1. 08p+(). 15p2
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*- 2.7
(R=0.4728) (2.8)
.J:l\7 :i-f'f*.ft.!i..!.~tt~~~:;t. Deviation ofrornModel ~;t*-
m~ (Replication)
P!!:l1I1 (Treatment)
441,0071 1 I·
I774,25626
41iI
2218,902.4 0.7871 1.9681iI
1.1409 1. 9681
1.9681.
1.96811.7553'IIiI
I1.405°1
I
i j
1
11'310'1I I
22'19,852.1'I
4i
2212,903.21,
4 I
115'~'14
I
424,6651
349, 5911
337,508
578,403
I195,8531
I490,386
1
283,8701
,
iI 436,747
IIi 294,049126
1 i11,509,312[53
(2.5) :et~~t
(Due to regreSSiOn)of equation 2.5
~~
(Devia t ion from)Model
(2.6) Jt~~
~.~(Zg (Total)
~ if.: (Error)
"!i. 2. 7 ~.i!* ~f'F~~!$itt~~~z Deviation from Model *5E'iZ ' EI3s."!i.~~'~m~tt*~~5%zT' F~~~~~,m~*~A~~!$i.*
ff:JJt.fiH~~:1J{:&~ ~M1'B~$:1J{M ~ifi:l:l'Bf'I: JtH~+ ' ~"!i.;iFJltf!Y ffpJ ffittJt"*JE8f'1:~u~~Z*E~~ffi.'illX8W~~u~~~~~"!i.ttl'B*li~~~.
WE? ~ Deviation from model*~~ , {J1Qt (2.5) JtI'B~:U~1$~+0 RZ 'gp;l!!115-fi~~*8 (2.5) J:t1'B~~l't:1F1([1Il*'(ZgJlt (2.5) Jt~.*~f'I:~~
1'f~"!i.ttl'B~~ffilto
i'il/j1itxf'l:l'B~~ffilt ' ~ jf. N.P. K .=.~~~~lb~~ , ·ftLi::;;:&Jt.%ti5it~o
T:
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Y=727.42+6.35N-6.94p+1O.13K+62.70y N+69.47y p-0.29K2(R=0.7952) (2.9)
Y =861.42+0.32N+ 1. 31p+3. 92K+0.02N2+0.01p2-0.04K2
(R=0.6527) (2.10)
Y=861.64+3.45N+2.86p-1.57K-13.29y N'-6.52y P+23.42V K(R=0.6510) (2.11)
~ 2.8 i!J,ift~k.1'f.:k.3..1..A.~tt..frit~~Deviation fromModel MJ:~~
~ (5J ILp1JIDI@m~l~ 1JIT 15 % l!l!fl fRB Ffj
:m:~ (Replication)I
7.234 11
I
~W (Treatment) 522,209 26
I(2. 9) it@!~ff(Due to regre- 330,290 6 I
ssion of equation 2.9) !
~~ (Deviation 191,919 20 9,596 1.0911 1.9898from model)
(2.10) it@!~ 322,339 6
~~ 199,870 20 9,994 1. 13631 1.98
(2.11) it9fJ~ 322.330 6
~~ 199,879 20 9, 9951 1.1364 1.9898
~ :&: (Error) 228.69 26
~~.[f[Z;J (Total) I 758,121 53 8,795
1~t$tjd'l=1::.~[1j;j:f'(itai8~zDeviation from Model ~5E~tm~ 2.8 BY~,li~~~*~~5%zT'F{j~~~~~~*~A1::.~~:f'(*~~~~~
~l:fFJiH~/J" 0 mJS'!j , ~aJa~*0(2.9)itEt:r Ffl~~+ 't&i'iliPif'x1'F0 (2.9):ct~~J(,1ftt1t~B-:j~~im~ 0
3§.!~~* " i'Jjut~fill.~J(,1ftt~t£Bj*lij;:~~:f'( , jf;~~~~1*ttZ. t fitfl7lJ~~ 2.90
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I I:e-~~JJi.~.Zt1ffii
*li~~~. RfiOC N J p J Nli I pI 1 K I VN j vi) I K3
it * # fF 10.6190! 6.35J 1.' 2. 7~ 1.09) - I - '-=--i--=~ ~ fx fFI~l 3.3~ 3.881--=-1-=-1-;·~1 0. 9711. 0811.21
- --* tE 5%ml1Hi7.k~ 0
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~(~*li~:Ii:) o~~~'.*-=~Z*li~~~.~T:
(1) _*#fF: Y=686.03+6.51N+0.6p-0.046W-0.037p3 ••• (3.1)
(2) ~~HfF: Y=727.47-6.35N-6.94p+10.13K+62.70y N+ 69.47y p-0.29K3 (3.2)
J:[ij-=~* ' 5tZUttJ..../f'[QJZ N. P. K ~.11t' JlljRJQ(*~f~~~*li~it
(Y) , l2S1Jlt (3.1) ~*5tZUQ(N~~ 0, 20, 40, 60, 80 0fT/01:Ji' mi P
~5tZU~~ 0, 3, 6, 9 0fT /01:Ji' ttJ....~l.'j~ffElJIUZ*li~:Ii:~*:m~ 3.1 ,
rn~l:RJ~~~~.*~fFzE#~m:li:~:Ib~*li~:li:M~~~~~o
~ 3.1 ... "".j.ffkliA",~;jfi;Jl'l .tI:0Jr/0'r:J!.
