Topic 3.1a – Short-Run Labour Demand
Professor H.J. Schuetze
Economics 370
Labour Demand
Let’s turn our attention away from
employees to focus on the behaviour of
employers or firms.
Recall that labour demand is:

the amount of labour that would be demanded
by firms at any given overall wage rate (w)
Unlike goods and services the demand for
labour is a “derived demand”


Labour is not demanded for final use or
consumption but as an input into production.
The demand for construction workers is linked
to the demand for new buildings.
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Basic Neoclassical Model
There are a few assumptions that are
fundamental to the model.
(i) Employers and employees are rational and
well informed.
(ii) Employees wish to maximize utility.
(iii) Employers wish to maximize profits.
The predictions of the model also depend
upon the degree of competition in the
market
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Competition
The four main degrees of competition are:
Product Market
Labour Market
1.
2.
3.
4.
1.
2.
3.
4.
Perfect Competition
Monopolistic Competition
Oligopoly
Monopoly
Perfect Competition
Monopsonistic Comp.
Oligopsony
Monopsony
Let’s start with the case where there is
perfect competition in the product and
labour markets
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Perfect Competition
What does perfect competition imply?
Product Market:
Labour Market:
Large number of sellers
Large number of workers
Sellers produce a
Workers are homogeneous
homogeneous product
Large number of
Sellers and buyers have
homogeneous Employers
perfect information
Workers and employers
have perfect information
No barriers to entry
These imply: horizontal
No barriers to entry
demand for product
These imply: horizontal supply
of labour
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Short and Long Run
Finally we will also need to distinguish between
the “short-run” and the “long-run”.
Short-Run:
Period during which one or more factors of
production cannot be varied (in our case capital).
Long-Run:
Period during which all factors can be adjusted.
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Short-Run Demand for Labour
Firm produces single output (Q) using 2 inputs,
capital (K) and labour (N).
In the short-run capital is fixed so K = K0.
The number of workers a firm is willing to hire
depends upon:
(i) The quantity of output that its workers are able
to produce.
(ii) The price the firm is able to charge for the
finished goods.
To see this, consider the following:
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Marginal Product of Labour (MPN)
The change in output that results when one unit of
labour is added to the production process
(holding all other inputs fixed)
MPN = Q/N
Usually assume “diminishing returns” set in at
some point
Example: Production line built for 10 people
If you only have one worker he/she will not be very
productive
Adding another worker will certainly increase production
by a lot since tasks can be shared
Eventually adding workers will increase production by a
lesser amount than the preceding workers
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Basic Neoclassical Model
We can depict this relationship as follows:
MPN increases up until 10
workers
Diminishing marginal product
beyond 10 workers
MPN
MPN
10
MPN1
N
The MPN curve could shift if the firm is able to
increase capital (i.e. a different short-run)
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Average Product of Labour (APN)
Equals total output (Q) divided by the total number
of workers employed (N)
APN = Q/N
MPN is related to APN as follows:
If the amount produced by adding an extra
worker (MPN) is greater than the average
product (APN) then APN will rise.
If MPN is less than APN then APN will fall
e.g. grades in this course
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Average Product of Labour (APN)
Thus, MPN will intersect APN at the maximum of APN
• APN rising when MPN is
above it.
• APN falling when MPN
is below.
APN
MPN
MPN
APN
N
• APN must be flat at point of intersection
• average = marginal (no change in average).
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Marginal and Average Revenue Product of Labour
The profit maximizing firm is only indirectly
interested in the number of units of output each
worker adds.
The direct determinant of labour demand is the
effect an additional worker has on the firms
total revenue (MRPN).
Marginal Revenue Product of Labour equals the
additional units produced by a worker (MPN)
times the increment in total revenue each of
those units would produce (MR).
MRPN = TR/N = TR/Q • Q/N = MR • MPN
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Marginal Revenue Product of Labour
However, under perfect competition MR = ?
MR = P , so MRPN = P x MPN
e.g. • One more labourer in an apple orchard
increases annual production by 3,000 bushels.
• Each bushel is worth $10
MRPN = $10 x 3,000 = $30,000
Average Revenue Product of Labour (ARPN) equals
the firms total revenue divided by the number of
workers
ARPN = TR/N = {P•Q}/N = P • Q/N = P • APN
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Marginal and Average Revenue Product of Labour
MRPN and ARPN equal MPN and APN multiplied by a
constant (P).
So, the same relationship holds for MRPN and ARPN
as did for MPN and APN:
MRPN
ARPN
MRPN
ARPN
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Deriving the Short-Run Demand Curve
For the firm, two decision rules follow from the
assumption of profit maximization
1. Because fixed costs (capital costs) must be paid
whether or not producing, the firm will operate as
long as total revenue exceeds total variable costs.
TC = FC + VC
if TR = VC ,  = TR - TC = - FC
Total losses = fixed costs.

