Unemployment:
Determining the Natural Rate of
Unemployment
Md. Nuruzzaman, Ph.D.
Director (Training), NAPD
Learning Objectives
• To learn that unemployment is the natural
consequence of labor force dynamics.
• To understand that the natural rate of
unemployment is determined in part by the
costs of employment turnover.
• To learn the differences between the various
types of unemployment and the policy
consequences of each.
Unemployment
• The unemployment rate is the number of
unemployed people, expressed as a
percentage of the labor force.
– Labor Force = (Civilian non-institutional
population over age 16 - People not in the labor
force (students, homemakers, retirees,
discouraged workers)
– Unemployed = Labor force - People who are
employed.
– Unemployment rate = People who are
unemployed/Labor force times 100
Natural Rate of Unemployment
• The natural rate of unemployment is the
percentage of the labor force that can normally
be expected to be unemployed for reasons
other than cyclical fluctuations in real GDP.
– The natural rate of unemployment is related to
the willingness of workers to voluntarily separate
from their jobs, job loss, the duration of
unemployment periods, the rate of change in the
pattern of demand, and changes in technology.
What Causes Unemployment?
• Frictional Unemployment
– Job Search
• It takes time to match workers and jobs.
• Structural Unemployment
– Skill Mismatch
• Unemployed workers’ skills do not match the needs of
employers.
– Location Mismatch
• Unemployed workers’ location do not match the location of the
jobs.
What Causes Unemployment?
• Cyclical Unemployment
– Real-Wage Rigidity
• The failure of wages to adjust, either rising or
falling, until labor supply equals labor demand.
• Real wage rigidity can be caused by minimum wage
laws, unions and collective bargaining, and
efficiency wages.
New-Keynesian Theory of
Unemployment
• Assumptions:
– The firm recognizes that its pool of workers is a
stock and that any given stock can be associated
with fast or slow labor turnover.
– The firm minimizes the costs of maintaining a
stock of employees by adjusting the real wage.
– The firm demands fewer workers as the real
wage rises, so employment is a decreasing
function of the real wage.
New-Keynesian Theory of
Unemployment
• Assumptions:
– The stock of workers sent to the labor market
by households is the “labor force.”
• Households supply more workers when the real
wage rises, so the labor force is an increasing
function of the real wage.
New-Keynesian Theory of
Unemployment
• The new-Keynesian theory differs from the
classical theory in that the wage does not equate
labor demand and labor supply.
• Rather, the wage is set at a point where there is
still a pool of unemployed workers.
• This wage is called the efficiency wage and the
level of unemployment associated with it is called
the natural rate of unemployment.
Flows Through the Labor Market
The supply of labor is a flow
into the labor market.
Stock of
Unemployed
Unemployment is the
stock of workers who are
not matched with firms.
The demand for labor is a flow
out of the labor market.
Macroeconomics, Roger Farmer, p. 177
Efficiency Wage Theories
• High wages make workers more productive
or efficient.
– Firms are reluctant to cut wages despite an
excess supply of labor because it would lower
worker productivity.
• Higher wages reduce labor turnover.
• Average quality of a firm’s workforce depends on
the wages paid.
• High wages improve worker effort.
New-Keynesian Theory of
Unemployment
w/P
LF
NRU
(w/P)*
The labor force (LF) is an
increasing function of the real
wage.
Employment, E(w/P), is a
decreasing function of the real
wage.
E(w/P)
0
E*
The efficiency wage does not
occur at the intersection of E(w/P)
and LF.
LF*
Employment and Labor Force
When the real wage equals the
efficiency wage, unemployment is
at its natural rate.
Turnover Cost and the Efficiency
Wage Model
• Assumptions:
– Firms must search for workers actively, but
they may vary the intensity of their search.
– Firms choose the wages they offer to minimize
their wage bills, which are comprised of
turnover costs and the real wage.
• One element of the wage bill is the real wage (w/P);
the other element is the cost of recruiting new
workers, C(w/P, L).
Turnover Cost and the Efficiency
Wage Model
• Assumptions:
– Turnover cost = C(w/P, L) = c(w/P)L
• Turnover cost, C, is a function of the real wage and employment.
– The firm can influence C by offering a different real wage and/or by
changing the number of workers it employs.
• C is inversely related to the real wage.
– Better-paid workers are more likely to remain with the firm; thereby,
lowering the firm’s turnover costs.