NP
0 20 40 60 80
0 686.03 797.83 872.83 911.03 912.43
3 687.50 799.30 874.30 912.50 913.90
6 688.30 800.10 875.10 913.30 914.70
9 688.43 800.23 875.23 913.43 914.83
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* 3.1 :tm&il~P tBMliFIHi~ , .llIJ*E.~:lHiNMlimll::ti1J!lii'iJiff~~* ' m:~~t~zNMlimll:a60~OOZ~o:tm&il~NtBMlimll:~'*E.~II:~~MPtB
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1I::m 686.03. 705.15. 723.43, ». 740.89 -01T:tm1:?t N=O tB~li~ 100, .llIJjttiHi~lim.?tZU~ 103.78 105.45 1k. 107.99 0 Im~~ N=O ~ , ~;lJP~1i!Iimliz*E.~limlt.llIJ~:m 100.22 100.33 1k. 100.35 0 Llt=:"%1Lmlt~
Jl.IJRJ9nN ti*E.~litBf1:m~~ P tB 17ft?i 0
83~' (3.1) it N. P 3iHiJJi1'M~ , ~1'~ N. P tB3iHiJJi ' ite1'~ P tBMlimlifflfiiJ ' NJf~zlm-rdl~m14*E.*~fflH7.Hig{§,~&il~ , :tm P=O ii'iJ N t:BO:ti1J!l¥.20~, *~fflSe:m 111.80 -01T, N=20 ~40.llIJ~75-01T' N=40~ 60:m 38.20 -01T ' ii'iJ N=60 ~ 00 ~Jl.IJft:~ 1.40 -01T (LltB¥Jl.¥R~:ilI
~i¥IJl.~) ,~P*1i!Ii¥.3-01T~, Jl.IJ N=O ~20~, ii~aI5e~~p=O~
#lim ' N=20 ~ 40Jl.IJe:m 75-01T '~f!f! N=40 ~ 60~ N=60 ~ 80 i¥I*~fflS17F~~ P = 0 ~#llm 0 ImW , =1'~jt.N1i!Iimlt~fiiJ , P~~zlm-oo~tt:J!j'~fflSffi:l$){§,~&il~ 0 IZSlLlt ' a N. P jtMliT~jt.m:*i¥I*E.~ltm~Mlim N. PJ'tJ"ltli ' RJ~?tzUrtl¥~1i!IimN~pm~)i~IJm:*~t~i¥IMlim.;jt~ 0 :tm.RMlimN~' 'i' N=70.76 -01T.llIJ~.m:~, .R1i!Iim P ~''i' P=8.11 -0IT.llIJ~
:fItt~ 0 J!t~~-=:jjJtft;jtl±l 0 item N=70. 76 J.fr. P =8.11 -01T~1i!Ii~m14
*E.~lnp~ N. P ;;r:1m*ll.~1i!IiFIUttftm~~)i¥lJttl'o1tj~il:i¥I*JI:~ 0
83* 3.1 ~RJ~JrI±l~~~M: (Elasticity of Production) , m~~~
5~M:~~~••~~~s~$~~~Jf~ltll:~~~s?t$zlt,~§z,W~
~Jf~~~l%~'~~~II:~~i¥Is~lt,jt.~_-0~:tmT:
EP _ 6.Y / 6 X .,,~ EP-~ dY-Y X - -Y"dX
EP=~~5¥M:1*.
6Y=~:Ii!j'~fflSffi
Y=~.
6X=~~Jf~.tii~fflSf5}
X=~~~~.1l:
:tm P = 0 ~' .llIJ~;;r:1m N Mlimll:z~~~~M:1*lt:tm* 3.2 HlTift ' 1i~~~~M:~lt1L~ii'iJ1fJ't!j':ttt~tt:J~~ , s1EJl:W/Nj~ 1 , 'i'~il)im:~z N 1i!Iiffl
ItTi¥I~~5¥M:~lt~~~,~~~~~.:ttt'83~~II:~~'~~5¥M:1*.~
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N Y I N/Y I ~~ =6.51-0.092N I EP I VIi
20 797.83 0.0251 4.67 0.1172
40 872.83 0.0458 7.83 0.1296
60 911.03 0.0659 0.99 0.0652
70.76 915.53 0.0773 0 0 ii:1Ul:lEi l!'Ji
80 912.43 0.0877 -0.85 -0.0745
100 877.03 0.1140 -2.69 -0.3067
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0.0014
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0.0001
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-0. 00201
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I dYPlY I dP =0.6-0.074PY
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I 688.331i
687.901 0.0174,
2
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::: ~:~~ ~.~:8.11 688.50, O.Ol1J 0
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7}ZU~1f~ O. 10. 20. 30. 0JTI0f:Jf.' ftA (3.2) Aq:tQtl1tillUJ;I;::kRGGIt ' :1m
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~ 3.4 .tj"~ff*$.A."'~;ff!iJl'l-¥-Ur : -0:fT / 0.~
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879.94952.24966.54922.84
W3006
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727.47799.77814.07770.37
8~7 59
o
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20 964.19 1098.82 1117.46 1116.6630 920.49 I 1055.12 1073.76 i--=-072~0 899.20 1033.83 W52.47 1051.67
20 10 971.50 1106.13 1124.77 1123.9720 985.80 1120.43 1139.07 1138.2730 942.W 1076.73 1095.37 1094.57
0 899.27 I 1033.90 W52.54 1051.74
30 10 971.57 1106.20 1124.84 1124.04
I20 985.87 1120.50 1139.14 1]38.3430 942.17 1076.80
!1095.44 1094.64
