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“喆學(xué)（108）：精讀期刊論文
《需求不確定性對(duì)綠色技術(shù)采用的消費(fèi)者補(bǔ)貼的影響》
模型（1）”
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Today,theeditorbringsthe
"Zhexue(108):Intensivereadingofjournalarticles
"Theimpactofdemanduncertaintyonconsumersubsidiesforgreentechnologyadoption"
TheModel(1)"
Welcometovisit!
本期推文將從思維導(dǎo)圖、精讀內(nèi)容,、知識(shí)補(bǔ)充三個(gè)方面介紹精讀期刊論文《需求不確定性對(duì)綠色技術(shù)采用的消費(fèi)者補(bǔ)貼的影響》模型,。
ThisissueoftweetswillintroducetheModeloftheintensivereadingjournalarticle"TheImpactofDemandUncertaintyonConsumerSubsidiesforGreenTechnologyAdoption"fromthreeaspects:mindmap,intensivereadingcontent,andknowledgesupplement.
一、思維導(dǎo)圖（MindMaps）
二,、精讀內(nèi)容（Intensivereadingcontent）
在政府補(bǔ)貼背景下,，電動(dòng)汽車等（略）場(chǎng)產(chǎn)品的供應(yīng)商需同時(shí)優(yōu)化定價(jià)（p）與生產(chǎn)量（q），構(gòu)成價(jià)格設(shè)定報(bào)童問(wèn)題,。研究通過(guò)分析加性和乘性需求不確定性模型（如線性與等彈性需求）,，對(duì)比確定性需求下的決策，量化忽略需求不確定性的成本,。結(jié)果表明,，明確考慮需求波動(dòng)可優(yōu)化政府補(bǔ)貼水平、價(jià)格及產(chǎn)量,，為企業(yè)評(píng)估精準(zhǔn)需求預(yù)測(cè)的價(jià)值提供依據(jù),，揭示僅依賴平均需求決策的潛在風(fēng)險(xiǎn)。
Inthecontextofgovernmentsubsidies,suppliersofoligopolisticmarketproductssuchaselectricvehiclesneedtooptimizebothpricing(p)andproductionvolume(q),whichconstitutesaprice-settingnewsboyproblem.Thisstudyanalyzesadditiveandmultiplicativedemanduncertaintymodels(suchaslinearandisoelasticdemand)andcomparesdecisionsunderdeterministicdemandtoquantifythecostofignoringdemanduncertainty.Theresultsshowthatexplicitlyconsideringdemandfluctuationscanoptimizegovernmentsubsidylevels,prices,andoutput,provideabasisforcompaniestoevaluatethevalueofaccuratedemandforecasts,andrevealthepotentialrisksofrelyingsolelyonaveragedemanddecisions.
加性需求不確定性模型定義為D(z,?)=y(z)+?,，其中z=p?r為有效價(jià)格,，y(z)表示確定性需求（期望值）,?為服從F?分布的隨機(jī)擾動(dòng)項(xiàng)。
TheadditivedemanduncertaintymodelisdefinedasD(z,?)=y(z)+?,wherez=p?ristheeffectiveprice,y(z)representsthedeterministicdemand(expectedvalue),and?isarandomdisturbancetermthatfollowstheF?distribution.
在政府補(bǔ)貼背景下,，供應(yīng)商需基于有效價(jià)格z=p-r優(yōu)化生產(chǎn)量q^*(p,r)和定價(jià)p^*(r),，政府則通過(guò)非凸優(yōu)化確定最優(yōu)補(bǔ)貼。定理1證明目標(biāo)約束在最優(yōu)時(shí)緊致,，確保解的有效性,。通過(guò)對(duì)比確定性需求（以期望值y(z)替代隨機(jī)需求）與隨機(jī)需求模型，分析指標(biāo)如補(bǔ)貼水平,、價(jià)格,、產(chǎn)量及利潤(rùn)、政府支出的差異,，揭示忽略需求不確定性對(duì)決策的影響,，為政策制定提供量化依據(jù)。
Inthecontextofgovernmentsubsidies,suppliersneedtooptimizeproductionvolumeq^*(p,r)andpricingp^*(r)basedontheeffectivepricez=p-r,andthegovernmentdeterminestheoptimalsubsidythroughnon-convexoptimization.Theorem1provesthatthetargetconstraintistightattheoptimaltime,ensuringthevalidityofthesolution.Bycomparingdeterministicdemand(replacingrandomdemandwithexpectedvaluey(z))withtherandomdemandmodel,thedifferencesinindicatorssuchassubsidylevel,price,outputandprofit,andgovernmentexpenditureareanalyzedtorevealtheimpactofignoringdemanduncertaintyondecision-making,providingaquantitativebasisforpolicymaking.
