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1、CapitalUtilizationandUnemploymentChapter91MacroeconomicsChapter9CapitalInputCapitalutilizationrateThefractionofthecapitalstockusedinproduction.κ(theGreekletterkappa)representtheutilizationrateforthecapitalstock,K.Y=A·F(κK,L)2MacroeconomicsChapter9CapitalInputκK,riseswithth
2、eutilizationrate,κ.Therefore,anincreaseinκraisesrealGDP,Y,foragiventechnologylevel,A,capitalstock,K,andlaborinput,L.3MacroeconomicsChapter9CapitalInputTheDemandforCapitalServicesFirmsmaximizerealprofitπ/P=A·F[(κK)d,Ld)]−(w/P)·Ld−(R/P)·(κK)d4MacroeconomicsChapter9CapitalInp
3、ut5MacroeconomicsChapter9CapitalInputTheDemandforCapitalServicesAssumethatthetechnologylevelrisesfromAtoA’.ThischangeraisestheMPKatagivenquantity.6MacroeconomicsChapter9CapitalInput7MacroeconomicsChapter9CapitalInputTheSupplyofCapitalServicesForagivenstockofcapital,K,owner
4、scansupplymoreorlesscapitalservicesperyearbyvaryingκ.Onereasontosettheutilizationrate,κ,belowitsmaximumisthatincreasesinκtendtoraisethedepreciationrate,δ.δ=δ(κ)Otherreasonsincludeutilitycostofcapital.8MacroeconomicsChapter9CapitalInputTheSupplyofCapitalServicesNetrealincom
5、efromsupplyingcapitalservices=realrentalpayments−depreciation=(R/P)·κK−δ(κ)·K=K·[(R/P)·κ−δ(κ)]Rateofreturnfromowningcapital=(R/P)·κ−δ(κ)9MacroeconomicsChapter9CapitalInput10MacroeconomicsChapter9CapitalInputOwnersofcapital(households)selecttheutilizationrate,κ,thatmaximize
6、s(R/P)·κ−δ(κ)Thesolutionisκ=κ∗11MacroeconomicsChapter9CapitalInput12MacroeconomicsChapter9CapitalInputThus,anincreaseintherealrentalpriceraisesthecapitalutilizationrate;thehigherrealrentalpricemakesitworthwhiletoraiseκdespitetheresultingincreaseinthedepreciationrate,δ(κ).1
7、3MacroeconomicsChapter9CapitalInputMarketClearingandCapitalUtilizationThesupplycurveslopesupbecauseanincreaseintherealrentalprice,R/P,motivatesahighercapitalutilizationrate,κ.Thetechnologylevel,A,doesnotaffectthechoiceofthecapitalutilizationrate,κ14MacroeconomicsChapter9Ca
8、pitalInput15MacroeconomicsChapter9CapitalInputMarketClearingandCapitalUtilizationWhenthet
