第27章 《佃農理論》英語原著 (21)

[24].Ibid.,p.111.SimilarconclusionsarealsoreachedinAmartyaK.Sen,"PeasantsandDualismwithorwithoutSurplusLabor,"JournalofPoliticalEconomy（October,1966）,pp.445-46.

[25].Johnson,"ResourceAllocation,"p.111.

[26].Ibid.,v.,pp.118-21.

[27].Ibid.,p.118.IntheassociatedfootnoteJohnsonwrote:

Ihaveestimatednetrentsoncrop-share-rentedfarmsinIowafrom1925through1946.From1925through1934netrentsonshare-rentedfarmsaveragedperhapsadollarperacrelessthanoncash-rentedfarms.From1935through1939thenetrentswereroughlythesame.From1940through1946netrentswereatleastfourdollarsanacremoreonshare-rentedthanoncash-rentedfarms.

[28].Ibid.,pp.119-20.

[29].Ibid.,p.120

[30].Ibid.,p.121.

[31].Ibid.,p.118.

[32].Ibid.,p.120.

[33].Ibid.,p.123.

C.ACorrectionofError

Toclarifythebasicdifferencebetweenthetheoryofsharetenancyderivedinthelastchapterandthetax-equivalentanalysis,asimplegeometricpresentationwillsuffice.Thisisillustratedinfigure5,whichisanexpandedversionoffigure4.Wearealreadyfamiliarwiththemarginalproductoftenantlabor,

,andthemarginaltenantreceiptundersharerent,

（1-r）.Accordingtothetax-equivalentapproach,equilibriumisatA,withtheamountoftenantinputequaltot1.

Infigure5,assumeagivenlandareawhichweholdfixedfor.

Theresultofthemoregeneralsolutioncanbederivedasfollows.Givenr=0.4whichdefines

（1-r）,ift2oftenantlaboriscontractuallystipulated,thelandowner'sshareofthetotalproductintheformofrentequalsareaEDBC,andthetenant'sshareequalsOECt2.Asdrawn,thetenant'sshareisstillhigherthanhisalternativeearning（areaOMBt2）,withareaMEAgreaterthanareaABC,whichmeansthatthetotalrent（areaEDBC）willbesmallerthanthatofawageorafixed-rentcontract（areaMDB）.Giventhemarginaltenantreceipt,

（1-r）,thecorrespondingaveragetenantreceiptwillbe（q/t）（1-r）,whichis40percentoftheaverageproductoftenantlabor,q/t,ateverypoint.Inthiscase,thelandownercansuccess-fullystipulatethatthetenantworkuptot3wheretheaveragetenantreceipt,（q/t）（1-r）,equalsthewagerate,implyingthatthetenant'sinefromfarmingisequaltohisalternativeearning.

Withtenantinputt3,however,thetotalrentreceivedbythelandownerwillbeequaltoareaMDBminusareaBNP,anamountofrentsmallerthanthatofownercultivation,awageorafixed-rentcontract.Tomaximizehiswealthwithasharecontractsubjecttotheconstraintoftenantcost,thelandownerwillthusraisetherentalpercentagetor*.Thechoiceofr*lowersthemarginaltenantreceipttothedottedlineGF,withareaMGKequaltoareaKBLThecorrespondingaveragetenantreceiptwillbe（q/t）（1-r*）,whichnecessarilycutsthemarginalproductoflabor,

,atB.Atthisnewrentalpercentage,thetenantlaborstipulatedist2,thelandowner'stotalrentequalsareaGDBI（whichequalsareaMDB）,andthetenant'sshareequalsareaOGIt2,whichisnogreaterthanhisalternativeearning（areaOMBt2）.Theequilibriumconditioncanbeiden-tified:atBwehave

wherer*istheequilibriumrentalpercentage.[1]Indeed,oneofthemainsourcesofconfusioninthetaxapproachisthemarginaltenantreceiptcurve,

（1-r）.Importantasitmayseem,itisonlyillusoryfordecisionmakingunderunrestrainedprivatepropertyrights.

Indeed,acloseranalysisrevealsthatpositionAisnotanequilibrium,evenifwefollowthetax-equivalentapproachtoanalysisofasharecontractandletthetenantmakethedecisionatthemargin.Supposetherearemanylandownersandeachlandownerdoesnotspecifythetenantinputperacre,sothatthetenantcanfarmanywayhedesires.Supposefurtherthatthereisnolawprohibitingthetenantfromworkingformorethanonelandowner.Thereisnoreasonforthetenanttochoosetoworkuptoti（infigure5）foronelandowner.Imaginethatthemarginaltenantreceiptcurvesineachofthesefarmsarenegativelyslopingalltheway.Tomaximizehisinefromfarming,thetenantwillchoosetodispersehisinputresourceovermanyfarmsuntilhisinputendowmentisexhausted,insuchawaythathismarginaline（ormarginaltenantreceipt）fromdifferentfarmsisequal.[2]Inthiscase,thetenantwillbereceivinganaggregateinehigherthanhisalternativeearning,andothertenantswillentertopete.

Permitourimaginationtoreachstillfurther.Supposeeachsuccessivetenantenteringintofarmingworksonseveralfarmsalso,andlikewiseequateshismarginalinefromdifferentfarms.Asthenumberoftenantsincreases,themarginalinefromdifferentfarmsforeachtenantwillfall,implyingrisesinthelandowners'rentalshares.Andtenantswillcontinueenteringaslongastheaggregateineforeachtenantishigherthanthealternativeearning.[3]Given

（1-r）asdrawn,andassumingthatthelandownerscontractuallyacceptanyamountoflabor,petitionamongtenantswillpushlaborinputoneachfarm（onesuchfarmisrepresentedbyfigure5）tot3.Theresulted"overcrowded"tillingimpliesthatrentalsharesarenotatmaximums.orgpetitionagainprevails.Givenhomogeneousfactorsofproduction,wealthmaximizationimpliesthatthelandownerswillchooseamongtenantswhoofferrentalpercentagesashighasr*,whilepetitionamonglandownersimpliesthatitwillnotbeanyhigher.Givenr*whichdefines

（1-r*）,theamountoftenantlaborpetitivelyofferedandcontrac-tuallyacceptedforeachfarmwillbet2.Themarketequilibriumthusreachedoccurswhenthemarginalproductoftenantlaborineachfarmequalsthemarginaltenantcost（pointBinfigure5）.