Transcript Production function and labor

Business, Government, and the
World Economy
Output and Employment
Outline of Topics
Markets work (move to “equilibrium”)
Long run equilibrium vs. short run adjustment
What factors measure long run economic
performance?
Output
Employment
Prices
The Ultimate Goal:
Sustainable Economic Growth
Long-term consistent increases in output
(GDP) is usually considered the most basic
benchmark of economic health.
Semester goal:
Establish how /why economic growth occurs
Production Function
The amount of output that an economy can
produce is believed to be a function of the
amount of capital used in a given period of
time (K), the number of workers employed (N),
and a productivity measure (A) or
Y = Af(K,N)
Where f( ) is a mathematical function relating
capital and labor to output.
An Example:
The Production Function
Cobb Douglas Production Function
Y=AKaN(1-a)
Where: 0<a<1
a = the share of income received by owners of
capital
1-a = the share received by labor
a = .3, 1-a = .7
A = total factor productivity
Economic Growth
Long run growth in output can occur in multiple
ways:
Increase in amount of labor
Increase in amount of capital
Shifts in allocation of income (a)
Increase in “A” total factor productivity
Constraints on Growth
Labor and capital exhibit diminishing marginal
returns to scale
Each additional unit has a smaller impact on
output than the previous one
Therefore consistent long-run economic growth
depends upon increasing productivity.
Graphing the production function
Often it is helpful to look at the production
function based on changes in one variable,
keeping the other inputs constant.
Production Function
Marginal Product of Capital
Marginal Product of Capital (MPK)
The additional increase in output resulting from
a one unit increase in capital.
From the graph each additional unit of capital
results in a small increase in output.
Diminishing MPK
307
391
567
Diminishing MPK
307
391
567
Approximating MPK
307
391
567
MPK
Marginal Product of Capital is positive
Marginal Product of Capital declines as capital
stock increases.
Labor
The impact of increasing labor input is similar
to the impact of increasing capital
We can graph the production function based
upon keeping the capital stock constant and
changing labor (next slide)
Production Function
(Changing Labor)
Supply Shock
Supply shocks (like the oil price shock we had
before) cause the amount of output produced
at a given level of output and labor to increase
or decrease.
This also impacts the MPK and MPN
Adverse Supply
(productivity) Shock
Productivity Shocks
Changes in productivity also impact the
marginal productivity of capital and labor
Gains in productivity can offset the declining
marginal productivity of labor or capital.
US Total Factor Productivity
The growth record
US Total output grew at a 2.54% average rate
from 1929 – 48 and a 3.7% rate from 1948 –
1973 However from 1973 – 2001 it grew at an
average of 1.9% Why???
A similar decline occurred in other developed
economies.
One report shows a productivity growth rate of
0.0% from 1973 – 1990.
Shigehara 1992
Quantity of Capital and Labor
Before investigating productivity in more detail
– need to understand how the amount of labor
and capital are determined.
The labor market
The goods market (consumption and
investment)
Demand for Labor
The amount of labor firms want to hire
Basic Assumptions
Workers are identical
Firms view wages as being set by a
competitive labor market
Firms will demand the amount of labor that
maximizes profit (where MPN = real wage)
Marginal Cost = wage, benefit = marginal
productivity of worker – Or in nominal terms
the marginal revenue product of labor)
Labor Demand Curve
The labor demand curve will have an inverse
relationship with the real wage (which equals
the MPN)
Real Wage
Labor Demand Curve
Labor
Factors that Shift ND
An increase in
Shifts ND to the
Why
Productivity
Right
MPN increases
with positive
supply shock
Capital Stock
Right
Higher capital
stock increases
MPN
Labor Supply
Real Wage
The labor supply curve will have a direct
relationship with the current real wage.
The economic benefit of working is the real
wage.
Labor
Shifts in the NS Curve
An increase in
NS will shift
Why
Wealth
Left
Can afford more leisure
Expected Future
Real Wage
Left
Can afford more leisure
Working Age
Population
Right
Increase in Labor
Supply
Participation Rate
Right
Increase labor supply
Labor Market Equilibrium
Real Wage
NS
ND
N
Labor
Temp Adverse Supply Shock
Real Wage
NS
ND
ND
Labor
Unemployment
The equilibrium level of labor represents the
full employment level of labor (which is not
zero).
