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THE MARKETS FOR FACTORSPART 1

ECA002/ECB037 Principles of Microeconomics

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Learning Outcomes• Firms’ demand for inputs is derived from the demand for

their output

• Firms will hire inputs up to the point where the extra cost is just equal to the extra contribution to revenue

• Economic rent is the return achieved in use in excess of the highest available alternative return in another use

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INPUTS (FACTORS)• LABOUR:

– Units: hours of work, workers– Price: wage, salary

• CAPITAL: Machines, equipment– Units: number of machines, tools or production lines– Price: Rental price

Other factors: LAND

Advice: Revise the chapter on production and costs

ASSUMPTION: Firms can not affect the market price of inputs (price-takers in the input markets)

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Competitive Factor Markets

• Characteristics1. Large number of sellers of the factor of

production2. Large number of buyers of the factor of

production3. The buyers and sellers of the factor of

production are price takers

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Competitive Factor Markets

• Demand for a Factor Input When Only One Input Is Variable– Factor demands are derived demands

• Demand for an input that depends on, and is derived from, both the firm’s level of output and the cost of inputs

• Demand for computer programmers derived from how much software Microsoft expects to sell

– Derived Demand provides a link between the markets for output and the markets for inputs

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Dinput

0

Quantity of input

Pric

e of

inpu

t

Dinput = f(Pinput)Quantity of input demanded as function of the price of the input

* Negatively sloped

* Derived demand:Derived from the demand for goods and services the input helps to produce

***** We explore the link between the markets for inputs and the market for outputs

Demand for an Input

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Factor Input Demand – One Variable Input

• Assume firm produces output using two inputs: – Capital (K) and Labour (L)– Hired at prices r (rental cost of capital) and w

(wage rate)– K is fixed (short run analysis) and L is variable– Firm must decide how much labour to hire

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Factor Input Demand – One Variable Input

• How does a firm decide if it is profitable to hire another worker?– If the additional revenue from the output of

hiring another worker is greater than its cost– Marginal Revenue Product of Labour (MPRL)

• Additional revenue resulting from the sale of output created by the use of one additional unit of an input

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Factor Input Demand – One Variable Input

• The incremental cost of a unit of labour is the wage rate, w

• Profitable to hire more labour if the MRPL is at least as large as the wage rate, w

• Must measure the MRPL

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Factor Input Demand – One Variable Input

• MRPL is the additional output obtained from the additional unit of labour, multiplied by the additional revenue from an extra unit of output

• Additional output is given by MPL and additional revenue is MR

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INPUT DEMAND IN THE SHORT RUN

In the short run, one of the factors is fixed (K).

(a) Profit maximizing rule:

Produce Q to satisfy MR = MC.

(b) Q= f(L).

We can link (a) and (b)

ADDITION TO REVENUES = ADDITION TO COSTS

BY USING ANOTHER UNIT OF INPUT

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ADDITION TO REVENUES:MARGINAL REVENUE PRODUCT (MRP)

MRP= MPP* Pwhere* MARGINAL (PHYSICAL) PRODUCT:

MPP=AQ/AL• P: Revenue per unit of output P Constant: Firms: Price takers in the final market.

ADDITION TO COSTS:• MARGINAL COST=>W (WAGE)W Constant: Firms: Price takers in the labour market.

PROFIT MAXIMIZING CONDITION:MRP= W

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Factor Input Demand – One Variable Input

where R is revenue and L is labour

( )( )

L

L

L L

RMRPLQ RMPP and MRL Q

R R QL Q L

MRP MPP MR

∆=∆∆ ∆= =∆ ∆

∆ ∆ ∆ = ∆ ∆ ∆ =

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Factor Input Demand – One Variable Input

• In a competitive market MR = P• This means, for a competitive market

))(( PMPPMRP LL =Graphically, diminishing marginal returns,

MPPL falls as L increases In equilibrium: MRPL=w

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Why is the demand for an input downward sloping?

MPP* P= W (1)W falls: firm needs to readjust the use of

inputs to reach again equilibriumP is constant, only way of readjusting is

reducing MPP* Law of Diminishing Returns: increasing L reduces MPP

**** If W falls, the demand for L increases

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How many workers to hire?• How much labour to use at current prices of input and output?• W= £360; Price of cutting boards = £20

Number of workers

Total number of cutting

boards/week

MPP(extra cutting boards/week)

MRP(extra revenues a

week)

0 0

1 30 30 600

3 55 25 500

3 76 21 420

4 94 18 360 (*)

5 108 14 280

(*) MRP = w : Profits maximized.

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Market Demand Curve• All firms demand for labour vary

substantially• Assume that all firms respond to a lower

wage– All firms would hire more workers– Market supply would increase– The market price will fall.– The quantity demanded for labour by the firm

will be smaller

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Industry Demand for Labour

MRPL1

Labour(worker-hours)

Labour(worker-hours)

Wage(£ perhour)

Wage(£ perhour)

0

5

10

15

0

5

10

15

50 100 150 L0 L2120

MRPL2 DL1

Horizontal sum ifproduct price

unchanged

L1

IndustryDemand

Curve DL2

Firm Industry

Product price falls

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The Industry Demand for Labour

• If wage rate falls for all firms in industry, all firms will demand more labour

• More industry output and supply for output will rise causing price to fall

• The increase in labour is smaller than if the product price were fixed

• Adding all labour demand curves in all industries gives market demand curve for labour

• The industry’s demand curve for an input is steeper than it would be if firms faced an unchanged product price.

