1.Dualitytheory2.Economiceffectsofpolicies(seepaperEvolutionoftheeconomicsofagriculturalpolicypage408)3.Cropinsurance4.Malthusianprincipleofpopulation5.Lawofdiminishingreturns6.Ricardianrent7.Ironlawofwages8.Productivityresidual9.Marketmargins10.Lucascritique11.TotalFactorProductivity12.Pricediscrimination1Inmathematics,dualityhasnumerousmeanings,andalthoughitis“averypervasiveandimportantconceptin(modern)mathematics”and“animportantgeneralthemethathasmanifestationsinalmosteveryareaofmathematics”,thereisnosingleuniversallyagreeddefinitionthatunifiesallconceptsofduality.Generallyspeaking,adualitytranslatesconcepts,theoremsormathematicalstructuresintootherconcepts,theoremsorstructures,inaone-to-onefashion,often(butnotalways)bymeansofaninvolutionoperation:ifthedualofAisB,thenthedualofBisA.Asinvolutionssometimeshavefixedpoints,thedualofAissometimesAitself.Forexample,Desargues'theoreminprojectivegeometryisself-dualinthissense.Manymathematicaldualitiesbetweenobjectsoftwotypescorrespondtopairings,bilinearfunctionsfromanobjectofonetypeandanotherobjectofthesecondtypetosomefamilyofscalars.Forinstance,linearalgebradualitycorrespondsinthiswaytobilinearmapsfrompairsofvectorspacestoscalars,thedualitybetweendistributionsandtheassociatedtestfunctionscorrespondstothepairinginwhichoneintegratesadistributionagainstatestfunction,andPoincarédualitycorrespondssimilarlytointersectionnumber,viewedasapairingbetweensubmanifoldsofagivenmanifold.3Cropinsuranceispurchasedbyagriculturalproducers,includingfarmers,ranchers,andotherstoprotectthemselvesagainsteitherthelossoftheircropsduetonaturaldisasters,suchashail,drought,andfloods,orthelossofrevenueduetodeclinesinthepricesofagriculturalcommodities.Thetwogeneralcategoriesofcropinsurancearecalledcrop-yieldinsuranceandcrop-revenueinsurance.Crop-yieldinsurance:Therearetwomainclassesofcrop-yieldinsurance:Crop-hailinsuranceandMulti-perilcropinsuranceCrop-revenueinsurance:isacombinationofcrop-yieldinsuranceandpriceinsurance4TheReverendThomasRobertMalthusFRS(13February1766–23December1834)wasaBritishscholar,influentialinpoliticaleconomyanddemography.Malthuspopularisedtheeconomictheoryofrent.Malthushasbecomewidelyknownforhistheoriesconcerningpopulationanditsincreaseordecreaseinresponsetovariousfactors.ThesixeditionsofhisAnEssayonthePrincipleofPopulation,publishedfrom1798to1826,observedthatsoonerorlaterpopulationgetscheckedbyfamine,disease,andwidespreadmortality.Hewroteinoppositiontothepopularviewin18th-centuryEuropethatsawsocietyasimproving,andinprincipleasperfectible.Malthusthoughtthatthedangersofpopulationgrowthwouldprecludeendlessprogresstowardsautopiansociety:Thepowerofpopulationisindefinitelygreaterthanthepowerintheearthtoproducesubsistenceforman.Malthusplacedthelonger-termstabilityoftheeconomyaboveshort-termexpediency.5Ineconomics,diminishingreturns(alsocalleddiminishingmarginalreturns)referstohowthemarginalproductionofafactorofproductionstartstoprogressivelydecreaseasthefactorisincreased,incontrasttotheincreasethatwouldotherwisebenormallyexpected.Accordingtothisrelationship,inaproductionsystemwithfixedandvariableinputs(sayfactorysizeandlabor),eachadditionalunitofthevariableinput(i.e.,man-hours)yieldssmallerandsmallerincreasesinoutputs,alsoreducingeachworker'smeanproductivity.Conversely,producingonemoreunitofoutputwillcostincreasinglymore(owingtothemajoramountofvariableinputsbeingused,tolittleeffect).6TheLawofRentwasformulatedbyDavidRicardoaround1809.Itwasthefirstclearexpositionofthesourceandmagnitudeoflandrents,andisamongthemostimportantandfirmlyestablishedprinciplesofeconomics.TheLawofRentstatesthattherentofalandsiteisequaltotheeconomicadvantageobtainedbyusingthesiteinitsmostproductiveuse,relativetotheadvantageobtainedbyusingmarginal(i.e.,thebestrent-free)landforthesamepurpose,giventhesameinputsoflaborandcapital[1]7TheIronLawofWages,isaproposedlawofeconomicsthatassertsthatrealwagesalwaystend,inthelongrun,towardtheminimumwagenecessarytosustainthelifeoftheworker.wagescannotfallbelowsubsistencelevelbecausewithoutsubsistence,laborerswillbeunabletowork.However,competitionamonglaborersforemploymentwilldrivewagesdowntothisminimallevel.8TheSolowresidualisanumberdescribingempiricalproductivitygrowthinaneconomyfromyeartoyearanddecadetodecade.RobertSolowdefinedrisingproductivityasrisingoutputwithconstantcapitalandlaborinput.Itisaresidualbecauseitisthepartofgrowththatcannotbeexplainedthroughcapitalaccumulationortheaccumulationofothertraditionalfactors,suchaslandorlabor.TheSolowResidualisprocyclicalandissometimescalledtherateofgrowthoftotalfactorproductivity.Thereporteddiscrepancybetweenoutputgrowthandinputgrowth9Marketingmarginsaredefinedasthedifferencebetweenpricesatdifferentlevelsinthesupplychain,withdueallowanceforlevel-to-levelproductionconversionrelationships.10.LucascritiqueTheLucascritiquearguesthatitisnaivetotrytopredicttheeffectsofachangeineconomicpolicyentirelyonthebasisofrelationshipsobservedinhistoricaldata,especiallyhighlyaggregatedhistoricaldata.thissimplenotioninvalidatedpolicyadvicebased