firm would lose this by shutting down.
if TR > VC  > - FC
Better off operating than shutting down.
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Deriving the Short-Run Demand Curve
2. If producing at all, the firm should produce the
quantity at which marginal revenue = marginal cost
These decision rules can be stated in terms of inputs
rather than output.
First define Total Revenue Product of Labour:
The total revenue associated with the amount of labour
employed = TRPN
1a. Produce providing the total revenue product of
Labour exceeds the total costs of labour; other wise
shut down.
2a. If it produces at all, the firm should expand
employment up until the point at which MRPN = MCN
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Deriving the Short-Run Demand Curve
wage
w1
w0
ARPN
MRPN
N1
N0
N
• With perfect competition
MC=AC=wage
• So, the firm hires up to
the point where MRPN =
wage
• If the wage = w0 the firm
will hire N0 workers.
The firm will shut down in the short-run if total cost of labour
(VC) exceeds the total revenue product of labour (TR)
i.e. if VC > TRPN or if VC/N > TRPN/N  w > ARPN
So at wages higher than w1 the firm would choose to shut
down.
The demand curve is downward sloping because of
diminishing returns.
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Implications of Equilibrium
Says something about how MPN is associated with
wage.
Firms produce up until MRPN = w
or P•MPN = w
Therefore, implies that at equilibrium MPN = w/P
The marginal product of labour equals the real
wage.
* The more productive you are the higher the real
wage you will receive in the short-run (PC).
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Monopsony
Suppose instead, that there is imperfect
competition in the labour market but competition in
the output market
For example, suppose that there is only one firm
purchasing labour in the input market
The firm’s labour supply curve is no longer
perfectly elastic at the going wage
Instead, the firm’s labour supply curve is the
upward sloping industry labour supply curve
Thus, the marginal cost of labour will vary with the
number of employees
Exactly how, depends on the type of monopsonist
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1. Perfectly Discriminating Monopsonist
Suppose the monopsonist is able to “price
discriminate”
i.e. pay each worker his/her reservation wage


By concealing the higher wages of new workers
Using non-wage mechanisms to pay new workers
Thus, the firms MC equals its supply curve
w
S=MC
wPM
MRPN
NPM
N
• The firm still hires up to
where MRP=MC
• The firm hires NPM workers
• Similar outcome to perfect
competition
• Unlike perfect competition,
however, the monopsonist
earns profits
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2. Non-Discriminating Monopsonist
In the more likely case where the monopsonist
can’t “price discriminate” we need to think
harder about what MCN will be
The MCN curve will lie everywhere above the
labour supply curve
This is because as the firm raises wages to
attract more workers (marginal workers) it also
pays those extra wages to existing
(intramarginal) workers
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Non-Discriminating Monopsonist
MCN
w
• Hire up to the point where
MCN equals MRPN (NM)
S
MRPM
wC
wM
• Read the wage off of the
supply curve (wM)
• Implications?
MRPN
NM NC
N
Compared to the perfectly competitive equilibrium
less labour is hired at a lower wage.
Monopsony implies w<MRPN
Monopsony profit = (MRPM-wM)NM
Sometimes referred to as monopsonistic exploitation
However, intramarginal workers receive sellers
surplus
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Bruggink and Rose (1990) Paper
Basic idea: owners accused of colluding in free
agent market after 85 and 86 seasons
Gained monopsony power which suggests that
players paid under MRP
Uses econometrics to estimate MRP
Premise: winning teams more popular (more revenue)
and player performance leads to wins?


Implies fans go to see teams not players
Still allows players to be a draw to the extent that their
play helps team win
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Empirical Model
Estimate how player performance affects winning and hence
revenue
Step 1. Estimate effect of team performance on wins
pctwin=3.30+426.19(TSA)+72.47(TSW)+63.54(CONT)-50.10(OUT)+e
pctwin mean = 500
TSA=relative slugging avg (bases/at bats)
TSW=rel strikeout/walks, and in/out pennant race
relative means team avg./league avg.
Says that for every percent above average in slugging, winning pct
goes up 0.4 percentage points
For strikeout/walk ratio, every percentage point above average
leads to a 0.1 percentage point increase in the win percentage
cont/out - if average team finishes around 500; team in contention
finishes at 564 and one that is out at 450
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Empirical Model
Step 2. Estimate effect of winning etc. on team revenue
REV=1522481+53070(PCTWIN)+1469440(SMSA)+1322698(STD)7376297(TWOTM)+e
REV mean = 30,935,231
STD=old stadium is insignificant
Says adding 100 pts to win(going from 500-600) adds about 5
million to revenue
Step 3. Estimate effect of individual performance on revenue
If subs step 1 into step 2 get effect of team performance on
revenue
For hitting: 53070*426*TSA = 22,607,820*TSA
For pitching: 53070*72*TSW = 3,821,040*TSW
If we know how a player’s performance affects team stats we will
have MRP
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Results
Can do this by substituting
1. hitter’s slugging average * % team at bats for team slugging avg
2. Pitcher’s strikeout/walk ratio * % of teams innings pitched for team
strikeouts to walks
Results:
Test if w/MRP is lower for free agents in 85-86 compared to 84

using gross MRP
1984 w/MRP = 0.961, 85-86 = 0.693 for a difference of 0.268
get p-values of between 5 and 11 (prob really no difference)
Therefore, in general supportive of collusion among owners!
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