Download Notes Chapter 3

 Market for (homogenous) labour
SE
DE
W1
WE
W2
EE
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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.
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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)?
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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)
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Production function
800
700
600
400
Q=f(X)
300
200
100
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10
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,2
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8,
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1,
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Production
500
Units of X
Production as a function of labour at
ONE particular level of all other inputs
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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))/ ΔE
Or mathematically
◦ the (partial) derivative of Q with respect to E at K = K0
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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
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Please note:
The Law of diminishing returns is not a low of
diminishing returns to scale (when use of all
factors is increased.)
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8,
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8
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6,
4
6,
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7,
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7,
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5,
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6
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2,
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2,
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3,
2
3,
6
0
0,
4
0,
8
1,
2
1,
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Production
Q( E )
APE 
E
Production function
800
700
Q
600
500
400
Q=f(X)
300
200
100
E
0
Units of X
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If MPE > APE , APE
If MPE < APE , APE
MP-curve
AP-curve
The decreasing part of the MP-curve
cuts the AP-curve in the AP-curve’s
maximum
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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)
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
VMPE = p • MPE
(if the firm is a price taker in the product market)
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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
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The firm’s demand for
labour
Marginal revenue product of
labour
(Physical) marginal
product of labour
The marginal cost of
labour
The price of the product
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VMP
Why is only the decreasing part
of the VMP.curve relevant?
W
W2
W1
E3
E2
E1
If the ”going wage” is w2 the firm
hires E2 workers – APE > MPE
E
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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.
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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)
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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.
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The wage elasticity of
labour demand
percent change in employment
 SR 

percent change in wage
E
E W
E W
E
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
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
W
E W W E
W
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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
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Ex:
Let
Q( E , K )  2 E K
be a production function.
Q(64, 225) = 240
Q(72, 200) = 240
Q(100, 144) = 240
Q(144, 100) = 240
Q(200, 72) = 240
Q(225, 64) = 240
It is possible to substitute labour and capital
for each other at a given level of production
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90
10
0
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0
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0
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0
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50
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10
20
K
Isokvant Q=240
K
400
350
300
250
200
K
150
100
50
0
L
E
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Leontief production function
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Isoquants are
negatively sloped and
convex to the origin.
Inputs can be
substituted but MP is
decreasing
Q increases
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The slope of an isoquant shows how much
capital is needed to replace each unit of
labour without decrease in production
MPK  K  MPE  E 
K
MPE

E
MPK
This is (minus) the Marginal Rate
of Technical Substitution, MRTS
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An isocost shows the combinations of inputs
that cost the firm the same amount.
If the cost of production is C = wE+rK
the isocosts are linear with slope –w/r
K
E
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
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.
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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
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(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.
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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 be
SUBSTITUTION EFFECTS and SCALE EFFECTS
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Employment when w increases
P is choice with lower wage
R is choice with new higher wage
E*-E1 is scale effect
E2-E* is substitution
effect
P
R
S
Q1
Q2
E2
E*
E1
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Use of capital when w increases
P is choice with lower wage
R is choice with new higher wage
K2
K1
K*-K1 is scale
effect
P
R
S
Q1
K*
K2-K* is
substitution effect
Q2
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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.
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percentage change in employment
E w


percentage change in wage
w E
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
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
 q1 
percent change in  
The elasticity of
substitution between
 q2   0
two factors of
 p2 
production is
percent change in  
 p1 
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.
qi,and pi are
quantitites and
prices of the two
inputs
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
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.
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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 =
percent change in use of factor i
 ik 
percent change in price of factor k
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
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
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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
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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.
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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.
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
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
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D1
Inelastic supply
D2
Elastic supply
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Perfect competition
W
W2
VMP
W1
E2
E1
E
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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)
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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.
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W
W
MCE
LS
WPC
WM
VMP
EM
EPC
E
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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
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SL
SL
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Monopsony
Perfect
competition:
Wmin
MLC
S
S
VMP
VMP
Employment 
Employment 
Wage 
Wage 
Unemployment 
Unemployment 
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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
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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.
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Economic downturn
Decrease in overtime
No new hirings
No short replacements for absent workers
No temporary workers
”Natural wastage”
Temporary lay-offs
Dismissals
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Economic upturn
Increase overtime
Less liberal with leave of absence
Use temporary workers
New hirings
◦
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◦
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◦
◦
◦
◦
◦
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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

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Reasons to prefer full time/long term workers:
◦ Overhead-costs for every (new) employee.
◦ Productivity is higher if workers learn on the job.
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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
54
Men
Women
LO
11
12
TCO
6
8
SACO
9
12
Not organised
24
34
LO – blue collar
TCO – lower to middle level white
collar
SACO – higher level white collar
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Age
15-24
25-54
55-74
Men
Women
51,1
63,2
9,4
12,7
8,7
8,2
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
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!
◦
Women
Men
Local
government*
6.3
6.0
Central
government
41.4
11.7
Private
52.3
82.3
* Municipal and county council
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
We know numbers employed and wages.
When they change is that supply or demand??
S1
S2
D2
D1
If both supply
and demand
functions shift
we observe two
points but we
don’t know
anything about
the underlying
curves!
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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.
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