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ELASTICITY OF DEMAND FOR INPUTS• Diminishing returns (+)

– If an input’s productivity does not fall rapidly, then its demand is elastic (decrease in its price will lead to higher demand)

• Substitutability (+)– If an input price increases, and a substitution exists,

then its demand will fall rapidly • Elasticity of supply of other inputs (+)• Fraction of input costs on total cost (+)

– The larger it is, the greater is the cost % increment following a rise in input price

• Price elasticity of the demand for the output (+)– Large decreases in output will impact input demand

more or less accordingly.

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E2

D

q0

E0

E1

q10

Quantity of output

S0

S2

S1

q2

[i].

Pric

e of

out

put

Price of the input falls

Supply shifts to the right (marginal cost curve shifts downwards)

Lower output price and higher quantity of output.

Higher the quantity of the input demanded.

***** The larger the proportion of TC accounted for by an input the larger will be the increase in the demand of an input by a reduction in its price.

Small input cost share

Large input cost share

The Principles of Derived Demand

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E2

De

q0

E0

E1

q10

Pric

e of

out

put

Quantity of output

S0

S1

q2

[ii].

Di

***** The more elastic the demand curve for the product, the more elastic is the demand for the input.

Da more elastic than Dl

Price of the input falls and as a consequence, the supply of the output shifts right

The increase in the output demanded is greater with the more elastic demand

Consequently the same applies to the demand for the input

The Principles of Derived Demand

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The Market Supply of Inputs

• The market supply for factor inputs is upward sloping– Examples: jet fuel, fabric, steel

• The market supply for labour may be upward sloping and backward bending

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The Supply of Inputs to a Firm

• The Supply of Labour– The choice to supply labour is based on utility

maximization– Leisure competes with labour for utility– Wage rate measures the price of leisure– Higher wage rate causes the price of leisure

to increase

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The Market Supply of Inputs

• The Supply of Labour– Higher wages encourage workers to

substitute work for leisure• The substitution effect

– Higher wages allow the worker to purchase more goods, including leisure which reduces work hours

• The income effect

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Competitive Factor Markets

• The Supply of Labour– If the income effect exceeds the substitution

effect the supply curve is backward bending– By using indifference curves and a budget line

graph, we can show how the supply curve can be backward bending

• Can show how the income effect can exceed the substitution effect

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Substitution and Income Effects of Wage Increase

Worker initially chooses point A:•16 hours leisure, 8 hour work•Income = £80

Q

P

w = £10

Income(£ per

day)

240

720

12 16 Hours of Leisure

0 8 2419

Wage increases to £30.New budget line RQ•19 hours leisure, 5 hours work•Income = £150

Substitution effectIncome effect

A

BC

w = £30

R

Income effect overrides substitution effect

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Income Effect <Substitution Effect

Income Effect >Substitution Effect

Backward-Bending Supply of Labour

Hours of Work per Day

Wage(£ perhour) Supply of Labour

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ECONOMIC RENT

• Definition: Any excess that the owner of an input earns over its reservation price (opportunity cost).

• Its existence and magnitude depend (among other factors) on the elasticity of supply.

Rent seeking = Seeking economic profits

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

Economic rent is ABW*

B

Economic Rent

Number of Workers

Wage

SL = AE

DL = MRPL

w*

L*

A

0

31

S

D1

p1

p0

q0

E0

E1

q10

Pric

e of

the

fact

or

Quantity of the factor

D0

Shift in demand for the input (Do -> D1):

Income of input owners increase by the pale blue area

Assumptions:

Perfectly competitive markets

Other prices constant

The determination of rent in factor payments

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S0 S2

S1

600

400

400 600

D

0

Quantity

E

800

200

200

1000

Pric

e [£

]The determination of rent in factor payments

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– A single demand curve is shown with three different supply curves.

– In each case the competitive equilibrium price is £600, and 4,000 units of the factor are hired.

– The total payment (£2.4 million) is represented by the entire dark and medium blue areas.

– S0 (perfectly inelastic): the whole payment is economic rent.

– S1 (perfectly elastic): rent = 0

– S2 : Part of the payment in economic rent.• Light blue area: what must be paid to keep 4,000 units in this market.• Dark blue area: economic rent.

The determination of rent in factor payments

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SUMMARY:

The Demand for Inputs

• It is derived from the demand for goods that they help produce.

• Profit-maximising rule (short run): MRP=w.

MRP is the marginal revenue of hiring an extra worker (hour of work). MRP= MPP*P

W is the marginal cost of hiring an extra worker (hour of work).

• Elasticity: Depends on substitutability of the factor, elasticity of demand for the output and the importance of the input for the firm.

Economic rent: Economic Profits obtained by the owner of the factor.