o102030 i
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o
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m-fiti' m~3.4tm[iniaffl N=10 0.IT' ~1J~i:m~JJEI& (N=P=K=O) §fit
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iltrJ1tm.:m~~~ , ~1tmk.fJ'.8t p~~;~/~, ~:?c~N ,-m:&~K~~ '~51
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EE~ 3.4 ?J1'~ilt.t.li~H:k:f1:z~-JJE#~~Jk.~1b'1%~ ' ;It.*E..~.~ih(f:ja5Ht, ~ P=K=O ~JtIJ:fr~ImN1iIlimll:z~~5fP.t1~Jk:trn~3.5m;iF~
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N 1 Y \ N/Y \ ~= -6.35+31.35IvN I EP I fill ?if(
I 1862.101
0.01161
880.74i 0.0227
24.37 882.22 0.0276
879.941 0.0341I
10
~ 3.6 $".tft;fk.1'F~;r:I6l P~m-i:'""F.:t..~.&.~·t±1~tt (K=N= 0)
P I Y PlY I ~~ = -6.94+34.741VI> I EPI
m !iii:
10 877.59 O.Ol1j 4.05 0.0462
20 899.20 0.02221
0.83 0.0184
25.06 901.47 00007~ 0.00 0.0000 ~Ib~:jl@ljl!i
30 899.27 0.03 -0.59 1- 0.01971
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if!. , QL1:-:::ff N=24.37 ..P=25.061k. K=17.46 0ITtm~~A (3'.2) A:t:f-1 'RJ?~~:btf*f1=:t1Ei~rrtB*lilli~~.~4ij1~f1{ 1141.89 0 IT 0
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EE (3.1) rl:RJJ2.(3jtl±il!**1fl'tj*£l~~flH!I~:tmr :
N=70. 76±5y796.8268+ 0.5216P-0. 0324p2_0.86956y...... (3.8)
~IJJjtJY1~~~ 750. 800, 850 1k. 900 0JT7tZIJ~A (3.8) rI:* , .l{IJ7tZIJ
j,rr~rI:
N =70. 76±5y0.5216P-0.0324P2+ 144.6568
N =70. 76::i::5y O. 5216P-0.0324P2+ 101.1788
N =70. 76±5y O~5216P-=-0-:b324j52+:57.7068
N =70. 76±5y iY:5Z16P"=0. 0324pa-+:K2228
(Y = 750)
(Y=800)
(Y =850)
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Ja..l::~rl:i8*£l~~"rf!J~:tm!lil 3.6 ?JTift' stt~lE~rI:**1±i N. P ~/I'l1I't:J
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(3) P~Kffi:fi~~(t-J:k:R~~:liEill~ (~ N=O)
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T ' ;ltiJr~JlEfl~.~m:j)' , 1tf..~m:1fflJ' 2N=3K=P ~~;j{1fflJ0
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". ..
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f
,,'D
------ ,.~P:~N'
---"~N
7'DI1 -·--P:/."SN
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I i./"p ,.I ,,----- ....
. "1'.>1, 1 /. /
I:.1
t/III1'
1
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21l1:=~K.p
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1,------- k·,-"p
K.:p
_.-.- K ':P'p, , ,
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r
a
1i1.tJI~~rN:U~~fiJflfi1:Kfifi111~ (t<.o)
Yc"'lIA~)
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1:W~urnu~tt:rHEt't~!I!~1E~~1t~D1!m.Ttt:r*.E~itZau~r,u.§ , 1lik~m~<fujttt. (Physical quantity) rp~mHfiiE. 0 ~i§z' ~Pik:;}li~rm~E!l5
1t~~fl*.EitZ.z~V~1t~'~*~HEt't!l!~~j(liz~~~~1ERtt:r~'
JlIJ1:jffj~.pg.tt:rlOC.ftf~E!iflt~:ML~- ~RTQ(~1~lOC*tt:r;flJiM 0 mJ~ [ij] J!:[;J\t*5fiUiM rp~
m~~T-jjfrnu1k.o
iW~~!iUff~1k. ' ~mmliHEiB~!I!~~*.{EitZ ' ~mli!l!~1E-f~~ii:
.au~1:tt:r:;}linif~m.~RTm*~itZ~rmtt:ritZ.'iliQ(~linif~m.~~
~? ~i§z ' f1P~li*Jiif~m.~nJZ*~lOC~? J!tf1P~*M?t:#Ttt:rm,L.' 0
~fmrp~m~7}:#TtR1Jl~rnum*lOC~HE#nJZ*J.tif1Pikij(~1E~~nJZ*~~~ii:
.au~~W~J.ti'.~J!t~WmWRT.pg.••au~~x~n~~ ~e)~••au~1:tt:ri1~mf1P~*:;}~itZ.Tit1!:l;HE#nJZ*ll!ti 0 ~Q(N;••au~~~*~l%1lJi
~~~~~tt:r~~,~~~~~~~itZm~®au~o
~1Jl1:~tt:r[ij]~'••aB~1::;}~~~:
MRS= ~~ = ~: (f1P~~nJZ*.~~itZ:i:au~z~~~~)
1:l:\; MRS ~ N. P =!I!~tt:rj§~ft~~, Pp ~P~~z1Ji~' PN ~N
~~z1Ji* 0 1:J:t~RT,*~~Q( N. P =!I!~fmZUz j§~~itZ:iJ£t*Z ' ~TJ:t:
dYdN = dN • dY = dP = MPPp= Pp (5 1)dp dY dP dY MPPN PN .
dN
:W; dP =MPPN= PN (5 2)lli ~& & .
