Chapter 9 Capital
Utilization and
Unemployment
Capital Input

Why relaxing the assumption on the inelastic
supply of capital?
 Empirical
evidence: the cyclical behavior of
capital utilization rate.

How do we relax the assumption?
 Introducing
the capital utilization rate .
Y  AF ( K , L)

affects the depreciation rate, hence the return to
capital.
Capital Input

The demand for capital service

w d R
d
d
 AF  ( K ) , L   L  ( K ) d
P
P
P
 Replacing K by K: capital services.

R/P is the real return on K.
demand curve for K is downward sloping.
 A positive shock shifts the demand curve to the
right.
 The
Capital Input

The demand for capital services.
Capital Input

The supply of capital services
 Machines
wear out faster if used more intensively.
   ( )
K
is invariable in the short run.
 Owners choose  to maximize the net income from
supplying capital services.
R
R

 K   ( ) K      ( )  K
P
P


This is equivalent to maximize the net real return from
owning capital.
Capital Input

The supply curve of capital services is upward sloping.
Capital Input

The market of capital services clears.
Capital Input

New results
 A positive real
shock increases current capital
utilization rate and the quantity of capital services.
 Higher capital utilization rate also contributes to
higher real GDP.
 Despite the higher depreciation rate, the interest
rate increases.
R
r     ( )
P
Empirical Evidence

The cyclical behavior of capacity utilization.
Unemployment

Why relaxing the assumption on full
employment?
 Determinants
of total hours worked:
Labor force: explained;
 Hours worked per worker: explained;
 Employment rate: unexplained.

 Determinants
of employment:
Labor force: explained;
 Employment rate: unexplained.

Unemployment

Basic concepts
 Labor
force: the number of persons who offer
themselves for work.
 Employment: number of persons with jobs.
employment rate=1-u
employment=labor force(1-u)
total hours worked=employment hours worked per
worker
Empirical Evidence

The labor force is relatively stable.
Empirical Evidence

The employment rate is highly procyclical.
Empirical Evidence

Hours worked per worker is procyclical.
Empirical Evidence

Importance of three determinants:
 The
employment rate is more important than hours
worked per worker;
 Hours worked per worker is more important than
the labor force.
What we have explained: fluctuations in the
labor force and hours worked per worker.
 What we need explain: fluctuations in the
unemployment rate.

A Model of Job Finding
A distribution of wage offers.
 Job search

 Pros:
future jobs with higher wage;
 Cons: low income from being unemployed .

Decision rule
 Reservation
real wage (w/P)’
 w/P>(w/P)’: accept the current offer;
 w/P<(w/P)’: keep on searching.
A Model of Job Finding
A Model of Job Finding

Implications
 Searching
explains unemployment.
 Higher  raises the reservation wage.
Lower job-finding rate;
 Longer expected duration of unemployment.

 Positive real
shock shifts the distribution to the
right.
The reservation wage increases, but to a smaller extent;
 Higher job-finding rate;
 Shorter expected duration of unemployment.

A Model of Job Finding

Why does the reservation wage increase
proportionally less than the wage offer?
 The
real shock is not fully permanent.
 Still less even if the shock is permanent.

Three scenarios:
#1: the initial state;
 #2: the final state;
 #3: Both  and the distribution are proportionally higher.

1 versus 3: the same job-finding rate;
 2 versus 3: higher job-finding rate in #2.
 2 versus 1: higher job-finding rate in #2.

A Model of Job Finding

Job separations and job findings
 Job-separation
rate :
number of job separation per month/employment
 The job-separation rate is barely cyclical.
 Job-finding rate
:
number of hires per month/unemployment
 The job-finding rate is procyclical.

Dynamics of unemployment
L=U-L
A Model of Job Finding

Natural unemployment rate
U-L
U
1

u 


U  L 1 L U   
n

Unemployment during economic fluctuations
 Unemployment
adjusts gradually;
 Lags behind the economic cycle;
 Job creation is still large in recession.