© Pilot Publishing Company Ltd. 2005 Chapter 13 Factor Market

© Pilot Publishing Company Ltd. 2005

Chapter 13

Factor Market


Contents:

• Factor Demand

• Factor Supply

• Other Points to be Noticed


Factor Demand


In factor markets

Firms demand factors to produce goods

Firms aims at maximizing wealth (by weighing

the gain from employing factors against the cost.)


Factor demand

is also called derived demand.

Because a firm demands factors only if there is

a demand for the good it produces.


Symbols:

Quantities of factors employed – A, B, C, ...

Factor (hire) prices – HA, HB, HC, ... Quantity of the good produced (product) – Q

Product price – P


Marginal factor cost (MFC)

Marginal factor cost curve

is the cost of employing an additional unit of a factor.

(MFC of a factor vs. MC of a good)


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)


Factor Supply Curve

= MFC curve = AFC curve

Shape of factor supply curve, MFC curve and AFC curve

$

Factor A0

H

As the firm can employ as many units of the factor as it desires without affecting H,the factor supply curve as well asthe MFC curve & the AFC curve arehorizontal lying at H.


Marginal revenue product curve

Value of marginal product (VMP)

VMP = MP x P

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.

Definitions:


When a firm employs an additional unit of factor,

its output will by MP and

its revenue will by marginal revenue product

Derivation:

MRP = MP x MR


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)

Derivation:


APMP

Output produced

0 Factor A 0

ARP=AP x AR

MRP=MP x MR

Factor A

Output produced

Shape of MRP curve and ARP curve

AP x AR=ARP

MP x MR=MRP

Derivation of MRP and ARP curve


H1 MRP (gain) MFC (cost)

The firm will not employ any units of the factor.

At H1 (=MFC)

Derivation of the factor demand curve


H2

M

A1

N

A2

At the factor price of H2

At M, MRP curve cuts MFC curve from below.

Either an or in factor employment would raise wealth.

A1 is wealth-

minimizing.

At N, MRP curve cuts MFC curve from above.

Either an or in factor employment would reduce wealth.

A2 is wealth-maximizing

At A2, ARP < AFC

Factor employmentat A2 brings losses. The employment is not worthwhile.

MFC = AFC


H3

A3

T

At the factor price of H3

At point T, MRP curve cuts MFC curve from above

At A3, ARP > AFC

Factor employment at A3 can maximize wealth.


Equilibrium conditions of factor employment

1. MRP = MFC1. MRP = MFC

2. MRP curve cuts MFC curve from above

(to determine the best employment level)

2. MRP curve cuts MFC curve from above

(to determine the best employment level)

3. ARP AFC

(to determine if it is worth employing)

3. ARP AFC

(to determine if it is worth employing)


So the factor demand curve is the portion of the MRP curve lying below the max. point of the ARP curve.

Provided that ARP AFC, the wealth-max. level of factor employment is A at which MRP=MFC=H.

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 the firms in the market.


Factor Supply


Income

Resource for own use (e.g., leisure)

N

M

R0R0 (e.g., 24 hours)

I0

Numerical value of the slope = Factor price (e.g., hourly wage rate)

Budget line of a price-taking factor supplier


Indifference map of a factor supplier

For a resource with reservation use (a good)

The indifference curves are convex to the

origin. Why?


Equilibrium of a factor supplier

I*

R*

A resource with reservation use (a good)

Amount of factor supplied


in price

Budget line tilts upward

Price effect

Substitution effect and income effect of a price change

The effect of a change in price can be decomposed into substitution effect and income effect.

A1A2


S.E.

Substitution effect Factor price cost of retaining the resource for o

ne’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.

A1A’


S.E.

A1A’

A2

Income effect

I.E.

factor price individual earns he keeps more units and supply fewer units in the factor market.

If the resource with reservation use is a superior good,

Factor price and quantity supplied arenegatively related.


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.


H’

S.E. > I.E.

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

Upward sloping factor supply curve


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.


H’

S.E. < I.E.



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.


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


Total payment to labour (W x L)Total payment to

other factors (TRP – W x L)

Total receipt (TRP = ARP x L)

Functional distribution of income

$

ARP

MRP

MFC=AFCW

0 LQuantity 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


B0

As more units of factor A are employed, factor B will be used

more intensively and productively

MRP curve of factor B shifts upward


Malthus’ law of population – a myth?

Population living standard of man (since MP & AP ) Population cease to expand when AP to the subsistence level

Malthus’ law of population


Why is the law not confirmed? Capital accumulation

MP & AP curve shifted upward greatly & rapidly.

Average living standard rose with population growth.

Investment on education Technological improvement Institutional improvement Specialization due to globalization


Income differential

In a price-taking factor market,

price of a factor (factor income) is determined by

the market D & S of the factor.


Income differential

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)


Income differential

market supply is determined by


amount of capital accumulated

size & structure of population

geographical distribution of labour

government policies

power of trade union


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.


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.


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.

Correcting Misconceptions:


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

Drop in the value of their output

1 $500

2 $1 100

3 $1 800

4 $2 600

5 $3 500


Survival Kit in ExamQuestion 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?

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© Pilot Publishing Company Ltd. 2005 Chapter 13 Factor Market