E!l (3.3) (3.4) ». (5.2) J:tRTQ(*tW..t:j:ttt:rit1!:l;HE#nJZ*~:W;••au.~T:
dE> 6.51-0.092N PNdN = O.6-0.074P Pp =a
~t:j:t a= ~: '{tf'Jr1:J:tRT~.Jl{au~~T:
N=70.6-a(6.522-0.804P) (5.3)
1:l:\;Z ~: ~~~ 2, 81k.14 :5tZllftA. J JlIJRT*~ z !t1Ji(tj••au.~1il
5.1 , lil1:®J.ti~f1P:fflW~ (Ridge line) '1EJ!tW.Rtt:r$l3I111J~1fl\'!1iA':5t:#T
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4"
~ ::&!ooJ?,
Jl, :=8-1j.
I !"N ::/4.."" ~
~~I iilJ'~~ftflir~·1..N f.f:l(>f\1~ ~ t~·
tt:1~ft ' 'i"1li~./:t (~; ) IJ'~' .~H!J~:t:ttJ:~ , ffiHJil.N~;fIr~jg'if!;i:~~ 0~~~N~~tt:1tt:11lim~ti~~~,~~~mN~~~~~~U'~Z'~*P~
~tt:11lim;f§ti~~~' 1li~./:t:t:*, .~H!J~JlU;f.\tt:t1~, ~~~~mp~~~
~~~J' ~Mf ~; =8 7J.14~, JlU N. P =~~tE=1'FPJ1Jm1:tTm:~JJE*,{1ilG*tt:J~Jl.g.1llamll7JJ~~ 5.10
~ 5.1 f:v J..-f'f N. P ..::.~;t. ~~Jiil{l#ttt. rJi{~JJe#A.$.~
1Jl~~m... (¥tiL: 0Fi'/0[jf)
N.P 1lim1:t ( ;: ) = 8I
N.P 1Jltfrlt ( ~: ) =14i'i 11y N I P ·N I P
750 I - I - 10.07 2.72I
3.64800 i 20.35 0.25 20.13I
850 33.45 1.85 32.25 4.69
900 50.74 4.92 50.47 6.31
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El:I:1i 5.1 iiJ~ , 1ti§~1la':;:ij-1Jn' fili'iffiftJ N. P -=~*fr~1ilHfll:-&:li1JlJ' Rim~lt ( ~: ) El:I 8 fj3'i 14 +~, :1i~N~~I't-J1JUtH§fl:fikfj1JlJ' :\JtH::P ~~B'J
m*1'§fl:fik~Y 0 mJ2(1:~IPJ-j£iltm y =800 ~, Jl.IJm·~B':J·N~~El:I20.35 ~
~ 20.13 -0.IT ' rm P ~~Jl.IJEl:I 0.25 ii3'i 3.64 -0ff 0
~~~i'i1Ii~f*f1:ftIa1ttJlE*'i-p.x;*~iiJEl:I (3.5) .. (3.6) .. (3.7) J).. (5.1)
~?1-2iU3ltl:!itmT:
PI"(1) N. P -=~~~·~1ttJlE*,1-p.x;;<f;.tlB~: (K=O .. p;-=a1)
N=0.041P-a1(0.09P-O.45V P +;la)(0.049P-0,49V P )+1.228 (5.4)
(2) K. N .::~~I't-.i~1ttJlE#p.x;*I!tJ~m; (P=O, ~: =aa)
54.052K=17.46+aa (10.948- V N-) (5.5)
(8) P. K .::~~(t:J~1ttJlE#p'x;*I!tJ~:m; (N=O. -~: =aa)
59.897K=17.46+aa (11.966- V P ) (5.6)
~J::ffi.:::~?1-2iU1JlJJ2(fiIM:m1il5.2, II 5.3 Rill 5.4 0 El:I1I 5.2 R]"Q{'l[l:!i
N. P .::~~zm~ltt\:li1JlJ ' Jl.IJ.J.iHII~t\fi:ti~' i'& PI': = 1. OOPp ft-J.J.iHII
~B~j[f)jj(!li 0 IiIl 5.3 *WiJ.iI!tJ~MN. K -=~~m*lt H'J:li1JlJffijfi::ti~ , 11
N(IIj!IA}
A
IIII
I
--_~I"_",,,
111~
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&>LL_~_........ ........_.--:_........_
m:"'.5 ~tt~V\~fA:t1llJ1l.~ K.N 1".:tl.U~·f~~t CPs=: &»
~__,,,,,?.sc~
~ ?.&5~
cl..--L_..L- -=__.L..-__........__
/'D
ffl-5.4 ~1~~~JiH~;1,( K. P~~7*1\'13f_~ (N '"' a)
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5.4 mift ' MH!f!!I~$)!il P. K -=J!~iWffr!t(f:jti:IJ!lii'Ot\ttti~, PK = 1. OOPp
-f!!I~'~ilift~re~p~'~iftK.P-=J!~ZiWffr~~m~'illPti~:I:~
ffl~K~*o
tm~jl!l*i*~.li +~~.li)j E#=fOOmtXI'BE#rJJjjjiWffr ' Jifti:$:~ (-fr N20%) ~0JT3.75G' ~7iIf~~ (-fr P18%) ~0JT1.75G' ~1t~(-frK60%)
~0JT 35G ° tmPfif~ N. P. K =J!~l'r':JJlE#iWffrJl.IJ~0JTN~~~ 18.55G 'P~~~ 9.4 5G' K ~~~ 5 5G ° J!t~E#.=.J!~l'r':ifWffr ' *~l'r':JJfiH!f!!I~tm
N. p -=J!~l'8tfl~f!!I~' ~P[iJ 5.2 m5ftl'r':J PK=2.00Pp f!!If& oK. N -=J!~flP