• The marginal benefit of an increase in the real wage equals the
reduction in turnover cost for a given increase in the real wage.
• The marginal benefit decreases as the real wage increases.
Turnover Cost and the Efficiency
Wage Model
• Assumptions continued:
– Per worker turnover cost = c(w/P)L
• Turnover costs are proportional to the number of
workers.
Choosing the Efficiency Wage
• Each firm chooses its wage rate to minimize the
cost of maintaining a pool of employed workers.
• The firm’s profit function is:
p = Y – w/P(L) – c(w/P)L
p
= Profit
Y
= Commodities supplied
w/P(L) = Cost of labor demanded
c(w/P)L = Turnover cost per worker
where
Choosing the Efficiency Wage
• Process for Choosing the Efficiency Wage
1. The firm minimizes costs per worker by
choosing the efficiency wage that makes w/P +
c(w/P) as small as possible.
2. Given the efficiency wage, the firm
chooses its level of employment (L) to
maximize profit.
Choosing the Efficiency Wage
• If the wage increases by one dollar, the
firm’s wage bill increases by one dollar per
worker.
– This is the marginal cost of a change in the
wage.
• If the wage increases by one dollar, the
firm’s turnover cost decreases.
– This is the marginal benefit of a change in the
wage.
Choosing the Efficiency Wage
MB
MC
MC
MB=c(w/P)
0
w/P*
w/P
The efficiency wage equates
the marginal benefit of
increasing the real wage to its
marginal cost.
Deriving the Efficiency Wage: Math
• c = 1 – 2(w/P) + (w/P)2
– Turnover cost depends on the real wage.
• Note that as w/P increases, turnover cost falls*
• dc/(w/P) = – (– 2 + 2(w/P))
– The marginal benefit is the slope of the cost function.
• We use the negative because the negative of a cost is a benefit.
• Note that the marginal benefit falls as the real wage rises.
• Marginal cost = 1.
*Where w/P is assumed to be <1, and if (w/P) >1, c = 0
Deriving the Efficiency Wage: Math
• Costs are minimized at the real wage where
marginal benefit equals marginal cost.
– Marginal benefit = – (– 2 + 2(w/P))
– Marginal cost = 1.
1
(1 – 2)/ – 2
½
= 2 –2(w/P)
= w/P
=
w/P
Choosing a Stock of Workers
• The firm pays a real wage and a turnover
cost for each worker.
– The additional cost means that at every real
wage the firm hires fewer workers than would
be predicted in the classical model.
Choosing a Stock of Workers
w/P
LDC represents the classical labor
wage to the marginal product of
labor.
EW represents the efficiency
wage employment curve. It
equates the real wage to the
marginal product of labor minus
the turnover cost.
LDC
EW
0
E
Choosing a Stock of Workers
w/P
The gap between LDC and EW
is turnover cost. It is smaller when
the real wage is higher because for
a high real wage, the turnover cost
is lower.
EC represents employment in the
classical model.
w/P
LDC
EW
0
E*
EC
E
E* represents employment in the
efficiency wage model.
Deriving the Labor Demand Curve:
Math
p = LD – (1/2)(LD)2 – (w/P)LD – c(w/P)LD
• where
•
•
•
•
Profit = P
The production function = LD – (1/2)(LD)2
The wage bill = (w/P)LD
Turnover cost = c(w/P)LD
Deriving the Labor Demand Curve:
Math
• c = 1 – 2(w/P) + (w/P)2
 w/P = ½ so c = ¼
• Marginal product = 1 – LD
• To maximize profit, the firm equates marginal
product to the real wage plus turnover cost.
1 – LD = (w/P) + c(w/P) = ½ + ¼ = ¾
LD = 1 – ¾ = ¼
New-Keynesian Theory of
Unemployment
w/P
LF
NRU
(w/P)*
E(w/P)
0
E*
LF*
Employment and Labor Force
At equilibrium, the efficiency
wage, (w/P)*, is chosen to
maximize profits.
When the real wage equals the
efficiency wage, the natural rate
of unemployment is the difference
between the labor force and the
quantity of employment.
Deriving the Natural Rate of
Unemployment: Math
• LS
=
w/P
=
½
– where
• LS = labor supply
• w/P = the real wage
• The natural rate of unemployment, U*, is
given by the difference between demand
and supply.
– U* = ½ – ¼
=
¼