Chapter 3

Productivity, Output, and

Employment

Introduction

• This chapter describes factors that

determine the level of output produced in

an economy.

• It also begins to develop our theory of the

economy.

Over the Next Few Chapters …

• Our strategy will be to develop theories for

– the labor market

– goods markets

– asset markets

• We argue markets in these sectors tend to

“equilibrate”

• We investigate what further implications

can be derived from the theory

Production

Production refers to the transformation of inputs

or resources into outputs of goods and services.

In other words, production refers to all of the

activities involved in the production of goods and

services, from borrowing to set up or expand

production facilities, to hiring workers,

purchasing raw materials, running quality

control, cost accounting, and so on, rather than

referring merely to the physical transformation of

inputs into outputs of goods and services.

For example

• A computer company hires workers to use

machinery, parts, and raw materials in factories

to produce personal computers.

• The output of a firm can either be a final

commodity or an intermediate product such as

computer and semiconductor respectively.

• The output can also be a service rather than a

good such as education, medicine, banking etc.

Production Functions in Economics

• In economics, a “production function" describes an empirical relationship between specified output and inputs. A production function can be used to represent output production for a single firm, for an industry, or for a nation. Just to illustrate, a production function of rice might have the form:

W=F(L,A,M,F,T,R)

• That is, production of rice (paddy) in tons (W) depends on the use of labor measured in days (L), land in acres (A), machinery in dollars (M), fertilizer in tons (F), mean summer temperature in degrees (T), and rainfall in inches (R).

Production Functions in Economics

• In most applications of production

functions, the input variables are simply

labor (L) and capital (C). The output is

usually measured by physical units

produced or, perhaps, by their value.

• Labor is typically measured in man-hours

or number of full-time-equivalent (FTE)

employees.

Long and short run production

function

• The short-run production function shows the

maximum quantity of good or service that can be

produced by a set of inputs, assuming the

amount of at least one of the inputs used

remains unchanged.

• The long-run production function shows the

maximum quantity of good or service that can be

produced by a set of inputs, assuming the firm is

free to vary the amount of all the inputs being

used.

The Production Function

• Output produced in an economy depends

on:

– The amounts of inputs available, for example

capital and labor, also raw materials

– The effectiveness with which these inputs are

used

The Production Function in

Equation Form

Empirical Production

Functions

Cobb-Douglas Production Function

Q = AKaL1-a

Estimation of Production Functions

Forms of Production Functions

– Cobb-Douglas Production Function

• Can be estimated by linear regression analysis

• Can accommodate any number of independent

variables

• Does not require that technology be held constant

• Shortcomings:

– Cannot show a firm or industry passing through

increasing, constant, and decreasing returns to scale

– Specification of data to be used in empirical estimates`

Estimation of Production Functions

• Statistical Estimation of Production

Functions

– Usually, the most important input is labor.

– Most difficult input variable is capital.

– Must choose between time series and cross-

sectional analysis

Estimation of Production Functions

• Aggregate Production Functions

– Many studies using Cobb-Douglas did not deal with individual firms, rather with aggregations of industries or an economy.

– Gathering data for aggregate functions can be difficult.

• For an economy: GDP could be used

• For an industry: data from Census of Manufactures or production index from Federal Reserve Board

• For labor: data from Bureau of Labor Statistics

A Production Function for the

U.S.

• The following production function

equation fits U.S. data well (See Table

3.1, next slide):

0.3 0.7Y AK N

Table 3.1 The Production Function of the

United States, 1979-2004

Production Function

Properties

• We normally plot output as a function of

one input, holding other inputs

conceptually fixed.

• The production function is upward sloping

(as we plot output versus an input, e.g.

capital).

• The production function becomes flatter as

we move from left to right (increasing labor

and output)

Figure 3.3 The production function relating

output and labor

Marginal Product of Labour and

Marginal Product of Capital

Marginal Product of Labour

Measure of the physical increase in the output of a firm or economy; it is the output that results from hiring one additional worker, all other factors remaining constant. Marginal Product of Capital

is the additional output resulting from the use of an additional unit of capital (ceteris paribus, or assuming all other factors are fixed).

Marginal Products

Useful properties

• Several Useful Properties :

• The Marginal Product of capital and the marginal Product of labor depend on both the quantity of capital and the quantity of labor used in production, as is often the case in the real world.

• K and L are represents the output elasticity of labor and capital and the sum of these gives the returns on scale.

• a + b = 1 Constant return to scale

• a + b > 1 Increasing return to scale

• a + b <1 Decreasing return to scale

Marginal Products

• There is a geometric interpretation of the marginal

product:

– The slope of the production function at a point (showing

output as a function of labor) is the marginal product of

labor:

• Properties of the production function, revisited:

– The marginal product of labor is positive.

– The marginal product of labor falls as the amount of labor

increases (holding the capital stock fixed).

