Labour Demand
Labour is a factor of production, and labour, like other factors, such as capital (machinery, etc) are
demanded by firms for production purposes.
The quantity of labour demanded depends on how much the firm the firm wishes to produce. The
quantity that the firm wishes to produce, in turn depends on how much it can sell at the market
price. Therefore, labour demand is a derived demand (as are other factors of production). Labour
demand is derived from the demand for the firm’s product.
Demand decisions fall into two categories: short run and long run demand decisions.
Recall from introductory microeconomics, in the short run, one or more factors are fixed (ex/ plant
size is fixed, but labour may vary). In the long run, all factors are variable.
Firms demand labour (and other factors) in order to maximize profits. Profits are a function of
both revenue (earnings from selling product) and costs (wages, and other factor costs)
We can think of demand in terms of it’s objectives: Max profits (or minimize costs), and it’s
constraints: Demand for product, supply of factors, & existing technology
How does a firm determine Labour Demand in the short run?
Assume that the firm is perfectly competitive. This implies that it cannot set prices, but must take
the market price as given.
Assume that the production possibilities of the firm are represented by a production function:
Q = F(K,N) where K is quantity of capital (machinery, etc.), and N is quantity of labour
This production function tells us how much a firm can product, Q, given any combination of inputs
of capital, K, and labour, N.
In the short run, K is fixed, so that quantity produced varies only by changes in labour input. For
now, we also assume that all employees work a fixed number of hours (i.e. 8), so we don’t
distinguish between workers and hours.
1
Demand for labour in the short run is derived from output and employment needs.
For output, a firm faces 2 decisions:
1. Should the firm produce at all?
2. If it produces, how much should it produce?
Recall from introductory microeconomics:
1. The firm will produce if it can cover it’s variable costs
2. The firm will produce until the cost of producing the extra unit, MC, equals the extra revenue
from selling that unit, MR. That is, it will produce until MC=MR
Remember that for a perfectly competitive firm, MR = P
(for a monopolist, MR is a decreasing function of quantity)
What costs does the employer face?
Fixed Costs (FC) = sunk costs, ex/ costs of capital, costs of plant
Average Variable Costs (AVC) = cost per unit of production (i.e. labour costs)
So what are the employment needs? These are determined by the quantity of labour required to
maximize profits.
To determine labour demand, we can restate profit maximization rules in terms of employment of
input as follows:
Total Revenue Product (TRP) – total revenue associated with amount of input employed
i.e. how much revenue does the firm expect from a given amount of labour input.
Marginal Revenue Product (MRP) – change in total revenue associated with a change in labour
input. i.e. how much extra revenue is generated by an additional unit of labour.
In these terms, the firm decision rules become:
1. Produce if TRP of labour exceeds the total costs associated with that input
(ex/ produce if TRPlabour > W*N)
2. Employ more labour until point where MRP = MC of labour
(i.e. until MRP labour = W)
2
TRP & MRP will depend on the productivity of labour for a given firm. That is, they will depend
on what the function F(K,N) looks like. Ex/ if Q= F(K,N) = K+N, then the function looks as
follows:
Q
Slope = 1
F(K,N)
K
N
However, generally we think of capital and labour increasing output in a non-linear manner, ex/
Q= F(K,N)=KN0.5 which would look something like this:
Q
N
We can work through an example of labour demand using the function
Q= KN0.5
Assume perfect competition, and let K=2 and P=30. What is TRP for 9 units of labour? We plug
these numbers into our production function to get: P*Q=30*(2*(9) 0.5) = 180
What is the MRP? We obtain the Marginal Revenue Product by taking the derivative of the
production function with respect to labour, N, and multiply this by marginal revenue, P. Thus, the
MRP=P*(½ KN-0.5) At K=2 and N=9, MRP = 30* = 10.
3
Recall the decision rules are:
Produce if TRPlabour > W*N
Employ until MRP labour = W
We can therefore, generate a labour demand schedule based on the information above:
If W=1, we wish to employ more and more workers until MRP=1. MRP = 1 when P*(½ KN)=1 that is when 30*( ½*2*N-0.5)=1, this occurs at N=900
0.5
Our labour demand schedule looks roughly as shown:
Wage
25
Wage
$3.00
$5.00
$10.00
$15.00
$20.00
$25.00
Labour Demand
100
35
9
4
2
1
20
15
10
5
Nd
1
100
Labour Demand
Therefore, the firm’s short run labour demand decision is simply to demand N such that MRPN=W
In your text book is an example of a general labour demand schedule as well as an ARPN schedule.
ARPN is TRPN/N, thus it increases with N until such point as the MRP falls below the ARP, that is,
until the added revenue product of an extra worker falls below the average revenue product of the
current workers.
W
W1
ARPN
MRPN
N
In a perfectly competitive market, the firm is a price taker. Thus, no matter how many workers
the firm hires, that single firm cannot change the wage rate. It must take the wage rate as given,
and hire accordingly.
4
Therefore, in a competitive market, the wage rate is the marginal cost and average cost. Why?