在一般需求函數(shù)y(p?r)下，價(jià)格設(shè)定報(bào)童問(wèn)題（如公式10）無(wú)法獲得閉式解,，需借助二分搜索等數(shù)值方法求解最優(yōu)價(jià)格psto,。假設(shè)條件（9）確保利潤(rùn)函數(shù)對(duì)價(jià)格的嚴(yán)格凹性，從而保證唯一最優(yōu)解,；若條件不滿足,，問(wèn)題仍可通過(guò)數(shù)值方法處理。對(duì)于線性需求,，關(guān)系式（15）提供了合理的充分條件,，簡(jiǎn)化分析。
Underthegeneraldemandfunctiony(p?r),thepricesettingnewsboyproblem(suchasEquation10)cannotobtainaclosed-formsolution,anditisnecessarytousenumericalmethodssuchasbinarysearchtosolvetheoptimalpricepsto.Assumptioncondition(9)ensuresthestrictconcavityoftheprofitfunctionwithrespecttotheprice,therebyensuringauniqueoptimalsolution;iftheconditionisnotmet,theproblemcanstillbehandledbynumericalmethods.Forlineardemand,relation(15)providesareasonablesufficientconditiontosimplifytheanalysis.
最優(yōu)生產(chǎn)量q?由預(yù)期需求y(z)與報(bào)童分位數(shù)(p?c)/p共同決定,，后者反映需求不確定性下的庫(kù)存策略,。政府通過(guò)調(diào)控有效價(jià)格z=p?r，確保預(yù)期銷量達(dá)到目標(biāo)采用水平Γ,。隨機(jī)需求下,，為避免缺貨，政府需激勵(lì)供應(yīng)商生產(chǎn)超出Γ的數(shù)量,，其差值由K(psto)量化,，體現(xiàn)需求波動(dòng)對(duì)生產(chǎn)決策的影響。
Theoptimalproductionquantityq?isdeterminedbytheexpecteddemandy(z)andthenewsboyquantile(p?c)/p,whichreflectstheinventorystrategyunderdemanduncertainty.ThegovernmentensuresthattheexpectedsalesvolumereachesthetargetadoptionlevelΓbyregulatingtheeffectivepricez=p?r.Underrandomdemand,inordertoavoidstockouts,thegovernmentneedstoincentivizesupplierstoproducemorethanΓ,andthedifferenceisquantifiedbyK(psto),whichreflectstheimpactofdemandfluctuationsonproductiondecisions.
最優(yōu)價(jià)格p滿足邊際成本等于邊際收益的條件（即c=p(1?1/Ed(p)),，其中Ed(p)為價(jià)格彈性,。盡管無(wú)閉式解，可證明需求不確定性會(huì)降低最優(yōu)價(jià)格及企業(yè)利潤(rùn),，凸顯風(fēng)險(xiǎn)環(huán)境對(duì)定價(jià)策略的抑制作用,。
Theoptimalpricepsatisfiestheconditionthatmarginalcostequalsmarginalrevenue(（略）,c=p(1?1/Ed(p)),whereEd(p)isthepriceelasticity.Althoughthereisnoclosed-formsolution,itcanbeshownthatdemanduncertaintyreducestheoptimalpriceandcorporateprofits,highlightingtheinhibitoryeffectoftheriskenvironmentonpricingstrategies.
定理1揭示了需求不確定性對(duì)最優(yōu)變量（有效價(jià)格z、產(chǎn)量q,、定價(jià)p及利潤(rùn)Π）的動(dòng)態(tài)影響,。通過(guò)量化噪聲幅度（如標(biāo)準(zhǔn)差σ）與關(guān)鍵指標(biāo)K(psto)的關(guān)系K(psto)≤0且隨噪聲增強(qiáng)單調(diào)遞減），可系統(tǒng)性比較隨機(jī)與確定性場(chǎng)景的差異,。例如,，均勻分布下K(psto)與σ呈線性關(guān)系（公式13），正態(tài),、指數(shù)等單峰分布亦類似。
Theorem1revealsthedynamicimpactofdemanduncertaintyontheoptimalvariables(effectivepricez,outputq,pricingp,andprofitΠ).Byquantifyingtherelationshipbetweenthenoiseamplitude(suchasstandarddeviationσ)andthekeyindicatorK(psto)(K(psto)≤0andmonotonicallydecreasingwiththeincreaseofnoise),thedifferencebetweenrandomanddeterministicscenarioscanbesystematicallycompared.Forexample,underuniformdistribution,K(psto)islinearlyrelatedtoσ(Formula13),andthesameistrueforunimodaldistributionssuchasnormalandexponential.