Putting the full employment level of labor into
the production function provides the level of
output at a given level of capital and total
factor productivity.
Real Wage
Unemployment : NS>ND
Unemployment
NS
ND
ND
NS
Labor
Fast Adjustment of Real Wages
If unemployment exists, the firm has the ability
to offer a lower real wage.
This should move the amount of labor
demanded to the amount of labor supplied
(move the economy toward the full
employment level of labor)
Measuring Unemployment
Household Survey vs. Establishment Survey
(indicators next time)
Distinguish between unemployed (actively
looking for work) and not in the labor force
(not looking for work and not employed)
Full Employment Output
The full employment level of output is then the
output produced at the full employment level of N
given as N – given the current capital stock K and
current level of productivity.
Note – This is the theoretical level of employment
– it does not depend upon the real interest rate
level
Y  Af (N, K)
Okun’s Law
First stated by Arthur Okun (chairman of
Council of Economic Advisors in Johnson
Administration)
Compares the level of full employment output
to current output based on amount of
unemployment above the full employment level
Should not be considered a “law” more of a
general rule…
Okun’s Law
Y Y
 2.5(u  u )
Y
Alternatvely by looking at the
growth rate and rearrangin g
% GDP  % GDP  2.5(u )
or
u  % GDP / 2.5  0.4(% GDP )
Okun’s Law restated
u  %GDP / 2.5  0.4(% GDP )
u  1.4  0.4(% GDP )
If the change in real GDP is 3.5% then the change in
unemployment is zero
In other words 3.5% is a long run sustainable growth
rate for the economy.
If percentage change in real GDP is zero,
Unemployment increases by 1.4%
Okun’s Law 1949 - 2008
Regression Statistics
R Square
Standard Error
Observations
0.75347824
0.52509958
60
Coefficients
Intercept
Real Rate of Growth
Standard
Error
t Stat
P-value
1.33481791 0.118896209 11.22675 3.58E-16
-0.38609966 0.028998644 -13.3144 2.76E-19
Graphical Representation
Policy Questions
What if there was a large negative
productivity shock that left the economy at
below the full employment level of output?
(high unemployment)
Could unemployment be decreased by
undertaking expansionary fiscal policy
(increasing government spending)?
What are the possible negative outcomes?
Theory Questions
Why could unemployment persist? (why would
wages not drop to bring the labor market to
equilibrium?
Sticky Nominal Wages and Prices (menu costs)
Sticky Real Wages and Prices
Sticky Real Wages (insider/outsider models)
Sticky Real Wages (government restrictions)
Wedges between private and social costs
Barriers to firing and unemployment benefits
Sticky Nominal Wages and Prices
Menu Costs
There is a cost associated with changing prices,
this keeps nominal prices fixed in the short
term.
Examples include remarking merchandise,
updating web sites, etc
More important if markets are not perfect (in
perfect competition having the “wrong” has
large consequences)
Sticky Nominal Wages and Prices
Monopolistic / Oligopolistic Competition
Not all products meet the requirements of
perfect competition (especially
standardization of goods and large number of
sellers)
“Kinked” demand curves
With a small number of competitors, the firms
will not change price unless the industry price
has changed.
Institutional constraints
Real Wage Rigidity
Efficiency Wages
Classical Argument – Most unemployment
results from short term mismatches between
workers and jobs (not all workers are identical)
Keynesian Argument - Mismatches are only
part of the problems. Unemployment can
persist because wages are slow to adjust to a
level that would clear the labor market.
Unemployment
Reasons why Unemployment might persist
Legal barriers to decreasing wage
Minimum Wages
Union Contacts
Reduction of Turnover costs
Training is expensive
Paying a higher wage may increase worker
productivity – Efficiency Wage model
Efficiency Wage Model
Shirking Model
If worker is paid only minimum needed, there
will not be much concern about being fired
(especially if there are many other similar
jobs)
Employee is more likely to “shirk”
responsibilities and be less productive
The effort a employee puts forth depends
upon the real wage received.