~Il 5.3 miftl'B PK=O.27PN f!!I~ ° K. P -=~~Jl.rJ~JrillI5.4 m/~1'8 PK=O.53Pp f!!I~o
III 5.2" Iill 5.3 Ik!iJ 5.4 J::fr~~f!!I~~l&m:.a~r'it~.Ji~ , tm1il5.2 mjftflP£(5ft~~~r~~:l:m® N. P -=~~f(:l:l'r':.it;l!.if.Rfr-~ii'OB ° ~gt~t'r1!~
~~~~rmf(l'r':;~~Z- °-8~.JlE~.J:m~~~~••ffl:l:' :tm.~••-=m*.BN=p~
1Ji!UTI~.~, Jl.1J-=~~.ffl:l:l¥J·;fJ1ifflP~1ill 5.2 J:~ OA ~ , J!t~tm*iJffr~
~;=2~,m~-=~~-=~~~.ffl:l:l'BnifJ:frm*~~~,~~~m~~~~~ii'O~~~~.nOOI'B-*~~,mBEfll'B~if~.~~~.iWffr~~'
:wJ~.EnX;*~iU~11f' ~J!t~11fEflnX;*f!!I~$RJBJUj.M:~Nil't:J~E#!8ifIt.rt!I~ (Optimum fertilizer ratio curve) °
J:mB~mili TM~f!!I~J:l¥J":fr~fi;;~-=~~~11f~EflnX;*I'B;fJ1if' jffiJI~
*;j'IJifjl'B;fJ1if&:'~~~f!!I*Jj[J: ' *mflP~*t/:i:fr~iWffr1j1f~Tzll~;j'Ij~~I'B~E
J!61-tIIllffl:l: o
~:7(;j'ljifjl'B~1t&:'~ii~l&1£:~~ii~nX;*' tm PN" Pr 7}ZU~NJ!~~*-ftl¥J"fWffr' N~Y?tZljft~NJ!~.ffl:l:~*E~:I: ' JUtOOZIj~iJ~{lH!1t~D.
N~D.Y , Jl.1J;jtIU1f*tml'~ :Py (D.Y) = PN (D.N)
M~~= ~:EE.a~E*'I·J!~~~:I:~~?HjIj~, ttx.NiD. Y ~D.N~+~RJfflT:rt~ift 0
dY PNdN = P y
J::rt~Mf*:I:t$RJEE:Jlt~ni*:IJ!lBllilJ)jz ' ~ 7t fi;;£(;j'ljifj, Jl.IJ :7t=P y • Y-PN' N
:@(; 7t=P y • f(N)-PN • N (~Y~N~OOf()
~~;j'ljifjll*' Jl.IHeLl::rtt.ti:N~?ts1t~z~~~flPRJ :
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dn- _p df(N) P-OdN- y'~- N-
+h<.§ • df(N) _ dY PNlV\.tif· <IN- dN =p-;
J:it:W'~;if-N~~(Bj!~1o.~:fJ~jj~nE#7d'liM:mlt (~; )~, ilU~1f;rrJo
~~~~~~~J:~~~~(B~~'W~::k~~~(B~~~~~#::kEiM:mlt'tb.RJJ:?,(Jt*I±l#4~~~~*'~7cR1:tzWl~ , f&{lZjSffft!ttJffiiJ!1o.~~~mWz~
Jl.p~a::k~IJ~~fi!l 3.50
Y(~/""J
""l-~Htf1rtflt(}~/P1
"F
1N"tm~*'l·~~~wHi.J:?,(J:~' a:k~Ij~Jb~1fil!lZU~~a::k~Ij~f.6Z*J1.it, ~
m N. P -=~~~10.~7d'l , Jl.1J~;rrJ~ (n') "tm-r :n-=Py • Y -PN' N-Pp· P
~-fre n- :ffla::k' Jl.lj~~ N. P fl;jjih~7tZ :an- BYaN =Py • 8N-PN= 0
~ ay = PI".Ill« aN P y
an- ayap =Py • ap -Pp=Q
~ 8Y_= P p
ap Py
tb.~a::k;rrlll'AI5RJEE1fil!lZU~~(B~::k;rrJlI'AJb*1~ , l:-=it:"tmmll* ' mm
~~ = ~: Jl.pmfjJHIl::k;rrJlI'A~W'~tJi}j{~~l: 0
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~~~n~~~*~~*z~~~~~~T:
ay P~aN =6.51-0.092N=py-=yN
~~ = 0.6 -0.074P= ~; =yp
m5ftJ:-=:a: ' RJ1~ :N=70.76-10.87TN (5.7)
P=8.11-13.51yp (5.8)
J:jffj-=:a:RJm1J:~1't1TN 1!z yP 11t{-\:.i\..' Il.D~*~ff::flPJ(t:J'JlE#:klifJl~lt
zT' ~::k*rJ~l!ti(t:J~~:&!Iim:i: 0 ~$: 5.2 Il.D~M!ItI~J,; PN=8Pp ~, ff::f
lPJJlEfl:kEfJl~ltr'~:k~~~~~p-=~~~:&!Iim:i:o
:k_a1Jt~PN=18.55C/0Jr Pp=2.315C/0Jf PN/Pp=8
ffE7tltl~*·1N~.E'····IP~.••••.Py ~E1Jt~N~m. iEfJl~ p~m:i: E~iI: -mt ?if{
Y(0ff/(5C/0ff) (rN=P!")(0n-j0~)1 (TP=PP) 1(0JT/0~10~)Py P y
7.74 2.39 44.28 0.298 4.08 887.14 :kJ1.~1!ffJl~
8.20 2.26 46.19 0.282 4.30 890.49:kE!&~~fJl~
8.35 2.22 46.63 0.272 4.37 891.49 ~ZP:!$)f.~
8.82 2.10I
47.93 0.262 4.57 894.34~i%1J~I t
$: 5.2 *7'c'2f.~ (P y ) {,HRiJl~if!t~il&H1±.ift~1L+-=1f..Il~m~ (B~
)j:i;:E~:ilk1Jf&Z~'IJ!1i't~*'!-' N. P -=~~fJl~Jl.IJ~~1Jtfr 0 N ~~(B~~i1l
