第16章 《佃農理論》英語原著 (10)

Undermutualagreements,economictheoryimpliesthatthetotalamountoftenantinputscontractedwillbetheamountwhichyieldsthehighest（q-f）/h,orwhichyieldsthehighestrentperunitofland.Sinceinfigure3themarginalfarmingcostalwaysequalszero,thehighestvalueof（q-f）/hcanbederivedasfollows.Foreveryupwardshiftoff/hasaresultofincreasingthestipulatedamountoftenantinput,thereisassociatedanupwardshiftofq/h.Theformerrepresentsthemarginalnonlandcost,whichincreasesataconstantrate（i.e.,constantmarginalfactorcostunderpurepetition）；thelatterrepresentsthemarginalproductivityofadditionaltenant（i.e.,nonland）input,whichincreasesatadecreasingrate（i.e.,decreasingmarginalproductoftenantinput）.[3]Thehighest（q-f）/h-associatedwithaspecificf/hcurve-isobtainedwhenthemarginalupwardshiftsoff/handq/hareequal,orwhenthemarginalproductoftenantinputequalsthemarginaltenantcost.Theassociatednonlandfarmingcost,whichdefinesf/h,coverstheleveloftenantinputsconsistentwithproductiveequilibrium.Tomaximizewealth,thecropschosentobeplantedorrotated,andthemethodofproduc-ingthem,are,bydefinition,thosewhichyieldthehighestpresentvalueoflandtothelandowner,thatis,whichmaximizerentalannuity.[4]Therelevantvalueof（q-f）/h,oraveragerent,fordecisionmakingisthusthehighestonederivedfromalternativepairsofq/handf/h.Tostateitmoreprecisely,thehighestvalueof（q-f）/hdefinesthecostoflandperacreasafactorofproduction.[5]

Themarginalproductofland,

—or

infigure2—cutsq/hand（q-f）/hattheirhighestpoints.Theequilibriumlandsizeassignedtothistenant,T1,iswhere（q-f）/hisatamaximum.Maximizingrentperacreoflandwillmaximizetherentalannuityfromthelandlord'stotallandholdings.Withtheequilibriumtenantlandsizedetermined（T1）,theequilibriumrentalpercentageequals（q-f）/hdividedbyq/h（atT下標內容）.Thatis,therentalpercentage,r,equalsar/apaslabeledinfigure3.Giventhisequilibriumpercentage,say70percent,weplotthemarginalcontractrentcurve,

r,asthispercentageof

ateverypoint.

Sincethetenantcontractstopayapercentageofthetotalproduct,asindicatedby

r,thecostoflandisnolongeraconstraintwithrespecttotheamountoflandthetenantwilluse.Tomaximizehisine,thetenantpreferstoemploylandtothepointwhere

iszero（whileholdinghisfarminginputsconstantascontractuallystipulated）.Thelandowner,ontheotherhand,willlimitthetenant'sholdingtoT1,andparceltheremainderofhistotalholdingtoothertenantsundersimilarcontractualarrangements.[6]ThelandownercannotsuccessfullyrestrictlandsizetolessthanT1,sincewithrentalpercentagerthetenant'salternativeearningwillbehigherelsewhereandhewillgiveupthetenancy.

Severaladditionalremarkscanbemade.First,notalltenantfamiliesareequallyproductive.Somewillbeabletoproducemorebecauseoftheirendowmentsofcertain"specific"factorsofproduction,forexample,varyingamountsofknowledge.Inpetitiveequilibrium,themoreproductivetenantswillbetheintramarginaltenants,andthef/hcurvethusdefinedwillincludetheimputedrentforthetenant.Thelandownerscannotsuccess-fullydiscriminateamongtenantsofvaryingefficiencieseveniftherearenocostsassociatedwithdiscrimination,becauseland-lordsemployingmarginaltenants（leastproductivetenants）willbidthemoreproductivetenantsawayfromadiscriminatinglandlord.

Second,eveniflandishomogeneous,thelandsizepertenantfarmmaynotbethesame.Defininghomogeneouslandaslandphysicallyidenticalandhavingthesamerentalvalueperunit-thatis,the（q-f）/hcurvesindifferenttenantfarmsyieldequalheightsattheirpeaks-thelandsizesfordifferenttenantswilldifferiftheproductionfunctionsofthesetenantsdiffer.[7]Thisalsoimpliesthattherentalpercentagefordifferenttenantfarmsmaynotbethesame.Thatis,inmaximizingtherentalannuityofhislandholdings,theownerwillassigndifferentlandsizesandchargedifferentrentalpercentagestodifferenttenantsiftheirproductionfunctionsrequiredifferentintensitiesoftenantinputs.Inequilibrium,givenhomogeneouslands,themarginalproductivityoflandforeachfarmmustbeequalateverymargin,foritisatthehighestvalueof（q-f）/hthatlandsizesaredivided.

Third,thefarmingcost（otherthanthecostofland）maybesharedbythetenantandthelandownerjointly.Inthiscase,thef/hcurverepresentsthebinedcost.Givenq/handf/hasinfigure3,thef/hminusthelandowner'sinputcostwillbelower,thusdefiningahigher（q-df）*/hcurve.Thishigher（q-f）*/hcurve（notdrawn）measuresnotonlythecostofland（rent）,butalsothelandowner'snonlandfarmingcost.[8]Therentalpercentagechargedbythelandownerwillaccordinglybehigher,withanupwardshiftof

rbythesamepercentageateverypoint.Theimplicationofthisisimportant:itdoesnotmatterwhetherthelandownerrequiredthetenanttoinvestmoreinlandandchargesalowerrentalpercentageorwhetherthelandownerinvestsinlandhimselfandchargesthetenantahigherrentalpercentage;theinvestmentwillbemadeifitleadstoahigherrentalannuity.[9]Itfollowsthatforanycontractthetenantdoesnothavetopossesstherequiredamountofinput.Ifwhathehasisinsufficient,thetenantmayraisethefarminginputsbycooperatingwiththelandowner,bysubleasing,byhiringfarmhands,byborrowing,orbyjointtenancywithanotherfamily.Moreover,thedifferenttenantinputrequirementsinfarmsofdifferentlandgradesandproductionfunctionswillmatchtenantswithdifferentinputendowmentsaccordingly.