Y

L

Figure 3.2 The marginal product of

capital

Diminishing Marginal Productivity

A decrease in how quickly the output of a

production process grows in response to

more of one input. Diminishing marginal

product is used to identify the point

of diminishing returns, at which adding more

of a material needed for production begins to

have less of a benefit to the output of the

process.

The Law of Diminishing Returns

As additional units of a variable input are

combined with a fixed input, after a point the

additional output (marginal product) starts to

diminish. This is the principle that after a

point, the marginal product of a variable input

declines.

The law of diminishing return

X

MP

Increasing Returns

Diminishing Returns Begins

MP

Example

If at one shop 1 person is working and if we employ 1 more person , then, total Productivity will increase at an increasing rate as they can have better division of labor now. Productivity will increase at an increasing rate till there are 6 workers and they are fully utilized. And if we will employ 1 more person then total productivity might increase, but the average productivity will fall, ie Productivity per person will fall due to 1 extra unit of labour. or we can say addition made by the 6th worker is less than the earlier unit (ie Marginal product of 6th unit of labour will fall.)

Example

Capital Input Labour Input Total Output Marginal Product Average Product of Labour

20 1 5 - 5

20 2 16 11 8

20 3 30 14 10

20 4 56 26 14

20 5 85 28 17

20 6 114 29 19

20 7 140 26 5

20 8 160 20 16

20 9 171 11 30

20 10 180 9 56

20 11 187 7 85

Stages Total Product

(TP)

Marginal Product

(MP)

Average

Product (AP)

Stage 1 Increases at an

increasing rate up to

point H later at

diminishing rate

Initially increases

and reaches the

maximum at point

G’ and after point

G’ begin to diminish

Increases and

reaches at its

maximum point

H’,which is at

the boundary

line of stage 1.

At point H AP

and MP are

equal

Stage 2 Continue to increase

at diminishing rate up

to point J and reaches

it maximum

Continues to

diminish and

becomes zero at

point J’

After reaching

its maximum it

begins to

diminish

Stage 3 Start declining Becomes negative Continue to

diminish but

always remain

greater than

zero

Supply Shocks

• Our production function shows that output

is a function of capital and labor inputs

• However, this function is subject to change

as a result of:

– Technological change

– Changes in regulatory environment

– Changes in the supply of inputs other than

capital and labor (e.g., energy)

Curve Shifts

• The production function is a multivariable

function

– Output depends on capital, labor, the

productivity parameter, and (implicitly) other

omitted variables

• So, if we plot output versus labor, we

conceptually hold the other variables fixed

– If any of those other variables change, our

plot of the production function must shift

Figure 3.4 An adverse supply

shock that lowers the MPN

The Labor Market

• We now consider the labor market

• We will now assume that capital is fixed (in

fact, the capital stock grows slowly over

time)

• In a typical business cycle, capital varies

little, but labor varies a lot

The Demand for Labor:

Assumptions

• The capital stock is fixed.

• Workers are all alike.

• Wages are determined in competitive

labor markets.

• Firms choose how much labor to employ

in order to maximize profit.

Profit Maximization and

Labor Demand

• A firm will hire an additional unit of labor

so long as the value of the extra output

produced by a worker is greater than (or

just equal to) the cost of the additional unit

of labor

Profit Maximization and

Labor Demand (Equations)

Notation

Profit Maximum

Summary

Demand for Labor

• At any given real wage, what quantity of

labor will a firm buy?

– Answer: The quantity that makes the marginal

product of labor equal the real wage.

The Demand for Labor

• The marginal product of labor and the

labor demand curve

– Labor demand curve shows relationship

between the real wage rate and the quantity

of labor demanded

– So the labor demand curve is downward

sloping; firms want to hire less labor, the

higher the real wage

Demand Shifters

• Factors that shift the labor demand curve

– Note: A change in the wage causes a

movement along the labor demand curve, not

a shift of the curve

– Supply shocks: Beneficial supply shock raises

MPN, so shifts labor demand curve to the

right; opposite for adverse supply shock

– Size of capital stock: Higher capital stock

raises MPN, so shifts labor demand curve to

the right; opposite for lower capital stock

The Supply of Labor

– The labor supply curve

• Increase in the current real wage should raise

quantity of labor supplied

• Labor supply curve relates quantity of labor

supplied to real wage

• Labor supply curve slopes upward because higher

wage encourages people to work more

The Supply of Labor

The Supply of Labor

• Factors that shift the labor supply curve

– Wealth: Higher wealth reduces labor supply

(shifts labor supply curve to the left,

– Expected future real wage: Higher expected

future real wage is like an increase in wealth,

so reduces labor supply (shifts labor supply

curve to the left)

The Supply of Labor

Labor Market Equilibrium

A Favorable Supply Shock

Effects of A Temporary

Adverse Supply Shock

Full Employment

• In the labor market, the demand-supply equilibrium determines the quantity of labor, the number employed. – We consider this to be the “full-employment” quantity

of labor.