Because each worker is paid W, so marginal cost is always W. And total cost is N*W, so average
cost is N*W/N = W.
Note then, in a competitive market, the outcome of the firm’s first decision rule, produce if
TRPN > W*N can be rewritten as: produce if ARPN> W, where W is average cost. Therefore, if
the wage ever rose above ARPN (in the graph above, if the wage ever rose above W1) the firm
would chose to shut down in the short run.
Note also, that in a competitive market, if the wage was below ARPN the firm would make profits,
therefore, more firms would enter the market. As more firms enter, labour demand in the industry
is increased, which pushes up the wage rates. This process continues until such point as no firm
wishes to enter or leave (zero profits)
Why would we expect MRPN to be downward sloping? We should expect this because of
diminishing returns to labour. Initially MRP might rise, but after more and more workers are hired
we would expect their added product to decline. This result is due to the nature of the short run.
In the short run capital is fixed. Therefore, initially, if you add workers to a fixed set of
equipment, productivity will rise. However, after a certain point, there will be too many workers
to efficiently use the equipment in one plant/firm. Each added worker will add smaller amounts of
output than the existing workers. Thus, the demand schedule is downward sloping: as the wage
falls, the firm is willing to hire more workers.
Note that the MRP is composed of 2 components: MRPN = MRQ * MPPN
That is, MRPN = (added revenue from one more Q) * (added Q from one more worker)
In a competitive market, MRQ is the price of the good and is fixed and independent of Q.
MPPN is the derivative of the production function with respect to labour.
Thus, for a competitive firm, MRPN = P*MPPN
MRPN is also known as the value of the marginal product VMPN of labour because it is the price
times the marginal product and therefore represents the added value of the worker.
So, we can write demand is determined such that:
MR = MRPN = MRQ * MPPN =VMPN = W = MC
Thus, real wage w=W/P = MPPN
And the demand for labour is the locus of points for which this equality holds, given that a firm
has decided not to shut down. That is, where P* MPPN = W
below the ARP curve
(represented by the dashed grey portion in the graph above).
For a monopolist, to sell one more unit of output, (s)he must lower his/her price; therefore, for the
monopolist, marginal revenue falls faster than price (the MR curve is always under the Demand
curve). So for the monopolist, the demand curve is the locus of points for which
5
MRQ * MPPN = W
As a monopolist hires more labour, both its MPP and MR fall, and so we would expect the demand
curve for a monopolist to be steeper than that of a competetive firm
How does a firm determine labour demand in the Long Run?
Recall that in the short run, capital is fixed. In the long run, the firm is not constrained by a set
amount of capital, but may employ both more labour and more capital as it requires.
However, deriving labour demand in the long run is similar to the short run in the fundamentals:
Demand is derived by determining how much labour is required to maximize profits at any given
wage rate.
Given a wage, we can determine the optimal number of workers to hire such that profit is
maximized.
There are 2 steps involved in calculation of labour demand:
1. At each level of output, the firm determines the least costly way to produce that level of output.
2. Firm chooses the level of output which maximizes profit.
For example, if I run a firm giving hair cuts, I determine factor demand in the following manner:
1. Least costly way to produce 3 haircuts: have 3 hairdressers (N) and 3 pairs of scissors (K)
Least costly way to produce 4 haircuts: have 4 hairdressers (N) and 4 pairs of scissors (K)
Least costly way to produce 5 haircuts: have 5 hairdressers (N) and 5 pairs of scissors (K)
…..Etc……
2. Profit maximizing level of output: chose from the above set the MR=MC of last hair cut
As above, output is determined by a function Q=F(K,N), but now K can vary.
Step 1 is characterized by an isoquant, labeled Q. An isoquant is analogous to an indifference
curve in that it shows several combinations of N and K that produce the same level of output, Q.
The isoquant, represents the technology which dictates how productive capital and labour are in
different ratios. As with indifference curves, higher isoquants (those further from the origin),
represent higher quantities. Unlike indifference curves, we can compare isoquants cardinally (that
is, we know exactly how much higher Q2 is than Q1.
6
Below is an example of isoquants. The slope of the isoquant is called the MRTS, the marginal rate
of technical substitution. This tells us how much of one factor may be substituted with another in
order to produce the same level of output.
K
Slope = MRTS
Q2
Q1
N
Notice that the MRTS diminishes as we move from left to right. This diminishing slope
demonstrates that the less of one factor, K, we use, the more of another factor, N, is required to
keep production at the same level.
Different technologies, F(K,N), clearly have different MRTS’. Haircuts require one pair of
scissors per hair dresser, but in lawn maintenance, weeding by hand may be replaced with weed
control by chemical application (fewer people, more equipment/chemicals).
In addition to the production technology, firms face factor costs. The cost of purchasing capital
and labour can be depicted graphically as well. An isocost line depicts the combinations of K and
N which a firm can employ for a total cost C. The isocost line is exactly like our budget line for
two goods, where the goods are K and N, and the prices of K and N are r and w respectively.