:b1!!miHl: rN=2.39 ~::!8 44.78 0Jf' &" rN ~3§. 2.26 ~,N=46.190JT'
ITJ]fi'!!, p~~s0·l&~;EJW:trffim:l:tt n=0.298 ~J,; 4.08 0fr ' &" n~?t 0.282
~ , P =4.30 0F1' , -RJnJl&7,(*iJ~~I't:J N. P -=~~(fj'~nUUlaJlE;j6j-:kR1J~lt
iffiJE' &"1Jlf<:k~~mll:j,', EZz' 1.~lt"J,~~m.l:gti'@1Jll0 jzgJlt' tfEilltl(B7(.~~ it3)'frMIJlE*'t:kR1J:ff\-lt~y ffij :l'ff1Jll 0
rmfi'!! ' ~j~JY]~~*IJ~J!~63FFiJw:J:?t*~ :P!"N=982.82/(rN+6.35)2 (rN=p~-) (5.9)
P=1206.87/(Tp+6.94)2 (TP= ~;) · · ·.. · · · ..· ..· .. ·.. ·(5.10)
K=17.46-1. 72rK (YK= ~; ) (5.11)
J:Jm=::a:*Jltf1fE:Z TN' yp 1!z rdlt{-\:.i\..' J}~*~ff::flPJl't:JJlEfl:kR1Jt
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:j:iHl;zT ' iI't:k;fJ1lMJ!B':lJ!~:&liiJfHI 0 1i. 5.311.p~~;tt~:rIJil'tiWi;fIJ~lMi!¥' :fr~
~ ;(£::ffllJ~~#:kli1JU~·.ItT1fU~~ (f:11JfUt:l:ll 0
:kli1lf~ PN = 18. 5 5G./0 fT Pp=9.4 5G./0Jr fffIllUB':l:k'l1Px=5 5G./0fT PN/Pp =2 ~.
Py PdPx=0.27 Pp /PK=0.53 y {Fm 1\((0rr/0
(x/0fT)TN I N I Tp I p I l"x I K I;f{)
I
I I
7.85 2.36 12.96 1.20 18.21 0.64 16.36 1129.26 .~1lf~
7.94 2.33 13.04 1.18 18.30 0.63 16.38 1129.46 !&fiffJj1Jt~
8.16 2.27 13.23 1.15 18.44 0.61 16.41 1130.28 &¥ZJS:l@1Jt~
8.67 2.13 13.47 1.08 18.76 0.58 16.46 1131.44 iI't~1lf~
~1i.:kR~~~~~.~~~~~~~li+~&¥~~m~~mA:kli~~1Jt
~Z~~~#'~#~J!~~1Jt~~~m~~~#~$~~#o
Ef:I1i. 5.3 mift ' ~*'1-~J!~iIl:~~«:r:&liiJlri:/iili~#:k'l1Jt~.It~~Pffjjiff
11r1' :tmJ2till:~:kli1Jt~~:fr~~«:r1J(~.It~jf.i!¥ ' JtIJ N =12.96'" P=18.21 ».K=16.36' iiUmMEIllU~:kli~.~1129.26 0fT ' &":kli~~~~iIl:~i!¥' JlU:frJ!~~tlfEJfll:J.tt1J[]~ N = 13.67 ... P= 18.76 If<. K= 16.46 , jl;mMEIllU«:r:klire:l:3P*11[]~ 1131.44 0fT" 0
:tm*:n~#~~~«:r1J~3P~ibMf' Jllj~JtJN~;fJJlM~B':Jn~#~~~iI't~~«:r
:&liim:il:3PMlz~ib' :tm1i. 5.4 , {£ K=O i!¥' P. N ... Pp If<. P, ~~{§'~itJ«:r
tf!f~T ' ~:fr~~{£::ffllJn~#:kli1J~.It(fJ"iIl:~~:&liimlt 0
EI31i. 5.4 0fift ' :fr~~:&liimIl:~MEiJlUif:J:k.ft~.WMifJE*'f:kEJJl~lta~ifiAJ'
ffa.!tf1.J1J' 'ii'*li1J(#r::f~ffJj, tm~ZJS~1J(~ 8.16 5G./0R ' rmn~*,HJl~ PN=18.5, Pp=9.4 JtJfi~R!I ~m PN=2.00Pp JlU~~:&liiffll:~ N=13.23 , P=18.44 0fT ' tm*: PN~~iiU PP *1J[]~ 18.5 x/0JrMf ' Jllj~~R!I~E13 PN=2.00Pp ~~ PN=1.00PP , Jft;i!¥P~~1J~l:7r[zgiiUJ.tt1J[]n~#:kli1J(~.lt, mQ{:fr~~tlfEfflll:-t!!~~ N=13.23' P=14.23 0fT' :kli~I:1l'E13 1041. 74 ~3i 1034.84 0Jr 0
:tlO*: N. P -=~~B':]t!tl~R!I~~k:~~ (~; =1), ii'ii:fr~~1J~~T~,
~#:k.ft1J~.lt3P~~p,[zgii'ii:fr~~«:r:&liiffl:l:-t!!~Z*W'~:kli~.~~Z
~WoOCZ':fr~~~~«:r~7r'~#:kli~~.It3P~*1J[]':fr~*tlfEmlt~:k
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8.16 18.5 9.4 5.0 2.27 1.15 0.61 13.23 18.44 16.41
8.67 18.5 9.4 5.0 2.13 1.08 0.58 13.67 18.76 16.46
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1129.46 401.99 3191.80 495.17 2696.63 J&~~1lt~
1130.28 402.81 3286.93 500.15 2786.78 &:f.L?:ltJfJ~
1131.44 403.97 3502.42 511.54 2990.88 it~1lt~
l:~* ~f!-JJ{1*-'frfi:kEfJ ~~!uttllliHEmJif1JIl{f:jmil: ' ffjjtllliHE~gjG*J{Ij~