• Also, if we use the production function to find the level of output produced when the labor input is at its full-employment level, we call that output the full-employment level of output:

,Y AF K N

Full Employment

• A situation in which all available labor resources

are being used in the most economically efficient

way. Full employment embodies the highest

amount of skilled and unskilled labor that could

be employed within an economy at any given

time. The remaining unemployment is frictional.

Labor Force: Each person over age 18 and below 60 is

considered as a Labor force in Pakistan

Households can assigned to one of three categories:

• Employed: If the person worked full time job or part time

job during the past week (or was on sick leave or

vacation from a job)

• Unemployed: If the person didn’t work during the past

week but looked for work during the past four weeks.

• Not in the Labor force: if the person didn't work during

the past week and didn't look for work during the past

four weeks (examples are full-time students age less

than 18, homemakers, and retirees).

Unemployment

• Long-run versus Short-run Unemployment: – Long-run: The natural rate of unemployment

– Short-run: The cyclical rate of unemployment

• Natural Rate of Unemployment – The amount of unemployment that the economy

normally experiences and does not go away on its own even in the long run.

• Cyclical Unemployment – Associated with with short-term ups and downs of the

business cycle and refers to the year-to-year fluctuations in unemployment around its natural rate

Types of Unemployment

• Frictional Unemployment

• Cyclical Unemployment

• Structural / Technological Unemployment

• Seasonal Unemployment

• Voluntary Unemployment

• Hidden Unemployment

Frictional Unemployment

• Frictional Unemployment - always some

unemployment due to workers voluntarily

changing employment

• Frictional unemployment – may reflect

acquisition of more skills and training. Duration

of unemployment depends on knowledge of

labour market and efficiency of job seeking.

Cyclical Unemployment

• Cyclical Unemployment or demand-

deficient unemployment occurs in the

downswing and recession phases of the

trade cycle.

• It is basically due to substantial reductions

in aggregate demand or total spending in

the economy.

Cyclical Unemployment

• The reduction in demand for goods and services

leads to a reduction in total output and ultimately

results in a reduction in demand for the labour

that produce those goods and services.

• Cyclical unemployment is considered serious by

governments of the world who are charged with

correcting flagging aggregate demand via

appropriate economic policy.

Structural / Technological

Unemployment

• Structural / Technological Unemployment refers to changes in the structure of the economy over time due to technology changes and changes in the pattern and nature of consumer spending.

• Technological change usually means that the demand for some types of workers increases, while others find their skills are no longer relevant

Structural / Technological

Unemployment

• Bank tellers under threat from automatic teller machines (ATM), the replacement of horse and carriage by the motor vehicle causing unemployment for blacksmiths are both examples of structural unemployment.

• Changes in consumer demand, will result in job losses in some occupations and gain in others. As compact discs replace records, for example, workers in records factories become redundant.

Seasonal Unemployment

• Seasonal Unemployment affects

occupations such as fruit pickers,

fishermen and shearers. Where the

nature of their work means that

employment may not be available for the

whole year.

Voluntary Unemployment

• Those able people who prefer for various

reasons to be without a job.

Hidden Unemployment

• Those people who have given up ‘actively

seeking work’ due to frustration, loss of

self esteem or despair – are more

commonly referred to as discouraged

workers or the hidden unemployed.

Okun's Law:

The quantitative impact on aggregate output of a

change in the unemployment rate is described by

Okun's law, a rule of thumb (rather than a "law") first

stated by Arthur Okun, chairman of the Council of

Economic Advisers in the 1960s during

the Johnson administration. According to Okun's law,

the gap between an economy's full-employment output

and its actual level of output increases by 2 percentage

points for each percentage point the unemployment rate

increases.20,21 We express Okun's law algebraically

as

Okun’s Law Statistics in Asian

Countries

Reasons for higher youth unemployment

Human capital: A number of students leave school or college with few

qualifications and therefore lack the human capital needed to find secure

employment

Experience: Younger workers have less experience in the labour market

and employers may decide to employ someone with a track record in work

that is perceived to be more productive. In recruitment freeze, younger

workers often miss out because of the experience factor.

Training costs: Some employers may not want to cover the extra costs of

training younger workers – preferring instead to take a free-ride on

employees who have received training in their previous job

Internships: There has been a decline in the number of internship

available for people leaving school aged 16. High quality vocational

education makes younger workers more employable.

Benefit reforms: Some economists believe that youth unemployment is

partly the result of the benefits system and that claiming benefit should be

made harder for those who have not taken paid work after leaving school

or college. For example, unemployment benefits could rise according to

how many years a person has been working and paying national

insurance