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~ Y=f (C)

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QX; Y =f (N.P.K)

J:it N.P.K %f':~~"~" ~1t~~E*'l-:=:~~0 Jti:~~Ul§lt~P~*~7};j)j'

*li~~~!lE~=.~~zM.t~%ijT~Jfl~ffi~oMtm~*liti~*'l-=.~~

B':J~~im. (Soybean crop production function) QX;m:ffl~E#1iZJJIlE!Jl~

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F 100­

1 %

m ~ 441,007\ 1 I 441'0071

1 t ;

!I m! 774 256! 26 ! 29,779 2 .6330 1. 931~', I I' I '

N 477,58d 2 238, 790j 21.1132"*1 3.369

P 100,823 2 I 50,4121 4.4573* I 3.3690:

K 26,7861 2 13,3931

1. 1842! 3.369°1

NxP 27,048\ 4 6,7621 0.5979 Ii 2.7426,

NxK I 35,885: 4 I 8,971! 0.7932 2.7426

P x K I 38, 9031 4 I 9' 72611

0.8599 I 2.7426

NXPXKI 67,231j 8 I 8,404 0.7431 I 2.3205

~ ~ I 294, 0491 26 I 11'31°1'

~~.~12Sl 11,509,3121 53 I

2.5574­

5.5263

5.5263

5.5263

4.1400

4.1400

4.1400

3.2884

fit%

2.5574

5.5263

5.5263

5.5263

4.1400

4.1400

4.1400

3.2884

1.9313

3.36901

I

3.369°1

'3.36901!

2.7426

2. 74261

2.7426!

2.32051

I

0.3545 I

1.4377

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20,085!

51, 5381

66, 9601

42, 6731

3,118I

12, 6451

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I12,284

1

8,79,

2

2

2

4

4

8

4

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522,2091 26!

103,075

1133,9201!i

85,3451

NxP

NxK

PxK

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50,58°1

38544, INXPXK

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(1) =i7CffiJltY=a+bN+CN2+dp+ ep2 ••••••••••••••••••••••••••••••••••••••••••••• (2.1)

(2) =;jzf9.!mf(Y =a+bN+CYN +dp+eyp (2.2)

(3) m-g.~M

Y=a+bN+CN2+dp+eyp (2.3)

Y=a+bN+CYN -I-dp-l-ep'' (2.4)

J:ffijeYAtm*t:E$J.lU(J'~jN.P~~~. , {~;~~1f~~!IWJ~M 0 tm*1f~JJl:q{~,

Jl.UIM€r4lB~ijt h!liij.J!~ 0

P.JTQ],~e-g.:!E~!mtt~ , :StlltfRJ~tr':i~fi~~~3lt1±l ' ~~Deviation from

Model ~'*5E~ , j!5Ejft~1f~~M:t0:!E~W;jf( 0

.l:j:r#f'Ftf:j:!E~[ll;jtt ' .R~1€ N.P =~*~~HVJIZSI* , ~RJ~~~Wi~~3ltl±ltm-F (2.5) ~~ (2.8) i~ , ~~R*-!! Deviation from Model) ~~5E

5@l±ljft~1f~"P:.M:~:!E~~!IllC0

.l:j:r#f'F : Y=686.03+6.51N-O.046N2+0.6p-o".037p 2

(R=O.6190) (2.5)

Y=697.58-0. 038N+ 26,449y'N + 4, 348p- 21, 043yp

(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

-7-

*- 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:

-8-

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'(*~~~~~

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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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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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880.74953.04967.34923.64

W3086

862.W934.00948.70905.00

W1222

727.47799.77814.07770.37

8~7 59

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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

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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

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10

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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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*'~*PJ!~f0~~*~K~oN=100rrzmr,NJ!~~mt®*roti~t

f0~V}.1~~I'f:TJ.:7T 0 ~m'! 100rrz{&~P~~'ltJ.:7rQ(~¥iJ~jgrf.ti N=24 {&X

~'liT~ 0 iii 4.6 * P=lO 0rrzf!f' Pii1J[]Jl.IJ~:i:/)),fi1;~J.:7T'~m'! 10 0JT{&~'IiJ.:7t-~-Jlt:jg~:i:1,J; P=25 iID{&~'liTI~ 0 .=:~ P tYg~~HB~Z iElIJli't~{~*, Y=f (O.P.O) ~ Y=f (10. P.O) tY:Jm:w.*~mr~~ Y=f(O.P.l0)

