1

Market for (homogenous) labour

WE

EE

W1

W2

SEDE

2

For the seller – labour is different from other commodities.

For the buyer? Starting assumption: For the firm, labour

is bought like other inputs. Input demand is DERIVED DEMAND

not consumption demand.

3

Basic assumption: The firm hires workers in order to MAXIMISE

ITS PROFITS The firm’s makes two decisions:

◦Produce what (how much)?◦Produce how (with what technology/what inputs)?

4

E – units of labour (hours or full time weeks or full-time worker years)

K – capital (machines, buildings, land, stocks etc.)

Production function: Q = Q(E, K). A more complex function would be Q=Q(E1, E2,…, K,N,…) or Q=Q(x1, x2,…, xn)

5

Production function

0

100

200

300

400

500

600

700

800

Units of X

Pro

du

cti

on

Q=f(X)

Production as a function of labour at ONE particular level of all other inputs

6

The slope of the production function shows how production changes with a change in (only) labour input.

The marginal product of labour (MPE): ◦ The increase in production when E increases by a small amount

(Q(E+ΔE, K0) – Q(E, K0))/ ΔEOr mathematically◦ the (partial) derivative of Q with respect to E at K = K0

At a fixed level of K MPE is different at different levels of E Marginal productivity may increase at small levels of E but

will eventually start to decline. THE LAW OF DIMINISHING RETURNS

Please note: The Law of diminishing returns is not a low

of diminishing returns to scale (when use of all factors is increased.)

7

8

Production function

0

100

200

300

400

500

600

700

800

00,

40,

81,

21,

6 22,

42,

83,

23,

6 44,

44,

85,

25,

6 66,

46,

87,

27,

6 88,

48,

89,

29,

6 1010

,410

,811

,211

,6 12

Units of X

Pro

du

cti

on

Q=f(X)

E

EQAPE

)(

Q

E

9

If MPE > APE , APE

If MPE < APE , APE

AP-curve

MP-curve

The decreasing part of the MP-curve cuts the AP-curve in the AP-curve’s maximum

10

Remember: With a different level of K, we get a different Q and a different MPE for each E

To each value of K corresponds another function Q(E) and another function MPE(E)

Analogously To each value of E corresponds a function Q(K)

and a function MPK(K)

11

VMPE = p • MPE

(if the firm is a price taker in the product market)

A profit maximising firm employs until: VMPE = MCE

Under perfect competition the firm is a ”price taker in the labour market”.

It takes w as given and MCE = w

12

The firm’s demand for labour

The price of the product(Physical) marginal product of labour

The marginal cost of labour

Marginal revenue product of labour

13

W1

W2

W

VMP

EE2 E1

Why is only the decreasing part of the VMP.curve relevant?

If the ”going wage” is w2 the firm hires E2 workers – APE > MPE

E3

14

Perfect competition: The marginal cost of increasing E by one unit is w The marginal revenue of increasing E by one unit

is p •MPE

The firm increases employment up to where w = p •MPE (1)

How many are hired depends on◦ the marginal productivity of labour◦ the wage◦ the price of the product.

15

In labour market: MCE ≠ w In product market: MRQ ≠ p

The firm employs and produces until: MCE = VMPE = MRQ *MPE (2)

◦ (1) is a special case of (2)

16

If wages increase, each employer hires less workers If each employer hires less workers, each employer

produces less. If all employers produce less, the aggregate supply

curve for the product shifts to the left.

Equlibrium price increases and the aggregate decrease in demand for labour is less than the sum of the decreases each firm would have made if it had been alone paying the higher wage.

17

E

W

W

E

W

W

E

E

WWEE

SR

in wage changepercent

employmentin changepercent

The wage elasticity of The wage elasticity of labour demandlabour demand

18

Both E and K can vary. The firm has a choice between

technologies. The same output can be produced with

different proportions of E and K An ISOQUANT shows the different

combinations of K and E that produce the same output

19

Ex: Let

be a production function. Q(64, 225) = 240 Q(144, 100) = 240Q(72, 200) = 240 Q(200, 72) = 240Q(100, 144) = 240 Q(225, 64) = 240

It is possible to substitute labour and capital

for each other at a given level of production

KEKEQ 2),(

20

Isokvant Q=240

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150

160

170

180

190

200

210

220

230

240

250

260

270

280

290

300

310

320

330

340

L

K K

E

K

21

22

Leontief production function

23

Isoquants are negatively sloped and convex to the origin. Inputs can be substituted but MP is decreasing

Q increases

24

The slope of an isoquant shows how much capital is needed to replace each unit of labour without decrease in production

K

EEK MP

MP

E

KEMPKMP

This is (minus) the Marginal Rate of Technical Substitution, MRTS

25

An isocost shows the combinations of inputs that cost the firm the same amount.