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JtIJ~ 12.38% ' m5l.tllliHE;fIj~~:kEiJ(~~* 0 ~J!t:kE1Jl~t\l:Tr' 1IIIiHE;fIJ1iii:~JiftJl] , :kE~~t\~1f;flJHIII 0
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y Jl =O.6P-O. 037pa
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mIil5.8m~, 'i"~: =4.00 ~~~~1i!li}fli:~ 27.28 0ff' EE1i!li~Ej.lJT1~
tBmr.~~143.36 0ff ' tm*E1J'(~Q.( 8.35 5f;/0FfiH"jf., Jl.tl~~fIt~1l97. 06
5f;/0~ffiillE*'t~*~ 911.16 5f;/0~ cap 27.28x8.25x4), =:'i~§~z~n
285.90 5G/0:~' IlP~1i!lillEflj~ ,fjXli'llit~RJQ.(3Jt~;tE ~; =3.22, 1.50l!z1.22
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iii 5.9 ~P~~it/f'1m11UtrltT1&~~1i!lim.it'&" ~; 7t JJU ~ ~ 0.45,
0.35, Q.30 ». 0.26 ~, ;lta~~l'81i!limii7tJJU~ 2.03 .. 3.38 ..4.08 lJ.4.57~fTo
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Yp= -6.90P+69.471/ NYx=10.13K-0.29K2
III 5.10, III 5.11 :&1iI 5.12 f!P~J:jlij:::iI:;B'jIllM 0
III 5.10 » 1iI 5.11 7tZU~ N. P =~~;ff/f'IPJ1JmltT1&~~1i!limii' &"N~~~*.E1llmlt~ 3.5 ~iilwl~1i!liml:~~ 10.13 ~fT' ITif1llmltit 2.5:& 1.5 ~1&~~1i!lim:l::~~ 12.55 ». 15.95 ~fT 0 &" P ~~~*.E1Jmlt~
2.5 .. 1.5lk. 1.0 ~JlUiil~~1i!li}1ll:7tZU~13.54'16.94lk. 19.14 ~fT' jfjj
=(it:j:r~~R!I~it 10 -¥1fLQ{T~~IIJi#4-J:fr ' ~~ N. P =~~l'81llmtjlJ15ld~
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J::~fBJjjUllj , {fi1ft!IHljfr.Il**~ , ~1JIBrr~~irimi\(;~~iri~ , ~1J;ff;if'ffl"lt!j
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Y=686. 03+ 6.51N+ O. 6P-0. 046W-0. 037P~ (R = O. 6190)
fOiJt:lH;kfF*E~~wHI~:~ 0
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-0.29K2 (R=0.7952)
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PO. 041P -al(O. 09P-0.45V P ) + alS(O. 049P -0.49v p~ +1.2285-
(K=O, al= ~: )
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K=17.46+a3(I1.966_5~~97) (N=O, a3= ~:)
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92,322 15,620 76,702
162,631 53,575 109,056
151,5761 49,924 101,652
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213,141
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(2)~fjH€ril:~Q{~~Wlftilltlr-J"t'<* 0
(3)M:§ Dt'<iHINi1flill!R~D it:JJkil: 0
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f{t~ 1. 2 ...~JJ.-1'- %*-ji1; .,t.·ft:ifj
C.I'f'I.tL: =f~~)
I
I41 1.2 101.7 0.4 6.0 0.69 1.89 8,730,256
42 1.4 100.4 0.5I
6.1 0.67 1.84 3,040,783
43 1.5I
95.6 0.6 6.0 0.64 1.75 9,349,574I
44 1.7 101.4 0.7 6.5
I
0.67 1.84 9,690,643
45 1.9 92.2 0.8 6.1 0.61 1.67 10,003,381
46 2.1 107.4 1.0 7.2 0.70 1.92 10,303,250
47 2.4 116.2 1.2 8.1 0.76 2.08 10,649,435
48 2.7 112.1 1.3 8.0 0.73 2.00 11,031,341
49 3.0 148.7 1.6 10.4 0.91 2.49 11,392,200
50 3.0 181.2 1.6 12.1 1.03 I 2.82 11,479,139
51 2.7 134.9 1.6 9.7 0.81I
2.22 11,935,400
52 2.7 196.3 1.6 12.9 1.05 2.88 12,253,500I~#*iJJjt : (1),1{t\.[f! "Taiwan Food Balance sheet"
(2);~.Atlf(ii'51&FQ(mr~&Fi&J1% "&F~AtI" I1P~l%i&.?
