Second,thefarminginputwhichdefinedfdoesnothavetobeonefactoralone.Theeconomicimplicationsofincreasingthef/hratioforseveraltenantinputswillbeessentiallythesame.Ifseveraltenantinputsareincreasedwhileholdinglandconstant,themeticulousreadermayrightlypointoutthatthemarginalproductofaparticularfactormayincreaseiffactorplementarityisstrongenough.Diminishingreturnsmustoperateforallincreasedtenantinputstogether,however,resultinginamarginalfarmingcost(whichincludesalltenantinputs)beinghigherthanthemarginalreturn.
[1].Notealsothatunder
oftheannualyieldthelandownercannotconvertasharecontracttoafixedrentcontracttoprotecthiswealth.
[2].Linearhomogeneousproductionfunctionisassumedhere.
B.IncreasedTenantInputs—IllustratedwithInputAdjustmentsforMultipleTenants
Theimplicationofincreasedfarmingintensityissoimportantthatitdeservesstillanotherexposition.Treatingtenantinputasanexplicitvariable,weatthesametimeexpandouranalysistoseveraltenants.Afewsimplifyingassumptionswillhelp.Letusassumethat(a)thelandowneremploysalargenumberoftenantsonhislandholdings;(b)thetenantsarecultivatinghomogeneousland,producingthesameproductwithidenticalproductionfunctions,andthustheinitialequilibriumrentalpercentageforeachtenantbeforethesharerestrictionisthesame;and(c)thereisonlyonetenantinput,saylabor.
Infigure7,totalproductismeasuredalongtheverticalaxis,andthenumberoftenantsortenantworkers,t,ismeasuredalongthehorizontalaxis.Thecurve
isthetotalproductoftenantworkers,withthetotallandholdingofalandownerheldconstant(withassumptiona).Itsshapeexhibitsdiminishingmarginalreturnstotenantlabor.ThecurveWtrepresentsthetotaltenantcostoffarming,withWrepresentingthewagerateandtthenumberofworkers(withassumptionc).Underapetitivetenantlabormarket,Wtisastraightline.Thecurve
isthetotalrentcurvegiventhelandowner'stotallandholdings.Itisderivedbysubtractingthetotaltenantcost,Wt,fromthetotalproduct,.
Withoutlegalsharerestriction,theequilibriumnumberoftenantsemployedwillbeot,wherethetotalrent
isatamaximum.Withotoftenantworkersemployed,thetotalrentwillbetb(=ta—ti),andtherentalpercentagechargedforeachtenantequaltotb/ta(withassumptionb).Inequilibrium,themarginaltenantcostequalsthemarginalproduct,i.e.,
=W=
Asaresultofthepercentagerentreduction(sayfrom70percentto40percent),theshareconstrainttothelandownerisrepresentedbythecurve
,whereQisthetotalproductand
istherestrictedrentalof40percent.Thatis,
is40percentof
ateverypoint.Thecurve
,ontheotherhand,representsthetotalshareforthetenantsastheirlaborinputvaries.Undertheconstraintof
andwithnoadjustmentinfarmingintensity,thelandowner'stotalsharewillbetd,andthetenants'sharetc(=ta—td).GiventhetenantcostconstraintofWt,however,thelandownerwillincreasetenantinputtot',whereboth
and
aremaximizedsubjecttotheconstraintsof
andWt;thatis,Wt=.
Employingtenantsot'onthegivenland,thelandowner'ssharewillbet'g,andthetenants'sharet'e.Tothelandowner,thetotalrentcurvesubjecttotheconstraintsof
andWtwillbetheheavyline
,whichriseswith
fromotogandkinksdownwardalongwith
Theportionof
fromgtokmeasuresthedifferenceof
andWt,whichmeansthattheconstraintofWtexceedsthecon-straintof
inthisportion.Thus,
hasadiscontinuousderiv-ative,andthemarginalreceipt,
,isundefinedatg,where
isatamaximum.[1]Ifthelimitofthephysicalconstraint(pointjinfigure)isnotreached,maximum
isattainedwhenWt=[123b],orthealternativeearningoftenantlaborequalsitsineasashareof
(seepointeinfigure).Restingatg(ore),therefore,isanewequilibriumbasedonthepremiseofrentalmaximizationsubjecttotheadditionallegalconstraintof.
Atthisequilibrium,themarginaltenantcost,
=W,isgreaterthanthemarginalproduct,.
Ifthetenants'alternativeearningsarelower,withwagerateW',thetenantcostconstraintwillberepresentedbythedottedlineW't.Giventhis,tomaximizeinethelandownerwillonlyallowtheincreaseintenantinputtot",where
isatamaximumandwherethemarginalproductoftenantlaboriszero.Withthelimitofthephysicalconstraintingfirst,theconstraintW'tisnolongerrelevantforthefarmingintensitydeci-sion.Thepeakof
willnowbeatj,wherewehave
Inthiscase,however,thetenantswillbereceivingresidualsovertheiralternativeearnings;andwithpensatingpaymentstothelandownerassumedaway,thenewequilibriumundertheconstraintof
beesundefined.Imaginethesituation:inducingtenantinputtot",thelandownerwantstopause;however,otherpotentialtenantseknockingathisdoor,offeringhimlargersharesandbribesforthetenancy.Nonetheless,theconditionwithW'tisnotimportanttoouranalysis,foratanyratefarmingintensityisincreasedundertheconstraintof.
Thoughthemarginalproductoflandcannotbeconvenientlyderivedinfigure7theeconomicimplicationsofthelegalsharerestrictionforresourceallocationareexactlythesameasthosederivedintheprecedingsection.Undertheshareconstraint,resourcesaredirectedtotenantfarmsfromownerfarms,fromtenantfarmsunaffectedbythesharerestriction,andfromenterprisesotherthanagriculture.Alternativelyandconcurrently,thetenantnowworkslongerhours,cultivatesthelandmoreintensively,andappliesmorecostlyfertilizers.Theextraresourcesallocatedtolandbytenantsontenantfarmsyieldlowerreturnsthansimilarresourcesemployedelsewhere.