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.

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 = MRPIf P > MR, VMP > MRP

Marginal factor cost is the cost of employing an additional unit of factor. (vs. MC of output)

Marginal factor cost curve

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)MFC = H (=AFC)

Assuming that the firm is a price-taker in the factor market that it cannot affect the prevailing factor price (H).

Factor Supply Curve

= MFC curve = AFC curve

Shape of factor supply curve, MFC curve and AFC curve

$

Factor A0

H

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.

Marginal revenue product curve

Value of marginal product is equal to marginal product times price.

VMP = MP VMP = MP xx PP

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.

Definitions:

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 MRP = MP xx MR 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)

Derivation:

APMP

Output produced

0 Factor A 0

ARP=ARAP

MRP=MRMP

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

ARP=ARAP

MRP=MRMP

Factor A

Output produced

As MP curve must finally be downward sloping, MRP curve must also be downward sloping.

Similarly, ARP curve must also be downward sloping.

MRP curve passes through the turning point of ARP curve.

Features:

H1 MRP (the gain) cannot cover MFC (the cost).

The firm will not employ any unit of factor.

At the factor price of HAt the factor price of H11

Derivation of the factor demand curve

H2

M

A1

N

A2

At the factor price of HAt the factor price of H22

At M, MRP curve cuts MFC curve from below.

Either or in factor employment raises wealth.

A1 is wealth-minimizing.

At N, MRP curve cuts MFC curve from above.

Either or in factor employment reduces wealth.

A2 is wealth-maximizing.

• However, at A2, ARP < AFC.

• So it is not worth for the firm to employ any factor to produce.

MFC = AFC

H3

A3

T

At the factor price of HAt the factor price of H33

At point T, MRP curve cuts MFC curve from above.

At A3, ARP > AFC.

Factor employment at A3 raises wealth.

Equilibrium conditions of factor employment

1. MRP = MFC2. MRP curve cuts MFC curve from

above(to determine the max. employment level)

3. ARP AFC(to determine if it is worth to employ)

1. MRP = MFC2. MRP curve cuts MFC curve from

above(to determine the max. employment level)

3. ARP AFC(to determine if it is worth to employ)

So the factor demand curve of a price-taking firm is the portion of MRP curve lying below the max. point of ARP curve.

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

Factor Demand CurveFactor 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 SupplyFactor Supply

Income

Resources for own use (leisure)

N

M

R0R0 (24 hours)

I0

Numerical value of slope = Factor price (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)

Its indifference curves are convex to the origin. Why?

I (Income)

0

U3 > U2 > U1

U1

U3

U2

Resource without reservation use (neuter)

For a resource without reservation use (a neuter)

Its indifference curves are horizontal line. Why?

Equilibrium of a factor supplier

I*

R*

Resource with reservation use (a good)

Amount of factor supplied

I

0 R0

Resource without reservation use (neuter)

U*

Resource without reservation use

I*

=R*

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.

AA11AA22

S.E.

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.

AA11A’A’

S.E.

AA11

A’A’AA22

Income effect

I.E.

Factor price an individual earns more keeps more and supply less resource 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 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.

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 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.

H’

S.E. < I.E.

Backward bending factor supply curve

Backward bending factor supply curve

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 Other Points to be Noticed

Total payment to labour (WxL )Total payment to

other factors (TRP - WxL)

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 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

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.

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.

Transfer Economic

L earning W rent

1 $20 $50

2 30 50

3 40 50

4 50 50

5 60 50

6 70 50

7 80 50

P

Q

S

PL

P

Q

S

transfer earning

P

Q

S

economic rent

P

Q

S

economic rent

transfer earningD

P

Q

S

transfer earning

D

units of factor of production

P

Q

S

D

economic

rent