t1~g.rB':J&F~Atl1Jrl.A1Ui-'fiI'ij0
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Cl:&P&P~AtI ~4-&F&P~AtI) tm'iJA2k.11-'fiI'ij 0
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*•• :~~~~~~~ .~~~*~*~19~
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*i*.ff\lJt : iltJW~7.I<fBZ~l:!fl:&~Jt!l~ *~.~t;¥R1#V\M 43~ilM~* ~ IiililJ : .~1=.~i$it'<Z7t:#T * ••~fr¥R32M 49~ 12 Jj
~~~:.~.~~~~n~Zm~ .~~IT*~7~2~ 43~
#I!I~ ~ iffiil!!ilff : *.H.1IlJ!~:ll:i:~_ .~liJfJ'E 115lli 2M 51 ~ 6~#I!I~ ~ ~gc* : 1'rn1E:lilli~:ll:i:~_ .~liJf~ 11 t!i1M 51 ~ 3~~~~:.~7.I<fB1=.~~~#~~~~m:i:z@~7t~ .~~~*~~=m
.~~~*~*~.~@~m~m ~~7~
#~~:.*~~~~~ml:!fl~~~:lillim:i:z~~7tw
.tJJ~:TI:*J!*~!t~f-l!~liJf~m 49 ~~*~:Mw~M~~~~~fl~~~~m:i:z@~7t~
.~~:TI:*J!*~.~@~liJf~ffl 50 ~Jerome. C. R. Li: Introduction to statistical inference I. 1957
Statistical inference II. 1964 Edwards Brothers.
INC. Am Arbor Michigan
E. O. Heady: Economics of Agricultural Production and Resources
use, NewYork. Printice-Hall INC. 1952E. O. Heady &. J. L. Dillon: Agricultural production function
Ames Iowa 1961T. A. Bradferd &. G. L. Johnson: Farm management Analysis, John
Wiley & Sons INC, New York 1953Richard H. Teftwich: The price system and Resources Allocation,
Revised Edition, New York, Holt Kinehart &
Winston. 1961S. Carlson: A study in the Pure Theory of Production, 1939C. E. Bishop & W. D. Tonasaint: Introduction to Agricultural
Economic Analysis. New York.
John Wiley & Sons. INC. 1958
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w. Y. Yang: Method of farm management investigations FAO.
1958
R. C. D. Allen: Mathematical Analysis for Economists Macmillan
Co. Ltd. London, 1956
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AN ECONOMIC ANALYSIS OF THE
RELATIONSHIP BETWEEN THE INPUT OF
CHEMICAL FERTILIZERS AND OUTPUT
OF SOYBEAN IN TAICHUNG
AND KAOHSIUNG AREA.
by
Yuan line Yang
SUMMARY
Production function expresses the functional relationships
between resource inputs and product outputs. The main purpose
of production function analysis is to compute physical input
-output coefficients for: (1) farmer's guidance in the use of
available but limited resources and (2) indicating optimum farm
organization or resource use. The farmers in Taiwan indeed
have been conscious of the benefits of applying chemical fertilizers
but how to use them effectively, economically and safely is
really a big problem.
This paper therefore is to be devoted to the studies on the
optimum application of fertilizer for soybean production. From
the view point of micro-economics, it is expected that the most
economical amount inputs of fertilizer and then optimum profit
obtained could be arrived by using a appropriate soybean
production function. Theories and methods used for this analysis
are from production economics. They include: (1) The analysis of
input-output relationship curves with more than two variables
(involving the prediction of soybean yields, production surface,
marginal productivity, iso-product curves ·and maginal rate of
substitution), (2) Single variable input-output curve analysis, (8)
Least cost line of fertilizer, (4) Economic optimum of fertilizer and
(5) The practical application of the results of this analysis.
The primary data used in this analysis were from the experi
ments of soybean production and fertilizer conducted in Taichung
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K= 17.46+aa(1O.948-54. 052/yN)
K= 17.46 + a3(l1. 966-59. 897/yP)
and Kaohsiung Agricultural Improvement stations in 1963, Based.. --
on the primary data, results following findings were obtained:
1. Soybean -production function:
Taichung: Y =686.03+6.51N+0.6P-0.046Ns-0.037p2
Kaohsiung: Y =727.47-6.35N-6.94P+10.13K
+62. 70vN+69.47YP-0.29K2
2. Iso-product curves:
Taichung: N =70.76±5j796.8268+0.5216P -O.0324p2_0.86956y
Kaohsiung: N = 163.31-1.0929P+ 10. 9401y'P-O. 15748y
±9.874j138.936-1.0929P+ 10.9401YP-O.15748y
(K=O)
K= 17.46± lOj28.1337-0.2189N+2.162y'N -0.03448y
(P=O)
K= 17.46± lOj28.1337-O.2189N+2.162YN -O.03448y
(N=O)
3. Least cost curves:
Taichung: N=70.76 -a(6.522-0.804P)
Kaohsiung:
N= p0.041P-al(0. 09P -0. 45yP) + a12(0.049P-0.49y'P+ 1.228)
(al=PN/PP )
(aa=PK/PN)
(a3=PK/PN)
4. Economic optimum of fertilizer nutrients:
Talchung: N= 70.76 -10. 87'YN
P=8.1l-13.51'Yp
Kaohsiung: N =982.82/('YN+6.35)2
P = 1206.87/('Yp+6. 94)2
K=17.46-1.72'YK
('YN=Pr-/Py , 'Yp=Pp/Py , 'YX=PK/Py )
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