Ch. 8: Factor Market
Derive demand
 The demand for any factor of production is
a derived demand since it is derived from
the demand for the product it helps to
produce.
Value of Marginal Product
 VMP = P x MP
Marginal Revenue Product
 MRP = MR x MP
 If P = MR, VMP = MRP
 If P > MR, VMP > MRP
Marginal factor cost curve
Marginal factor cost is the cost of employing an
additional unit of factor. (vs. MC of output)
Assuming that the firm is a price-taker in the factor
market that it cannot affect the prevailing factor price (H).
So the cost in employing each additional unit of factor
in a price-taking factor market is the same, equal to H.
MFC = H (=AFC)
Shape of factor supply curve, MFC curve and AFC curve
As the firm cannot affect the factor price, it must faces a
horizontal factor supply curve lying at H, which coincides
with MFC curve and AFC curve.
$
H
Factor Supply Curve
= MFC curve
= AFC curve
0
Factor A
Marginal revenue product curve
Definitions:
Marginal revenue product (邊際生產收入) is the
gain from employing an additional unit of factor. (vs.
MR of output)
Average revenue product (ARP) is the gain from
employing an additional unit of factor in average.
Value of marginal product is equal to marginal
product times price.
VMP = MP x P
Derivation:
In employing an additional unit of factor, output of a
firm increases by MP and its revenue increases by
marginal revenue product (MRP) is equal to marginal
product times marginal revenue.
MRP = MP x MR
If the firm is a price-taker in the product market,
MR = P  MRP (= MP x MR) = VMP (= MP x P)
If the firm is a price-searcher in the product market,
MR < P  MRP (= MP x MR) < VMP (= MP x P)
Shape of MRP curve and ARP curve
Output produced
Output produced
MRP=MRMP
AP x AR=ARP
ARP=ARAP
MP x MR=MRP
AP
MP
0
Factor A
0
Derivation of MRP and ARP curve
Factor A
Features:
As MP curve must finally be
downward sloping, MRP curve
Output
must also be downward sloping.
produced
MRP=MRMP
Similarly, ARP curve
must also be downward
sloping.
ARP=ARAP
Factor A
MRP curve passes
through the turning
point of ARP curve.
Derivation of the factor demand curve
At the factor price of H1
H1
MRP (the gain)
cannot cover MFC
(the cost).
The firm will not
employ any unit of
factor.
At the factor price of H2
M
N
A1
A2
H2
MFC = AFC
At N, MRP curve
At M, MRP curve
cuts MFC curve
cuts
MFC
curve
• However,
at A2,
from
above.
from
ARP below.
< AFC.
Either  or  in
factor
Either
• So
itemployment
is 
notor  in
reduces
wealth.
factor
worth employment
for
the firm
raises
wealthtoAemploy
any
2 iswealth.
maximizing.
factor to produce.
A1 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 raises wealth.
A3
Equilibrium conditions of factor employment
1. MRP = MFC
2. MRP curve cuts MFC curve from
above
(to determine the max. employment level)
3. ARP  AFC
(to determine if it is worth to employ)
Provided that ARP  AFC, the wealth-max.
level of factor employment is: MRP=MFC=H
So the factor demand
curve of a price-taking firm
is the portion of MRP curve
lying below the max. point
of ARP curve.
Factor Demand Curve
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 firms in the market.
Factor Supply
Budget line of a price-taking factor supplier
Income
N
Numerical value of slope
= Factor price (Hourly wage rate)
I0
0
M
Resources for
R own use
R0 (24 hours)
(leisure)
Indifference map of a factor supplier
For a resource with
reservation use (a
good)
Its indifference
curves are convex to
the origin. Why?
For a resource without
reservation use (a neuter)
I (Income)
U3 > U2 > U1
U3
Its indifference
curves are horizontal
line. Why?
U2
U1
0
Resource
without
reservation use
(neuter)
Equilibrium of a factor supplier
Resource with
reservation use
(a good)
I*
Amount of factor
supplied
R*
I
I*
U*
Amount of factor supplied
0 =R*
R0
Resource
without
reservation use
Resource
without
reservation
use (neuter)
Substitution effect and income effect of a
price change
The effect of a
change
price
Priceineffect
can be
decomposed
into
in price
substitution effect
and income
Budgeteffect.
line
tilts upward.
A2 A1
Substitution effect
Factor price  cost of retaining the resource for
own use increases  to max. U, an individual supply
more units of resource in the factor market
Factor price and quantity supplied
are positively related.
S.E.
A’
A1
Income effect
S.E.
A’
If the resource with reservation
use is a superior good
Factor price  an individual earns
more  keeps more and supply less
resource in the factor market
Factor price
and quantity
supplied are
I.E.
negatively
related.
A
1
A2
Backward bending factor supply curve
When factor price is low, the quantity supplied is small.
Even if the factor price rises by 10%, the increase in
income is rather small.
Moreover, at the beginning, the individual still owns a
large amount of the resource.
So, when H rises, the individual is willing to supply
more, i.e., substitution effect (A) is larger than income
effect (A). The factor supply curve is upward sloping.
When factor price is low, a rise in factor price from H1
to H’ will raise the factor supplied  S.E. > I.E.
Upward sloping
factor supply curve
H’
S.E. > I.E.
Backward bending factor supply curve (Con’t)
When factor price is high, the quantity supplied is
large. Even a 10% rise in income will raise the income
by a very large amount.
Moreover, the individual now owns only a very small
amount of the resource.
So, when H rises, he desires to keep more of the
resource for own use, i.e., substitution effect (A) is
smaller than income effect (A). The factor supply
curve is downward sloping.
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
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?
Other Points to be Noticed
Functional distribution of income
$
Total receipt
(TRP = ARP x L) Total payment to
labour (WxL )
Total payment to
other factors
(TRP - WxL)
W
0
ARP
MFC=AFC
L
MRP
Quantity
supplied
of labour
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
When the firm employs one more unit of factor A, factor
B will be used more intensively and productively.
So MRP curve of
factor B shifts upward.
B0
If the factor market is price-searching or the market
is controlled by a central authority or an institution,
the factor price is no longer determined by market
demand and market supply of the factor.
Then, H may not reflect the productivity of the factor,
i.e., H  MRP.
Transfer Earning
 Transfer earning is the minimum amonut
that a factor must earn in order to prevent it
from transferring to another use.
Economic Rent
 Economic rent is the return over and above
the opportunity costs of the resources
employed in alternative uses.
L
1
2
3
4
5
6
7
Transfer
earning
$20
30
40
50
60
70
80
W
$50
50
50
50
50
50
50
Economic
rent
P
S
PL
Q
P
S
transfer earning
Q
P
S
economic rent
Q
P
S
economic rent
transfer earning
D
Q
P
S
transfer
earning
D
Q
units of factor of production
S
P
economic
rent
D
Q