producers/sellers. In a market economy, the inputs [land ®, labor (L), capital
(K) and entrepreneurial ability] are owned by individual agents who make
decisions about the amount of each input they want to supply. The decisions
of the producers determine the demand for the inputs. Remember that the
decisions of the producers reflects the preferences and ability
In the goods markets, each individual consumer will maximize their utility
MU
MU
MU
X =
Y = ⋯=
N , subject to: P Q + P Q + ⋯ + P Q ≤ BUDGET
P
P
P
X
X
Y
Y
N
N
X
Y
N
when:
This is an equilibrium condition. The consumer cannot alter their
expenditure and improve their welfare or increase their utility. Income
(budget), preferences (MUN) and the relative prices determine the outcomes.
The market demand reflects these conditions to the market. The demand
function is a schedule of the maximum price (reservation price) that buyers
are willing and able to pay for a schedule of quantities of a good in a given
period of time (ut), ceteris paribus. The supply function in the market reflects
the opportunity cost or producing each unit of output. It can be defined as the
minimum price (reservation price) that the seller will accept for each unit of
output. Market equilibrium is determined by the interaction of the buyers and
sellers.
268
14 Markets for Inputs and Distribution of Income
The equilibrium of the buyers and market equilibrium depends on the
income of the buyers. The way in which income is distributed in a system
determines the allocation decisions. The judgment about the criteria used to
distribute income has both an ethical and efficiency dimension. In most social
groups, it is considered desirable that income be distributed in proportion to
the contributions to the achievement of objectives. Clearly, most societies
make exceptions: most societies refuse to let individuals who are incapable of
making contributions do without resources and goods to support life. In
industrial societies there is a range of judgments regarding what things should
be provided. At one extreme few resources are provided. At the other extreme
a higher level of comfort is considered appropriate.
From an efficiency perspective, each factor should receive a share of
income in proportion to the factor’s contribution to the value of the output.
John Bates Clark (1847-1938) was one of the architects of the “marginal
productivity theory of income distribution.” In concept the idea is simple, in
practice it is difficult to measure the contributions of each factor to the
production process.
The production process was described by a production function. In its
simplistic form it is: Q = f(labor, kaptial, land, technology, . . . ) The
marginal product of each factor describes the contribution of each factor to the
production of the output. The marginal product of a factor can be described
as:
ΔQ
MP ≡
, the change in output ( Q ) caused by a change in F ( the factor )
F
ΔF
With the use of calculus the marginal products of a set of inputs can be
described as partial derivatives. Given a production function:
269
14 Markets for Inputs and Distribution of Income
Q = ALαKβ , the marginal products of the factors is:
∂ Q
MP =
= AαLα− 1 K β
L
∂ L
∂ Q
MP K =
= AL α K β−1
∂ K
If the marginal products are known and the relative prices of goods in the
markets reflect the values of the outputs, the value of each factors
contribution can be calculated as the product of MPF and the price of the
output. The marginal productivity theory of income distribution suggests that
the income share each factor of production should receive is determined by
the marginal product of the input and the price of the output. The change in
the value of the output associated with a change in an input is called the
value of marginal product (VMP) or the marginal revenue product
(MRP). Originally the VMP was used to describe the demand for an input into
production process for a purely competitive firm and the MRP was used to
describe the demand for an input used to produce a product where market
power (a negatively sloped product demand) existed. Most texts currently use
MRP as a generic term that covers both VMP and MRP.
14.1 A. THE DEMAND FOR INPUTS
T he demand for a factor of production is a derived demand. You do not
have a direct demand for an auto mechanic: rather you have a demand for an
automobile that functions properly. The demand for the mechanic is a derived
demand. You probably do not have a demand for 2X4’s (they really aren’t 2”
by 4”), you have a demand for a house that is constructed with the lumber.
The demand for an input is determined by the relative value of the good
produced and the productivity of the input.
270
14.1 A. The Demand for Inputs
The demand for an input can be derived by using the production function
(the MP for an input) and the price of the good. The marginal revenue product
is shown in Table IX.1.
Table IX.1 shows a short run production function. Capital is fixed at 4 units.
As labor is added, the output (Q or TP) increases at an increasing rate. In this
example the marginal product of labor (MPL) declines from the first unit. This
makes the MRPL or demand for labor less messy.
