Macroeconomics
Chapter 9
28
The Labor Force, Employment, and Unemployment
Macroeconomics
Chapter 9
18
Capital Input

The Cyclical Behavior of Capacity Utilization

The Federal Reserve computes capacity utilization by expressing a sector’s output of goods as a percentage of the estimated “normal capacity” of each sector to produce goods

employment rate= 1 − u
Macroeconomics
Chapter 9
21
The Labor Force, Employment, and Unemployment

Employment =（1 − u）·Labor force

Total working hours = （1 − u）·Labor force ·working hours per worker
Macroeconomics Chapteroyment, and Unemployment

A Model of Job Finding
Macroeconomics
Chapter 9
27
The Labor Force, Employment, and Unemployment
Chapter 9
10
Capital Input

Owners of capital (households) select the utilization rate, κ, that maximizes (R/P)· κ−δ(κ)
The solution is κ = κ∗
Macroeconomics

The technology level, A, does not affect the choice of the capital utilization rate, κ
Macroeconomics
Chapter 9
14
Capital Input
Macroeconomics
Chapter 9
15
Macroeconomics
Chapter 9
19
Capital Input
Macroeconomics
Chapter 9
20
The Labor Force, Employment, and Unemployment

Basic Concepts and Empirical Patterns

u = number unemployed/labor force = ( labor force− number employed) /labor force = 1 − (number employed/labor force) = 1 − employment rate
= (R/P) ·κK − δ(κ) ·K = K· [(R/P)· − δ(κ)] κ

Rate of return from owning capital = (R/P)· − δ(κ) κ
Macroeconomics Chapter 9 9
Capital Input
Macroeconomics

Y= A·F(κK, L)
Macroeconomics
Chapter 9
2
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.
Macroeconomics
Chapter 9
3
Capital Input

The Demand for Capital Services

Firms maximize real profit
π/P = A· F[(κK)d, Ld)] − (w/P)· d − (R/P)· L (κK)d
Macroeconomics
Chapter 9
4
Capital Input
Macroeconomics
Chapter 9
5
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.


δ = δ(κ)

Other reasons include utility cost of capital.
Macroeconomics
Chapter 9
8
Capital Input

The Supply of Capital Services

Net real income from supplying capital services = real rental payments − depreciation
Chapter 9
24
The Labor Force, Employment, and Unemployment
Macroeconomics
Chapter 9
25
The Labor Force, Employment, and Unemployment



The equilibrium business-cycle model is probably satisfactory for understanding fluctuations in the labor force and hours worked per worker. The real wage rate, w/P adjusts to equate the quantity of labor supplied,Ls, to the quantity demanded, Ld. However, this approach leaves unexplained the most important factor— the fluctuations in the employment rate or, equivalently, in the unemployment rate.
Macroeconomics
Chapter 9
17
Capital Input

Market Clearing and Capital Utilization


i = (R/ P) ·κ − δ(κ) Rate of return on bonds = rate of return on ownership of capital Increase in the technology level, A, raises the rate of return from owning capital, the interest rate, i, increases. The interest rate is still procyclical in the model.
Macroeconomics
Chapter 9
22
The Labor Force, Employment, and Unemployment
Macroeconomics
Chapter 9
23
The Labor Force, Employment, and Unemployment
Macroeconomics
Macroeconomics
Chapter 9
6
Capital Input
Macroeconomics
Chapter 9
7
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.
Macroeconomics
Chapter 9
13
Capital Input

Market Clearing and Capital Utilization

The supply curve slopes up because an increase in the real rental price, R/P, motivates a higher capital utilization rate, κ.
Chapter9
Capital Utilization and Unemployment
Macroeconomics