®i8~ , Mc~NJ!~f0~~~K~~~* 0 ~~fil4. 7 J.:'=:~Kf0~~HB~-W[ZSl

KJ!~J't:J*1J!liID~t~i!tY:JJ.:7l~-Jlt:jg.~:i:1,J; K=17 1&X;'a;i!f0T~ 0 11l?~'=:

~~~HB~f0iE~i't~~~z,~Q(~~P~~f0~~*~NJ!~,~Q(jg~~

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- 29-

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~ .. tm.ZN•• 'mJ;ltf!l!~#1'iJQ(.m~M~'M~0~1i!lim.p=~,

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-30-

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- 31-

E!rkEt£mlm{!(RfQ{*~:='JJ:*~%:l:t~ntlimil:tr'~:k_~t£mE!ll~' :klllil 4.8

~f;Ylj, ~NRPtJ'~j~ei5-l:t~~1: 1 ~,'lltlj;£Efi%';iij Nap J:~I±I N=K J'B-Wi*~ OG, l;( OG fFfi%';[ti Nap ® ~iil[z(s1ID OEFG , miM:z(siii~t£mlm:fI:r5(J'B

LL EllJ~ , J:J,jJft~N ~ Pft:\1rl:t~~ 1: 1 ~~:kEt£~E!Il~ 0 fI1lJmfL~Q{ Oy

*HrfFil§iili:~~lm Nap ®ljSlm~t£~lmJ'B:X~ , om;}f:J\'.:'ln~fI1l N. P !81rl:t~

tft[mliT(t:i:kE~~EI!I~ 0

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N=30 ~, P=N ~~,tfJ:7f¥ N=40 ~RP~;~TI(~' mil;( P=O.lN ~rzffii

flf.Hjt~, 13.NAA300JTz1ffiiJ.{i(~~~~~{tB-=~0 mQ{N~*lUUIlj>

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-32 ~

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~tr~~ttfxf'F N.P. K :=:~~tE~fP1!E~.Jt~»lIimtTtt:T~~IffH~' 7IJ~T

OO:=:l1rpo iii 4.11 fflDt K=O~, Bi31t~P.N-=~~tE~fP1!El~Jt¥1iilim.l:

Ttt:T~i1l'i:rlH~ 0 N~~#lH~~j)'ltt' .Qtl P=1.5N ~~4i3i:~{if!-=~~[*i'P=N~,,*rp , P=O.5N *,,*T ' ffffJ2.t P. N -=~~tE~fP1ftl.~.Jt¥1iilimtTfJ'g~~

Etil~Q( P=1.5N ~{ti~~0 iii 4.12 .QIJl!'ifk: P=O ~J2.t1m K. N -=~~tE~

fP1~El~.Jt¥1iilimtTtt:T:1E~iI!I~ 0K=1.5N ~tE N=13 J2.t1~U!t~tI1~{if!-=~'

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mr~' ~3I~1I'tjg~t~~ K=N ~1§~1Il€~' 1tf.. N=13 Q{1&~ K. N -=~

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f'FN.P~K:=:~~tEl!'ifk:.Jt~»lIim.Ttt:T*E~~I1!I~'.Jt~~~:1E~I1!I~tt:T

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-34-

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~'

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m~~T-jjfrnu1k.o

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~? ~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:

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~~~~~tt:r~~,~~~~~~~itZm~®au~o

~1Jl1:~tt:r[ij]~'••aB~1::;}~~~:

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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

- 35-

4"

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Jl, :=8-1j.

I !"N ::/4.."" ~

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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

-36-

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

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- 37-

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-38-

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~

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J!61-tIIllffl:l: o

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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 :

- 39-

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

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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

-40 -

~~~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

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8.16 2.27 13.23 1.15 18.44 1,041.74 2.27 13.23 2.27 14.23

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1,036.92 1.38 16.45 1.38 17.43 1,045.68

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2.5 1.5 0.5 12.55 16.60 16.94 1126.64 399.17 3257.23 531.10 2,726.13

2.5 1.0 1.0 12.55 15.74 19.14 1128.07 400.62 3269.06 540.64 2,728.42

2.5 1.0 0.5 12.55 16.60 19.14 1128.74 401.27 3274.36 479.93 2,794.43

1.5 2.5 1.0 15.95 15.74 13.54 1125.64 398.17 3249.07 599.90 2,649.17

1.5 2.5 0.5 15.95 16.40 13.54 1126.29 398.82 3254.37 529.19 2,715.18

1.5 1.5 1.0 15.95 15.74 16.94 1132.61 405.14 3305.94 531.02 2,774.99

1.5 1.5 0.5 15.95 16.60 16.94 1133.26 405.77 3311.25 470.30 2,840.95

1.5 1.0 1.0 15.95 15.74 19.14 1134.71 407.24 3323.08 479.85 2,843.23

1.5 1.0 0.5 15.95 16.60 19.14 1135.36 407.89 3328.38 419.14 2,909.24

j. 5.10 $}Pfl:fk.{1~~-t.;ijt~;.~~m"'Jt..ffi~'l*$..