The constant price at all levels of output (PX = $11 at all output levels) is
the result of the firm being in a purely competitive market: the demand faced
by the firm is perfectly elastic.
The marginal revenue product is a measure of the value of the output that
is attributable to each unit of the input. The first unit of labor “produces “ 8
units of output (MPL = 8). These 8 units of output can be sold for $88
(PX=$11, MPL1= 8: so PX*MPL= 8*11=88). The maximum that an employer
would be willing to pay the first unit of labor would be $88. The MRP of the
second worker is $77. The second worker produces 7 units of output valued at
$11 each.
271
14.1 A. The Demand for Inputs
Table XI.1
Short Run Demand for Labor in Pure Competition
(MP
Kaptial (fixed)Labor (L) Q, TP
MP
L)PX
L
Product price, PX MRPL
4
0
0
$11
4
1
8
8
$11
$88
4
2
15
7
$11
$77
4
3
21
6
$11
$66
4
4
26
5
$11
$55
4
5
30
4
$11
$44
4
6
33
3
$11
$33
4
7
35
2
$11
$22
4
8
36
1
$11
$11
4
9
36
0
$11
$0
The MRP of each unit of input is the maximum an employer would be willing
to pay each unit of input and can be interpreted as a demand function. Notice
that if 35 units could be sold, 7 units of labor would be hired. The MRPL7 is
$22. The maximum the employer would be willing to pay the 7th unit of labor is
$
The MRP is the maximum the employer
(Wage)
will pay each unit of labour in a given
A
period of time given the productivity (MP)
and the price of the output (PX). At a wage
of WR, the firm will hire N workers. All N
workers are paid the same wage rate; i.e.
there is no price discrimination.
The wage bill or expense is shown as area
0NRWR, measure by NWR. the producer
W
R
R
surplus is area WRRA. The producer
surplus is not the same as profit. The
payment to the fixed factor must be
subtracted from the producer surplus to
calculate profit.
MRPL
0
N
L/ut
Figure IX.1
272
14.1 A. The Demand for Inputs
$22. Wage/price discrimination is technically illegal, all workers are paid $22.
The employer gains $66 on the first unit of labor ($88-$22), $55 on the
second, $44 on the third, $33 on the forth, $22 on the fifth, $11 on the sixth
and nothing on the seventh. This is shown graphically in Figure IX.1
The MRP of an input used by a firm with market power (a negatively sloped
demand for it output) is shown in Table IX.2.
Table XI.2
Short Run Demand for Labor For Firm in Imperfect Competition or Monopoly
Labor
(MP
Kapital (fixed)
Q, TP
MP
L)PX
(L)
L
Product price, PX
MRPL
4
0
0
$13
4
1
8
8
$11
$91
4
2
15
7
$10
$70
4
3
21
6
$9
$53
4
4
26
5
$8
$39.00
4
5
30
4
$7
$28
4
6
33
3
$6
$19
4
7
35
2
$6
$12
4
8
36
1
$6
$6
4
9
36
0
$6.00
$0
Note that the only difference in Table IX.1 and IX.2 is that he price of the
output must be decreased if more units are to be sold. This makes the
demand for the input relatively more inelastic.
273
14.1 A. The Demand for Inputs
$
B
WH
G
WR
H
0
J
L/ut
Figure IX.2
14.1.1 SUPPLY OF INPUTS
T he individual agent who owns the input will decide how much of a factor
they want to offer for sale at each price offered for the input. A worker must
decide how many units of labor (hours, days, weeks, years, etc) they will offer
for sale at each possible wage rate. The supply of labor is a function of the
wage rate, the value of leisure, alternatives available, taxes and other
circumstances. Generally it is believed that more labor will be offered for sale
at higher wage rates, up to a point. Owners of other factors of production
(land, capital, entrepreneurial ability) make decisions that determine the
supply functions of those factors. Figure IX.2 illustrates several possible supply
functions. The segment HGB is one possibility, it represents a supply where
the worker is willing to offer more labor at higher wage rates. The maximum
labor that will be offered for sale is at point B. At a wage rates higher than WH,
the supplier substitutes leisure for income and offers less labor for sale as the
274
14.1.1 Supply of Inputs
wage increases. Another possibility is a supply of labor that is represented by
segment WRGB. A horizontal segment at the prevailing wage rate is caused by
a worker or workers who refuse to work at any wage that is less than the
prevailing wage, WR.
