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Chapter 13
Factor Market
© Pilot Publishing Company Ltd. 2005
Contents:
• Factor Demand
• Factor Supply
• Other Points to be Noticed
© Pilot Publishing Company Ltd. 2005
Factor Demand
© Pilot Publishing Company Ltd. 2005
In factor markets
 Firms demand factors to produce goods
 Firms aims at maximizing wealth (by weighing
the gain from employing factors against the cost.)
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Factor demand
is also called derived demand.

Because a firm demands factors only if there is
a demand for the good it produces.
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Symbols:
 Quantities of factors employed – A, B, C, ...
 Factor (hire) prices – HA, HB, HC, ...
 Quantity of the good produced (product) – Q
 Product price – P
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Marginal factor cost curve
Marginal factor cost (MFC)
 is the cost of employing an additional unit of a factor.
(MFC of a factor vs. MC of a good)
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Marginal factor cost curve
Assumptions:
1. The firm is a price-taker in the factor market.
2. It cannot affect the prevailing factor price (H)
& hence MFC is a constant equal to H.

MFC = H (=AFC)
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Shape of factor supply curve, MFC curve and AFC curve
$
As the firm can employ as many units of
the factor as it desires without affecting H,
the factor supply curve as well as
the MFC curve & the AFC curve are
horizontal lying at H.
H
Factor Supply Curve
= MFC curve
= AFC curve
0
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Factor A
Marginal revenue product curve
Definitions:
Marginal revenue product (MRP)
 is the gain from employing an additional unit of
a factor. (MRP of a factor vs. MR of a good)
Average revenue product (ARP)
 is the gain from employing a unit of a factor
on average.
Value of marginal product (VMP)

VMP = MP x P
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Derivation:
When a firm employs an additional unit of factor,
 its output will  by MP and
 its revenue will  by marginal revenue product

MRP = MP x MR
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Derivation:
In the product market,
 if the firm is a price-taker,
MR = P  MRP (= MP x MR) = VMP (= MP x P)
 if the firm is a price-searcher,
MR < P  MRP (= MP x MR) < VMP (= MP x P)
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Shape of MRP curve and ARP curve
Output produced
Output produced
MRP=MP x MR
AP x AR=ARP
ARP=AP x AR
MP x MR=MRP
AP
MP
0
Factor A
0
Derivation of MRP and ARP curve
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Factor A
Derivation of the factor demand curve
At H1 (=MFC)
H1
MRP (gain)  MFC (cost)

The firm will not employ
any units of the factor.
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At the factor price of H2
 At N,
M,MRP
MRPcurve
curve

M
N
A1
A2
H2
MFC = AFC
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cuts
cuts
MFC
curve

AtMFC
A2, curve
from
above.
from
below.
ARP
< AFC
 Either an  or 
factor
Eitheremployment
an  or 
in
 Factor employment
in factor
employment
would
reduce
wealth.
at A2 brings losses.
would raise wealth.
The