If the cost of production is C = wE+rKthe isocosts are linear with slope –w/r

K

E

26

To maximise profits firms must:◦minimise the cost of producing the chosen output◦maximise production at the chosen level of cost.

This happens only at a point of tangency between an isoquant and an isocost.

These points are on the EXPANSION PATH of the firm.

Which point on the expansion path the firm chooses depends on the price of the product.

27

28

The firm will choose input combinations on the expansion path.

Each point on the expansion path represents one level of production.

The cost of inputs at that point is the minimum cost of producing that output.

The cost function of the curve C(Q) shows this minimum for each Q.

MC is the slope of this cost function – the change in cost as the firm moves outwards along the expansion path.

The firm will choose the level of production, Q*, where MC = MR and the input combination where the isoquant for Q* is tangent to an isocost

29

(Assume perfect competition & r and p constant.)

The isocosts become steeper. More capital intensive technology becomes

more profitable. At every point on every isoquant, cost and

marginal cost increases. The MC-curve moves upwards-leftwards. The firm will decrease production. It will

choose the tangency point of another isoquant with another isocost.

30

A wage increase has two effects on employment:

1. Changed relative prices will make the firm change the capital/labour ratio

2. Changed MC will make the firm decrease output. Decreased output will make the firm use less inputs.

There will beSUBSTITUTION EFFECTS and SCALESCALE

EFFECTS

31

PR

S

Q1

Q2

P is choice with lower wage

R is choice with new higher wage

E2 E1E*

E*-E1 is scale effect

E2-E* is substitution effect

Employment when w increases

32

PR

S Q1

Q2

P is choice with lower wage

R is choice with new higher wage

K2

K1

K*

K*-K1 is scale effect

K2-K* is substitution effect

Use of capital when w increases

33

If both capital and labour are ”normal” inputs the scale effects of both are negative.

The substitution effect increases K and decreases E.

The total effect on E must be negative, the total effect on K depends on the size of the effects.

34

E

w

w

E

in wage change percentage

employmentin change percentage

The long run labour demand elasticity > short run labour demand elasticity

Estimates of labour demand elasticity vary depending on the time and place, the level of aggregation, the method used (assumptions about the production function)

Hamermesh’s survey: Many studies find ε -0.3

Swedish studies (Ekberg, Walfridsson) -0.3 & -0.2

Scale effects included: -0.65

Lower elasticity for highly educated workers

Lower for white collar than for blue collar

Higher for young than for older workers

35

The elasticity of substitution between two factors of production is

The size depends on the shape of the isoquants.

If they are perfect substitutes a change in relative price leads to no change at all or a total switch

If they are perfect complements, the elasticity is zero.

0

pp

in changepercent

qq

in changepercent

1

2

2

1

qi,and pi are quantitites and prices of the two inputs

36

Empirical estimates of capital/labour substitution elasticities vary:◦ For whole or large parts of economies 0-1, most

often 0.4-0.8◦ Swedish estimates: wide range at different times

and different industries and different for different groups of workers.

37

Factor i will be employed at the level where VMPi=MPi*p

If the price of one factor goes up, what happens to demand for the others?

The cross-elasticity of demand between factor i and k =

k factor of pricein changepercent

ifactor of usein changepercent ik

38

If δik< 0 factors i and k are complements in production◦ An increase in the price of k shifts the demand

curve for i leftwards

If δik> 0 factors i and k are substitutes in production◦ An increase in the price of k shifts the demand

curve for i rightwards

39

Many studies find that skilled labour (or white collar) and capital are complements while unskilled (or blue collar) labour and capital are substitutes.

Worker groups with different skills and characteristics can be substitutes or complements.

40

Demand for labour/one type of labour is less elastic:◦ If it is very essential to production and

difficult to replace either by capital or other labour.

◦ If demand for the final product is inelastic.◦Their wages make up a small part of total

costs of production.◦ If the supply of complements to it is

inelastic and that of substitutes elastic.The less elastic demand is, the greater the

scope for unions to increase wages with small loss in employment.

41

Assume: Two groups of workers, A & B, are complements◦ wages of group A demand for both groups◦ Demand for labour of type B their wage wB . If supply

is inelastic, wB much and the firm reduces output less.