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7.85 18.5 9.4 5.0 2.36 L20 0.64 12.96 18.21 16.36

7.94 18.5 9.4 5.0 2.33 1.18 0.63 13.04 18.30 1&.38

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

ffE illU ~:1 tllliHE~Jifnil~$ffi 1JIIi1ii'!1!""~1JIIi!llJjrl!!"J~:kIi~il: 'OiIi ?&Kg/ha ~il: I~fl7G/0 ft/0fJi. ft/0fJi.

Kg/ha I fJi. .~

1129.26 401. 79 3154.05 492.73 2661.32 it{!ff)H~

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~

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YN = 6. 51N- 0. 046N8

13J~ , 1IIIiHE~:kEm:i:W P ~#IYIB':jmmf*9l'HIEB (3.1) 5t31t1{l> 0

-51-

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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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0.35, Q.30 ». 0.26 ~, ;lta~~l'81i!limii7tJJU~ 2.03 .. 3.38 ..4.08 lJ.4.57~fTo

~~~t$f;i;f'F1iTQ{~ (2.2) iI:;*~1i!liIE1&*E~ii~1IZU=.~~Ml'8 ~1*tmT:

- Yn= -6.35N+62.701/ N

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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-54-

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~1II!im N=13.23, P=18.44 Jj( K=16.41 0fi-ffijfiJ~::k.£jP130.280JT'

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fOiJt:lH;kfF*E~~wHI~:~ 0

Y =727.47-6.35N-6.94P+l0.13K+62. 70YN +69.47y P

-0.29K2 (R=0.7952)

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24.37 0JT' P~~~ 25.06 0fr' K~~~ 17.46 0iT' .~~.it~0t&1,141.89 0Jr 0 ~ij~*4..:.::.~~tJfi'i~Wii:l§g~ (15"N20%) 3&!$UiU5 (15"P18%)2k~At~ (15" K60%) Jltl.*:l:lf!m4.i0~1:.~ 918.79 0J?' *R~tilamwa~~353.8 0rr·, 3&!iilfi~U5 45.05 0JT 0 7i?it:li:tl!.l!\[4.i0t&:30.~ 1,141.89 0iT~tiIa

mWii:~~ 120 0JT' 3&!~~~ 138.8 0iT' i';1t~ 28.3 0iT' J1t;¥fjX~{J;J.FiJ

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- 56-

PO. 041P -al(O. 09P-0.45V P ) + alS(O. 049P -0.49v p~ +1.2285-

(K=O, al= ~: )

54.052 PIr)K=17.46+as(10.948-l7N) (p=o, as= PN

K=17.46+a3(I1.966_5~~97) (N=O, a3= ~:)

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N=982.82/(rN+ 6.35)SP = 1206.87/(rp+6. 94)2K= 17.46-1. 72rlr

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______1 - IfTI~L_ _ cc _

42 1 28,225 17,4261 617 1121,5861 27,501 94,0851 139,012I I[I,

43 i 30,048 20,3101 676 101,688 10,074 91,614 121,998I I

44 I 34,510 24,151 700 117,585 4,528 113,057 141,736

45

46

37,5051 26,442

41,029 33,054

705

806

93,667

104,4

l7,4001 86,267

I

6,6761 97,782

120,109

137,512

54,438: 53,011 974II

55,223: 52,6451

976

47

48

,19

50

51

52

47.8,

53, 7851

I 59,66~!i

59, 582t

41,682

44,451

52,653

53,900

870

826

882

905

94,344 12,200 82,144

92,322 15,620 76,702

162,631 53,575 109,056

151,5761 49,924 101,652

69.1 ,6." 53.703

193,6471107,4971 86,150

136,026

136,913

215,284

205,476

153,318

213,141

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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"

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-59 -

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.~~~~ ,m. IT $ hilY ~ 54~ 2 Jj R~

*~m:~~~~~ ~~~~*~*~

~m71 : ~~iDt.n-~ ~ ~ $ ~ *B 51 ~ 10 Jj

~ ~~~~~:~*~Z±~ .~~~~~~m ~~12Jj

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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

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#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

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.~~: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

-60 -

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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