巴罗宏观经济学现代观点9章.pptxVIP

Capital Utilization and UnemploymentMacroeconomics Chapter 91C h a p t e r 9 Capital InputMacroeconomics Chapter 92· Capital utilization rateThe fraction of the capital stock used in production.κ (the Greek letter kappa) representthe utilization rate for the capital stock,K.Y= A· F(κK, L) Capital InputMacroeconomics Chapter 93· κK, rises with the utilization rate, κ.Therefore, an increase in κ raises real GDP, Y, for a given technology level, A, capital stock, K, and labor input, L. Capital InputMacroeconomics Chapter 94· The Demand for Capital ServicesFirms maximize real profitπ/P = A·F[(κK)d, Ld)]– (w/P)·Ld ? (R/P)·(κK)d Capital InputMacroeconomics Chapter 95 Capital InputMacroeconomics Chapter 96· The Demand for Capital ServicesAssume that the technology level rises from A to A’. This change raises the MPK at a given quantity. Capital InputMacroeconomics Chapter 97 Capital InputMacroeconomics Chapter 98The Supply of Capital ServicesFor a given stock of capital, K, owners can supply more or less capital services per year by varying κ.One reason to set the utilization rate, κ, below its maximum is that increases in κ tend to raise the depreciation rate, δ.δ = δ(κ)Other reasons include utility cost of capital. Capital InputMacroeconomics Chapter 99· The Supply of Capital ServicesNet real income from supplying capital services= real rental payments ?depreciation= (R/P) · κK ? δ(κ) · K= K·[(R/P)·κ ? δ(κ)]Rate of return from owning capital= (R/P)·κ ? δ(κ) Capital InputMacroeconomics Chapter 910 Capital InputMacroeconomics Chapter 911· Owners of capital (households) select the utilization rate, κ, that maximizes(R/P)·κ?δ(κ)The solution is κ = κ? Capital InputMacroeconomics Chapter 912 Capital InputMacroeconomics Chapter 913· Thus, an increase in the real rental price raises the capital utilization rate; the higher real rental price makes it worthwhile to raise κ despite the resulting increase in the depreciation rate, δ(κ). Capital InputMacroeconomics Chapter 914· Marke