巴罗 宏观经济学现代观点 第9章.pptx

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Capital Input
Capital utilization rate
The fraction of the capital stock used in production.
κ(the Greek letter kappa) represent the utilization rate for the capital stock, K.
Y= A· F(κK, L)
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Capital Input
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.
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Capital Input
The Demand for Capital Services
Firms maximize real profit
π/P = A·F[(κK)d, Ld)]
−(w/P)·Ld −(R/P)·(κK)d
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Capital Input
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Capital Input
The Demand for Capital Services
Assume that the technology level rises from A to A’. This change raises the MPK at a given quantity.
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Capital Input
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Capital Input
The Supply of Capital Services
For 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.
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Capital Input
The Supply of Capital real e 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)
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9
Capital Input
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Capital Input
Owners of capital (households) select the utilization rate, κ, that maximizes
(R/P)·κ−δ(κ)

The solution is κ= κ∗