EA Session 20: EA Session 20: August 23, 2007August 23, 2007

Overview• Typology of Situations to be covered

• Equilibrium in Competitive Factor Markets– Characteristics of Competitive Factor Markets

– Demand for Factor Input with Only One Variable Factor

– Distinguishing between Marginal Revenue Product (MRPL) & Value of Marginal Product (VMPL) of Labor

– Comparing Input and Output Market Equilibrium Conditions

– Firm’s Demand Curve for Labor (with Variable Capital)

– Industry Demand for Labor

– A Firm’s Input Demand in a Competitive Factor Market

– Labor Market Equilibrium under Competition & Monopoly

– Economic Rent

Typology of Situations

Typology 1 2 3 4 5 6 7 8

Seller(Product) comp m’ply comp m’ply comp m’ply

comp m’ply

Buyer(Labor) comp comp m’sny m’sny comp comp

m’sny m’sny

Seller(Labor) comp comp comp comp m’ply m’ply

m’ply m’ply

Characteristics of Competitive Factor

Markets

1) Large number of buyers & sellers of the factor of production

2) The buyers and sellers of the factor of production are price takers

Demand for Factor Input with Only One Variable Factor

• Demand for factor inputs is a derived demand, derived from factor cost and output demand.

• Measuring the Value of a Worker’s Output– Marginal Revenue Product of Labor (MRPL)

– MRPL = (MPL)(MR)

• In a competitive product market – MR = P => VMPL=P.MPL

Marginal Revenue Product (MRPL) &

Value of Marginal Product (VMPL) of

Labor

Hours of Work

Wages($ perhour)

VMPL = MPLx P

Competitive Output Market (P = MR)

MRPL = MPL x MR

Monopolistic Output Market

(MR <P)

w* SL

In a competitive labor market, a firm faces a perfectly elastic supply of labor

and can hire as many workers as it wants at w*.

Hiring by a Firm in theLabor Market (with Capital Fixed)

Quantity of Labor

Price ofLabor

VMPL = DL

L*

The profit maximizing firm willhire L* units of labor at the point

where the marginal revenue productof labor is equal to the wage rate.

Can we interpret this point of equilibrium as MR=MC?

A Shift in the Supply of Labor (e.g., due to baby boom/ female

entry)

Quantity of Labor

Price ofLabor

w1S1

VMPL = DL

L1

w2

L2

S2

Comparing Input and Output Market Equilibrium

Conditions

• Input market equilibrium condition:– Under monopoly: MRPL = MR.MPL = W => MR =

W/MPL = MC

– Under competition: VMPL = P. MPL = W => P = AR = MR = W/MPL = MC

• So, input market equilibrium condition is the same as the profit-maximization condition in the output market

VMPL1 VMPL2

When two or more inputs arevariable, a firm’s demand for one input

depends on the marginal revenue product of both inputs.

Firm’s Demand Curve for Labor

(with Variable Capital)

Hours of Work

Wages($ perhour)

0

5

10

15

20

40 80 120 160

When the wage rate is $20, A represents one point on the firm’sdemand for labor curve. When the wage rate falls to $15, the MRP curve shifts, generating a new point C on the firm’s demand for labor curve. Thus A and C are on the demand for labor curve, but B is not. Thus, demand curve for laboris more elastic in the presence of anothervariable factor, which opens up scope for substitution.DL

A

B

C

• Assuming all firms respond to a lower wage– All firms would hire more workers.– Market supply of output would increase.– The market price of output will fall. – The quantity demanded of labor by the

firm will be smaller, given lower output price.

– Thus, industry demand curve would be less elastic as compared to the curve w/o

any price fall.

Industry Demand for Labor

VMPL1

Derivation of the Industry Demand for

Labor

Labor(worker-hours)

Labor(worker-hours)

Wage($ perhour)

Wage($ perhour)

0

5

10

15

0

5

10

15

50 100 150 L0 L2

DL1

Horizontal sum ifproduct price

unchanged

120

VMPL2

L1

Industrydemand

curve withprice falling

DL2

Firm Industry

Step 1 Step 1More labor=>More output=>Less price=>VMPL shifts back

step2

Step 2

SMarket Supplyof fabric

A Firm’s Input Demand in aCompetitive Factor Market

Yards ofFabric (thousands)

Yards ofFabric (thousands)

Price($ peryard)

Price($ peryard)

D

Market Demandfor fabric

100

ME = AE10 10

Supply ofFabric Facing Firm

50

Demand for Fabric

VMP

Observations1) The firm is a price taker at $10.2) S = AE = ME = $103) ME = VMP @ 50 units

SL = AE

SL = AE

DL = VMPL DL = MRPL

VMPL =P *MPL

Labor Market Equilibrium (typology 1 & 2)

Number of Workers Number of Workers

Wage WageCompetitive Output Market Monopolistic Output Market

wC

LC

wM

LM

vM

AB

WC

LC

With monopoly, w↓, L ↓, Q ↓

(VM – WM) =‘exploitation of labor under monopoly

Labor Market Equilibrium

• Equilibrium in a Competitive Output Market– DL(VMPL) = SL

– wC = VMPL

– VMPL = (P)(MPL)– Markets are efficient

• Equilibrium in a Monopolistic Output Market– MR < P– MRP = (MR)(MPL)

– Hire LM at wage wM

– vM = marginal benefit to consumers

– wM = marginal cost to the firm

Labor Market Equilibrium

• Equilibrium in a Competitive Output Market– DL(VMPL) = SL

– wC = VMPL

– VMPL = (P)(MPL)– Markets are efficient

• Equilibrium in a Monopolistic Output Market– MR < P– MRP = (MR)(MPL)

– Hire LM at wage wM

– vM = marginal benefit to consumers

– wM = marginal cost to the firm

Total expenditure (wage) paidis rectangle 0w* AL*Economic Rent

Economic rent is ABW*

B

Economic Rent

Number of Workers

Wage

SL = AE

DL = VMPL

w*

L*

A

0

The economic rent associated with theemployment of labor is the excess of wages

paid above the minimum amount neededto hire workers.

How can rent toLabor disappear?

EconomicRent

s1

EconomicRent

s2

Land Rent

Number of Acres

Price($ peracre)

Supply of Land

D2

D1

Why is economic rentincreasing?