第17章 《佃農理論》英語原著 (11)

Letusnowreviewthesolutionconditions.Thehighestvalueofrentperunitofland,（q-f）/h,isderivedwhenthemarginaltenantcostequalstheassociatedmarginalproductoftenantinput.Asillustratedinfigure3,giventhehighestvalueof（q-f）/h,thelandsizepertenant（T1）isdetermined,andthecorrespondingrentalpercentage,r,willbear/ap.AtthedividinglineT1,therentperacreofland,thatis,ar,（q-f）/horrq/h,equalsthemarginalproductofland,.

AtT1also,wehavetheuniqueconditionfortherentalpercentage

Thisisidenticalwithourmathematicalsolution,wherewehave

sinceinourmathematicsweassumeonlyonetenantinput,f=Wt.

[1].Theimportantdistinctionhereisbetweenlandandinputsotherthanland.Thesubstitutionbetweenlaborandfarmingequipment,forexample,isnotyetimportantinthistheoryandisignored.

[2].Forsimplicityofpresentation,allvaluesaremeasuredinrealterms.Note,however,thattheannualyield,q,mayincludeavarietyofcrops;giventheirrelativemarketprices,thevalueofeachmaybeexpressedintermsofonecrop,sayrice.Andpaymentsfortenantinputsandlandwilllikewisebeinrice.

[3].Toavoidsemanticproblems,weassumeheretheincreaseofonetenantinputonly.Ifseveralinputsareincreased,asisusuallythecase,therelevant"shifts"toconsiderarewhenq/hincreasesatadecreasingrate.Ineithercase,thetheoreticalouteisthesame.

[4].Giventheappropriatediscountrate,

,andthefutureinestreamfromtheland,Y1,Y2……,Yn,YinotnecessarilyequaltoYj,thereexistsa

,calledtherentalannuity,suchthat

Iftheprivatelandrightisperpetual,wehave

,whereV0isthepresentvalueofland.

[5].Thenotionthatrentisacostofproductionbegan,perhaps,withJ.S.Mill.AndImaintainherethatitisthehighestrentperunitoflandwhichreallycounts,foritisfromthisthatthelandvalueisderived.

[6].Itremainstoshowhowthelastplotoflandbelongingtothesamelandlordisallocated,sinceitmaybetoosmallforonetenantfamily.Oneansweristhatatenantmayberentinglandfromtwoormorelandlordsatthesametime,employinglandmarginsfromboth.Likewise,atenantmayownasmallareaoflandhimself,rentinganextramarginfromalandlord.Thisisevidentintheexistenceofpart-ownerfarmers.Therefore,ifthelandsizeofthelastplotassignedtoatenantfamilyissmallerthantheequilibriumsize,thetenantwillemploypartofhisresourceselsewhere,possiblyoutsidethefarmingsector.

[7].Theterm"landhomogeneity"employedhere,whichpresupposesidenticalmarketlocation,renderstheunambiguouscondition:Giventhesamemaximumvaluesof（q-f）/handthesameratiosoftenantinputstolandindifferentfarms,therentalpercentageswillbethesame.Differentproductionfunctionsassociatedwithdifferentcropswillrequiredifferentintensitiesoftenantinputs.Ontheotherhand,giventheproductionfunction,therentalpercentageandthelandsizepertenantwilldependon（1）tljefertilityoflandand（2）thecostoftenantinputs.

[8].Notethatthepeakofthishigher（q-f）*/hcurvewillbetotheleftofT1.Thisisnotrelevanttolandsizedivision,foritwillleadtoalowerrentperacre.ThedividinglineisstillT1,wherethe（q-f）/h,orthenetreturntoland,isatamaximum.Buttherentalpercentageinthiscasewillbe（q-f）*/hatT1dividedbyq/h.

[9].Thefactthatmostleasesundersharetenancyarenotperpetualhasbeenattackedasinsecuretenurewhichleadstomisallocationofresources.Butitisnomoreinsecurethanthepositionofhiredfarmhandswhoaresubjecttodismissalincaseofpoorperformance.Indeed,atemporaryleaseisaneffectivedevicetoinsureefficientallocation.Theargumentthatnonperpetualleasestendtodiscourageinvestmentisincorrect.Wefindtheperiodofleasevariesaccordingtothetypeofcontractandtheassetholdingsofthecontractingparties,andthefrequencyoftenantdismissalhasbeensmall.Forafullerdiscussion,seechapter4,sectionC.

D.orgparisonwithFixedRentandtheMarketCriteriaofShareContracting

Anumberofquestions,boththeoreticalandempirical,relatedtosharetenancydeservefurtherinquiry,andIshalltrytopressthemintheremainingchaptersofthisbook.Inthissection,however,answerstotwoquestionsaresought.

Letusbeginwiththequestion:Whatarethedifferencesbetweenfixed-rentandsharecontracts?Underprivateownershipofresources,thebasicdifferencebetweenfixedrentandsharetenancyliesinhowthechosenlabor-landratio（ortheratioofnonlandinputstoland）isexpressed.Withfixedrent,giventherentperacre,thetenantstateshowmuchlandhewillemploy,andhealonedecides-subjecttotheconstraintofpetitionaswithsharetenancy-theamountofnonlandinputstobemittedforeveryproductionrun.Undersharetenancy,however,thelandownerandthetenantmutuallydecidetheintensityofnonlandtolandinputs.Ineithercase,thewealthmaximizingvaluedeterminesthelandsizeperfarmaswellasotherinputsemployed.Sincethesetofconstraintsfordecisionmakingisthesameforthetwotypesofcontracts,thesameresourceuseisimplied.