14.1.2 MARKET FOR INPUTS
T he market for an
$
input includes all potential
buyers and sellers of an
B
W
input. The demand reflects
H
S
the decisions of the buyers
of the inputs and is based
G
W
on the MRP for the factor.
R
WL
The supply function
MRP
H
w
represents the decisions of
MRP
the factor owners to supply
1
the input at various prices.
0
T
L/ut
Figure IX.3 represents a
F
J
Figure IX.3
market for labor. MRP
represents the demand and S is the supply of L. The market equilibrium
occurs at point G where the quantity of labor offered for sale is equal to the
quantity of labor that is demanded at a the wage rate WR. J units of labor are
hired.
An increase in the productivity of labor or the price of the good produced
(PX) will increase the demand (MRP). A decrease in productivity or PX will shift
the MRP to the left (MRP1). If worker are unwilling to work for less than the
market wage, WR, the supply is represented by line WRGB. The level of
275
14.1.2 Market for Inputs
employment would fall to F units of labor. If HGB were the relevant supply,
unemployment would fall to T units and the wage would fall to WL.
If the MRP increased so the wage rate exceeded WH, workers would supply
a smaller quantity of labor in a given period of time.
14.1.3 INCOME DISTRIBUTION
I ncome distribution can be described as a functional or personal
distribution. The functional distribution of income describes the allocation of
income among the factors of production. The distribution of income among the
members of society, individuals and families, is called the personal distribution
of income.
Adam Smith, David Ricardo, Karl Marx and other early economists were
primarily concerned about the distribution of income among social classes that
were partially based on economic criteria. During the feudal era labor (serfs)
and land owners (aristocracy and church) were the important factors of
production. Generally, the social classes were the serfs, aristocracy and clergy.
Economic behavior was coordinated by a complex set of social institutions that
were based on deontological ethics (duty). Reciprocity and command were the
primary organizing mechanisms. Markets existed and were used in many
cases. Market towns and fairs were used to allocate some goods while labor,
land and many goods were allocated through obligations specified by tradition
and command.
The personal distribution of income describes the allocation of income
among economic agents. In most modern, industrial societies, markets are the
primary organizing institution of economic processes. Markets determine the
allocation of income as well as the allocation of scarce resources. Other social
276
14.1.3 Income Distribution
institutions such as welfare and philanthropy play a minor role in the personal
distribution of income.
Irvin Tucker ( mi
croE C
ONOMICS for Today , South-Western 2000, p 283)
shows the distribution of income based on the head of household. His data is
based on the Census data and is shown in Table IX.3.
Table IX.3
Income Distribution Based on Head of Household - 1997
Irvin Tucker, m
icroE C
ONOMICS for Today , South-Western 2000, p 283
Characteristic By Head of
Median Income
Household
All Families
$44,568
Male
$32,960
Female
$21,023
Age 25-34
$39,979
Age 65+
$30,660
Head non High School Grad
$25,465
Head High School Grad
$40,040
Head with Bachelor’s degree
$67,230
The information in Table IX.3 poses several issues. When considering
income distribution by age of household, there is a “life cycle” of a person’s
earnings and needs that should be considered. It should be noted that the
distribution of wealth and income are two related but different problems.
Another issue is the role of education and training. Disease and the industrial
revolution significantly altered the social classes and the distribution of
income. Technological change is a fundamental feature of modern industrial
societies and will change the nature and role of education and training in the
distribution of income.
277
14.1.3 Income Distribution
A “Lorenz Curve” can also describe the personal distribution of income. A
Lorenz curve can be used to show either the distribution of income or wealth
and can be applied to the world, a country or a sub category of individuals
(the military, lawyers, or . . . ). A Lorenz curve plots the cumulative proportion
of income units and cumulative proportion of income received when income
units are arrayed from lowest to highest.
The data for a Lorenz curve is shown in Table IX.4. (Irvin Tucker,
mi
croE C
ONOMICS for Today , South-Western 2000, p 282) The income
distribution is arrayed from lowest to highest. The data in Table IX.4 suggest
that the income distribution became more equal from 1929 to 1970 and less
equal from 1970 to 1997. The trends in income distribution are subject to
controversy. There are many forces that influence income distribution. It is
highly unlikely that the MRP is the single determinate of the income share
received by a factor or individual who