A2employment
is wealth- is
maximizing
 Aworthwhile.
not
1 is wealthminimizing.
At the factor price of H3
At point T, MRP curve
cuts MFC curve
from above
H3
At A3, ARP > AFC
T
Factor employment at
A3 can maximize wealth.
A3
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Equilibrium conditions of factor employment
1. MRP = MFC
2. MRP curve cuts MFC curve
from above
(to determine the best employment level)
3. ARP  AFC
(to determine if it is worth employing)
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Provided that ARP  AFC, the wealth-max. level
of factor employment is A at which MRP=MFC=H.
So the factor demand curve is
the portion of the MRP curve
lying below the max. point of
the ARP curve.
Factor Demand Curve
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Market factor demand curve
A factor is demanded by many different firms,
e.g., clerks are employed in hospitals, schools,
accounting firms, etc.
So the market factor demand curve is equal to
the horizontal sum of factor demand curves
of all the firms in the market.
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Factor Supply
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Budget line of a price-taking factor supplier
Income
N
Numerical value of the slope
= Factor price (e.g., hourly wage rate)
I0
0
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M
Resource for
R own use
R0 (e.g., 24 hours)
(e.g., leisure)
Indifference map of a factor supplier
For a resource with
reservation use (a good)
The indifference curves
are convex to the origin.
Why?
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Equilibrium of a factor supplier
A resource with
reservation use (a good)
I*
Amount of factor
supplied
R*
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Substitution effect and income effect of a price change
The effect of a
Price effect
change in price
can bein price
decomposed into
Budget effect
line
substitution
upward
andtilts
income
effect.
A2 A1
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Substitution effect
Factor price  cost of retaining the resource for
one’s own use the individual will keep fewer units
& supply more units in the factor market.
By the S.E., factor price and
quantity supplied are positively related.
S.E.
A’
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A1
Income effect
S.E.
A’
If the resource with reservation use is
a superior good,
factor price   individual earns 
 he keeps more units and supply fewer
units in the factor market.
Factor price
and quantity
supplied are
I.E.
negatively
related.
A1
A2
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Backward bending factor supply curve
 When the factor price is low, the Qs is small. Even if
the factor price  by 10%, the  in income is rather small.
 At the beginning, the individual still owns a large amount
of the resource for his own use.
 When H rises, the individual is willing to supply more,
i.e., income effect (A) < substitution effect (A).
The factor supply curve is upward sloping.
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When factor price is low, a rise in factor price from H1
to H’ will raise the factor supplied  S.E. > I.E.
H’
Upward sloping
factor supply curve
S.E. > I.E.
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Backward bending factor supply curve (con’t)
 When the factor price is high, the Qs is large. Even a 10%
rise in income will raise the income by a very large amount.
 The individual now owns only a very small amount of the
resource for his own use.
 This time, when H rises, the individual desires to keep
more units of the resource for his own use & supply less,
i.e., income effect (A) > substitution effect (A).
The factor supply curve is downward sloping.
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When factor price is high (above H’), a rise in factor price
from H’ to H2 will lower the factor supplied  S.E. < I.E.
S.E. < I.E.
H’
Backward bending
factor supply curve
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Q13.3:
If the resource with reservation use is an inferior good,
what will be the shape of the factor supply curve of an
individual?
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Other Points to be Noticed
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Functional distribution of income
$
Total payment to
other factors
(TRP – W x L)
Total receipt
(TRP = ARP x L) Total payment to
labour (W x L)
W
ARP
MFC=AFC
0
MRP
Quantity
supplied
of labour
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L
Factor employment and marginal revenue product
When the firm employs one
more unit of factor A

MPA and MRPA 
(along the curve)
A0 A0+1
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As more units of factor A are
employed, factor B will be used
more intensively and productively

MRP curve of factor B
shifts upward
B0
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Malthus’ law of population – a myth?
Malthus’ law of population
 Population   living standard of man 
(since MP & AP )
 Population cease to expand when AP 
to the subsistence level
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Why is the law not confirmed?
 Capital accumulation
 Investment on education
 Technological improvement
 Institutional improvement
 Specialization due to globalization
 MP & AP curve shifted upward greatly & rapidly.
 Average living standard rose with population growth.
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Income differential
In a price-taking factor market,
price of a factor (factor income) is determined by
 the market D & S of the factor.
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Income differential
In a price-taking factor market,
market demand is determined by
 productivity of the factor
(e.g., ability, training and working experience)
 price of the product (depends on its D & S),
 discrimination
(e.g., against the female, youngster & minority)
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Income differential
In a price-taking factor market,
market supply is determined by
 amount of capital accumulated
 size & structure of population
 geographical distribution of labour
 government policies
 power of trade union
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If the factor market is price-searching,
(or controlled by a central authority / an institution)
factor price is NOT determined by the market D & S
of the factor
 H may not reflect the productivity of the factor
i.e., H  MRP.
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Correcting Misconceptions:
1. MRP is the same as VMP.
2. The demand curve for a factor is the MRP
curve.
3. If a firm is a price-taker in a factor market,
the factor demand curve is horizontal.
4. Substitution effect must be negative.
© Pilot Publishing Company Ltd. 2005
Correcting Misconceptions:
5. The higher the factor price, the larger
the quantity supplied of a factor.
6. As the average living standard rises with
population growth, the law of diminishing
returns is falsified.
7. The hire price of a factor must reflect its
marginal productivity.
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Survival Kit in Exam:
Question 13.1: Presently, a firm employs five workers. When
the workers are on their sick leave, the value of their output
drops. The table below shows the situation. If the wage rate is
$650, how many workers should the firm employ?
No. of workers on their
sick leave
1
2
3
4
5
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Drop in the value of their
output
$500
$1 100
$1 800
$2 600
$3 500
Survival Kit in Exam
Question 13.2:
Suppose a firm employs only two factors, land and
labour. The total return is distributed among them.
If the firm fires several workers, what will happen to
(a) the marginal product of labour and that of land?
(b) the total return of labour and that of land?
© Pilot Publishing Company Ltd. 2005