Assume: Labour of type A and capital are substitutes.◦ wA firm wants to substitute capital for labour

◦ If supply of capital is elastic, increase in demand price of capital , reducing the incentives for the firm of substituting from labour to capital

42

D1

D2

Inelastic supply

Elastic supply

43

Perfect competition

VMPW2

W1

E1E2

W

E

44

Can occur due to: A very restricted local labour market

(”company town”, ”bruksort”) Very high degree of specialisation (perhaps

unique to the firm) Segregation/discrimination Monopoly (public or private)

45

A discriminating monopsonist pays each worker his/her reservation wage. Employment is = EPerfect comp. but all workers except the last get less than wPC

A non-discriminating monopsonist pays all workers the same wage. Therefore the cost of hiring an additional worker > the wage of that worker (if labour supply is upward sloping). Both employment and wage will be less than under perfect competion.

46

W

WPC

W

WM

EEPCEM

LS

VMP

MCE

47

Can be set by legislation or in collective agreements.

Effects:◦ On distribution of income (tend to equalise)◦ On employment (usually negative but the

evidence is mixed and disputed).◦ Encourages structural change

48

SLSL

49

Wmin

VMP

S

MLC

S

VMP

Employment

Wage

Unemployment

Perfect competition:

Monopsony

Employment

Wage

Unemployment

50

A firm dominates employment in a small town. The price of its product is 10 SEK. The firm’s production function is : Q = 20E – 0.005 E2

Q = production E = Employment. a) What is the firm’s labour demand function DE ? What is its labour demand if w= 150 SEK? b) Assume that the firm is a monopsonist in this labour market and that labour supply is given by. w=50+0.2E What is MCE

Calculate the firm’s DE and the wage, w. c) The state sets a minimum wage w=150, How many workers will the firm employ? a) VMPE=p*MPE=10*(20-0,01E)=200-0,1E Profit maximisation requires that VMPE=MCE=w DE is given by: w=200-0,1E E=2000-10w w=150 => E=500 b) The labour cost of the firm : E*w = E*(50+0.2E) = 50E+0.2E2

MC E : 50+0.4E MC E =MRP E 50+0.4E= 200-0.1E E = 300 To employ 300 workers the firm has to pay w=50+0.2L=50+60=110 c) With a minimum wage S E =0 for w<150 MC E =150 ´Profit maximisation requires that VMP E =150 =>E=500

51

Transaction costs Search and hiring costs Training costs for new employees Severance pay Negotiations, law suits Loyalty, work climate Reputation as an employer Uncertainty about how lasting and how big

an up/downturn in product demand/business cycle will be.

52

Economic downturn◦ Decrease in overtime◦ No new hirings◦ No short replacements for absent workers◦ No temporary workers◦ ”Natural wastage”◦ Temporary lay-offs◦ Dismissals

Economic upturn◦ Increase overtime◦ Less liberal with leave of absence◦ Use temporary workers◦ New hirings

53

Reasons to want part-time/seasonal workers◦ Demand for the good or service produced may vary over the

day, week or year.◦ A temporary job (fixed term contract) can function as a work

trial◦ A temporary worker may replace a temporarily absent

employee◦ Productivity per hour can be higher with fewer hours per

day/week Reasons to prefer full time/long term workers:

◦ Overhead-costs for every (new) employee.◦ Productivity is higher if workers learn on the job.

54

Total Men Women

1987 12.0 9.7 14.2

2004 15.1 13.1 17.1

4th quarter 2010

15.4 13.8 17.2

55

Men Women

LO 11 12

TCO 6 8

SACO 9 12

Not organised 24 34

LO – blue collarTCO – lower to middle level white collarSACO – higher level white collar

56

Age Men Women

15-2451,1 63,2

25-549,4 12,7

55-748,7 8,2

57

The public sector is an important employer, particularly for women◦ On the one hand, has some monopsony power◦ On the other, not necessarily profit maximising!

◦ * Municipal and county council

Women Men

Local government*

6.3 6.0

Central government

41.4 11.7

Private 52.3 82.3

58

We know numbers employed and wages. When they change is that supply or demand??

If both supply and demand functions shift we observe two points but we don’t know anything about the underlying curves!

D2

D1

S2S1

59

Solution to the IDENTIFICATION PROBLEM? Find instrumental variables that make one

curve shift but not the other. But it is always a matter of the researcher’s

judgement if the instrumental variables are well chosen.