有效價(jià)格zsto=y?1(Γ?K(psto))隨噪聲幅度增加而降低,，其確定性場(chǎng)景（無(wú)噪聲）達(dá)到最大值z(mì)det=y?1(Γ),。生產(chǎn)量需額外補(bǔ)償∣K(psto)∣以應(yīng)對(duì)缺貨風(fēng)險(xiǎn)，導(dǎo)致隨機(jī)需求下的產(chǎn)量與定價(jià)均低于確定性場(chǎng)景,，且差距隨噪聲擴(kuò)大而增大,。
Theeffectivepricezsto=y?1(Γ?K(psto))decreasesasthenoiseamplitudeincreases,anditsdeterministicscenario(nonoise)reachesthemaximumvaluezdet=y?1(Γ).Theproductionvolumeneedstobecompensatedadditionally|K(psto)|tocopewiththeriskofout-of-stock,resultinginthattheoutputandpricingunderrandomdemandarelowerthanthoseinthedeterministicscenario,andthegapincreasesasthenoiseincreases.
三、知識(shí)補(bǔ)充（Knowledgesupplement）
加性模型（AdditiveModel）是一種統(tǒng)計(jì)學(xué)和機(jī)器學(xué)習(xí)中常用的建模方法，其核心思想是將多個(gè)變量的影響以相加的方式：（略）
Theadditivemodelisacommonlyusedmodelingmethodinstatisticsandmachinelearning.Itscoreideaistocombinetheeffectsofmultiplevariablesinanadditivemannertodescribetherelationshipbetweenthetargetvariable(dependentvariable)andmultiplepredictorvariables(independentvariables).Unliketraditionallinearmodels,additivemodelsalloweachvariabletoaffectthetargetvariablethroughnonlinearfunctions,sotheyaremoreflexibleindealingwithcomplexrelationships.
加性模型的特點(diǎn)：
Characteristicsofadditivemodels:
1.靈活性：每個(gè)變量可以獨(dú)立使用非線性函數(shù)（如樣條函數(shù),、核平滑等）,，無(wú)需假設(shè)全局線性關(guān)系。
1.Flexibility:Eachvariablecanusenonlinearfunctions(suchassplinefunctions,kernelsmoothing,etc.)independentlywithoutassumingagloballinearrelationship.
2.可解釋性：每個(gè)變量的貢獻(xiàn)可以單獨(dú)可視化,，便于理解變量如何影響目標(biāo)變量,。
2.Interpretability:Thecontributionofeachvariablecanbevisualizedseparately,makingiteasiertounderstandhowthevariableaffectsthetargetvariable.
3.降維能力：通過(guò)避免變量間的高階交互項(xiàng)，減少了模型復(fù)雜度,。
3.Dimensionalityreductioncapability:Byavoidinghigh-orderinteractiontermsbetweenvariables,themodelcomplexityisreduced.
4.適用性：廣泛用于回歸和分類問(wèn)題（如廣義加性模型）,。
4.Applicability:Itiswidelyusedinregressionandclassificationproblems(suchasgeneralizedadditivemodels).
常見(jiàn)的加性模型類型包括：
Commonadditivemodeltypesinclude:
1.廣義加性模型（GAM）：通過(guò)鏈接函數(shù)（如logit、log）將加性項(xiàng)與目標(biāo)變量連接,，支持更廣泛的分布類型,。
1.Generalizedadditivemodel(GAM):connectsadditivetermstotargetvariablesthroughlinkfunctions(suchaslogit,log),supportingawiderrangeofdistributiontypes,
2.加性回歸樹(shù)：以梯度提升機(jī)（如XGBoost、LightGBM）為代表,，通過(guò)疊加多個(gè)弱學(xué)習(xí)器（如決策樹(shù)）逐步優(yōu)化預(yù)測(cè)結(jié)果,。
2.Additiveregressiontree:representedbygradientboostingmachines(suchasXGBoost,LightGBM),graduallyoptimizespredictionresultsbysuperimposingmultipleweaklearners(suchasdecisiontrees);
3.結(jié)構(gòu)化加性模型：針對(duì)時(shí)空數(shù)據(jù)等特殊結(jié)構(gòu)，引入時(shí)間趨勢(shì)或空間平滑項(xiàng),，增強(qiáng)對(duì)數(shù)據(jù)特性的捕捉能力,。
3.Structuredadditivemodel:forspecialstructuressuchasspatiotemporaldata,introducestimetrendsorspatialsmoothingtermstoenhancetheabilitytocapturedatacharacteristics.
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翻譯：谷歌翻譯
參考資料：谷歌,、ChatGPT
參考文獻(xiàn)：MaximeC.Cohen,RubenLobel,GeorgiaPerakis.TheImpactofDemandUncertaintyonConsumerSubsidiesforGreenTechnologyAdoption[J],ManagementScience,2016,62(5):（略）.
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