S shaped Effort Curve
As real wage increases (especially if it increases
above the minimum the firm would need to
pay, productivity of the worker increases.
Staring from a real wage of 0 effort is very low
then starts to increase for each increase in real
wage
At some point there is diminishing effort for
each increase in real wage.
Effort Curve
Effort
Real Wage
The firm will want to maximize the amount of
effort per unit of real wage paid or E/w, In
other words maximize the effort per dollar of
real wage or the efficiency of the worker
The slope of a straight line from the origin will
be equal to E/w
Assume that the market clearing level of real
wage is wA in the next graph However w* is
the level that Maximizes E/w
Effort Curve
Effort
Effort Curve
E*
EA
WA
W*
Real Wage
Real Wage Rigidity
In the efficiency wage model, the real wage is
dependent upon the effort curve, not the levels
of labor supply and demand.
It is possible for unemployment to persist at
the efficiency wage.
Unemployment : NS>ND
NS
Real Wage
W*
Unemployment
ND
ND
NS
Labor
Insider Outsider Relationships
Union negotiations pose restrictions on wage
rates. They protect those who are a members
of the organization (insiders)
If wages increase faster than productivity, it is
possible for the constraint to force firms to look
for other sources of employment.
Barriers to market clearing wages
An increase in the minimum wage will have
little impact if the wage is currently below the
market clearing wage, if it increases above
equilibrium it can reduce employment.
Empirical evidence suggests that there is little
evidence between the ration of minimum
wages to average wages and inflation.
Wedges:
Private and Social Costs
Taxes, social security etc create a wedge between
what the employer pays and what the worker receives
(the cost to the employer is much higher than the
nominal benefit to the worker)
The difference has a larger consequence if the worker
does not recognize the benefit received (future
pension, healthcare etc)
A high level of these cots can create a disincentive to
work.
Extensions of Sticky
Wages and Prices
When responding to changes in demand firms
react to changes in demand by changing the
amount of production, not changing prices
If this is the case firms will increase production
if demand at a fixed price is higher than
expected (This implies that the economy can
produce above full employment in the short
run)
Extensions of Sticky Prices
Effective Labor Demand
If the firm is willing to meet demand at a given
price, you need to look at the effective labor
demand curve.
Labor demand looks at the quantity of labor
needed to produce a level of output at a given
productivity level and capital stock.
Effective Labor Demand
Labor N
Output
Full Employment Output
Revisited
The full employment level of output is then the
output produced at the full employment level of N
given as N – given the current capital stock K and
current level of productivity.
Note – This is the theoretical level of employment
– it does not depend upon the real interest rate
level
Y  Af (N, K)
The FE line
We want to build a model based upon
equilibrium in the labor, goods and asset
market.
Each market will be represented by a line
representing equilibrium in the respective
market on a graph with output (X axis) and real
interest rates (Y Axis).
The FE line
Real Interest Rate, r
The FE line is then a vertical line at the real
level of output
FE Line
Y
Output, Y
Shifts in the FE line
Factors that shift the inputs in the production function
will impact the FE line (assuming fast adjustment)
FE Shifts
Why?
If MPN h labor demand h
Beneficial Supply
Right
Shock
houtput for same inputs
(Productivity h)
Increase in Ns
Right
hequil employment
hCapital Stock
Right
hOutput with same labor
and productivity
Real Interest Rate, r
The FE Line:
Increase in Capital Stock
FE0
Y
FE1
Output, Y
FE line with efficiency wages
If efficiency wages are correct, the level of
output corresponds to the amount of labor
demanded at the efficiency wage (There could
be large amounts of unemployment for a long
period of time)
Anything that shifts Labor Supply – will not
impact FE because the Efficiency wage is slow to
adjust. (productivity etc that move Labor
demand still shifts FE)
Indicators of Labor Markets
Weekly Unemployment Claims
Continuing Unemployment Claims
Unemployment Rate
Household Survey (60,000 Homes)
Establishment Survey (400,000 companies and
agencies)
Help Wanted Advertising Index (conference board)
ADP Employment Report (400,00 businesses)