Isocost: C = rK +wN
The end points of the isocost line are easy to determine. As with two goods, we determine the
vertical intercept by calculating how much K we can purchase if we only purchase capital. That is,
if we spend our entire budget on capital, how much can we buy? This amount is: K = (C- wN)/r,
where N is zero. So max K is C/r. Likewise, max N is C/w.
The slope of our cost line is -w/r.
7
We add isocosts to our graph and note immediately that cost minimization is graphically similar to
utility maximization. A firm minimizes costs at any given level of output, by choosing that
combination of N and K, such that the isoquant is just tangent to the lowest isocost possible.
K
K2
Slope = -w/r
K1
Slope = MRTS
K0
E0
K3
Q1
N0
N1
N2
N
Here we have two cost lines C1 = r*K1 + w*N1 & C2 = r*K2 + w*N2 , where C2 > C1 .
The firm can produce Q1 in several ways. For example, it can use K3 capital and N1 workers at a
cost of C2 but, why would it do that when it can use only N0 workers and K0 capital to produce the
same amount at a lower cost of C1?
Note that the cost minimizing point E0, is located at the point of tangency, that is, at the point
where the slope of the isoquant curve equals the slope of the lowest isocost curve. Algebraically,
this is expressed as:
MRTS = MPN = w
MPK r
Thus, cost minimization for any quantity occurs where the relative value of the marginal product
of labour equals the relative price of labour (both relative to the equivalents for capital).
Step 2: the profit maximizing quantity is that level of output for which the marginal revenue equals
the marginal cost. If the marginal revenue were less than the marginal cost, then decreasing
production by one unit would increase profit.
8
Profit maximizing level of output cannot be seen in our cost-minimization diagram. For profit
maximization we would map marginal cost for each level of output (given cost minimization), and
marginal revenue, and profit maximization would be where the two intersect as shown below for
the case of perfect competition:
Price
MC
P
Q*
Quantity
Deriving the labour demand schedule:
Lets assume that Q0 is the profit maximizing output given the current wage rate and cost of capital.
With this information, we have one point on our labour demand curve.
K
Slope = -w0/r0
C0/r0
K0
E0
Q0
N0
N
C0/w0
w
w0
N0
N (Labour Demand)
9
What happens if we increase the wage rate, say from w0 to w1 ? The cost of hiring N0 workers, and
K0 capital is now higher. Cost is now C1 instead of C0. Then, as we see below, the isocost line
changes, and it’s slope is steeper because the cost of labour is higher. Now Q0 is no longer
minimizing cost at N0 , K0.
K
C1/r0
Slope = -w1/r1
C0/r0
K0
E0
Q0
N0
C1/w1
C0/w0
Slope = -w0/r0
N
How will the change in the price of labour affect the profit maximizing quantity?
Higher prices for labour will increase the marginal cost of production for all levels of production
for a perfectly competitive firm. As we see in the graph below, this is represented by a shift
upward of the MC curve. All firms in the industry face this higher marginal cost and will therefore
produce less. The supply curve for the industry will shift left resulting in an increase in price. The
increased price will result in a lower optimal quantity produced.
S1
Price
MC1
Price
S0
MC0
P1
P0
D
Q1 Q0
Quantity
10
qt
q0
Output
note: the scenario for the monopoly is similar (see text p.151)
We can then return to our isocost/isoquant graph to determine the effect on labour demand:
K
C1/r0
Slope = -w1/r1
C2/r0
C0/r0
K1
K0
Q0
Q1
N1
C2/w1 C1/w1
Slope = -w0/r0
N
C0/w0
N0
Now the firm minimizes cost of Q1 at K1 , N1. Where N1 < N0.
Note: we cannot immediately state whether total costs will be higher or lower because of the wage
change, the net effect depends on the magnitute of the increase in wage relative to the reduction in
costs from reducing quantity.
We can plot N1 onto our labour demand graph, as below:
wage
w1
w0
Nd
N1
N0
N (Labour Demand)
And we have a second point on our labour demand curve.
For brevity, I connect the dots. But generally, we derive the demand schedule by varying wage
and determining the profit maximizing output, and then cost minimizing labour, for each wage.
The demand schedule is downward sloping according to economic theory. There are two effects:
Substitution effect- less expensive labour (wage), substitute away from capital and into labour
11
Scale effect- increase scale of operations as labour (wage) becomes cheaper.
These effects are decomposed in the same manner as we decompose the substitution and income
effects for the income-leisure model.
K
Slope = -w1/r1
ES
KS
K1
K0
E1
E0
Slope = -w0/r0
Q0
Q1
N1 NS N0
N
Substitution (E0 to ES ) – reduction in labour due to w change
Scale (ES to E1 ) – reduction in labour due to decrease Q
In the short run, capital is fixed; therefore there is no substitution effect in the short run.
Thus, the downward slope of the short run labour demand curve is the result of scale effects and
diminishing marginal returns to labour.
In the long run, the firm can substitute away from labour as well. Therefore, in the long run, the
response to a wage change on labour demand is greater, and the slope of the labour demand curve
steeper. Wage
W1
W0
MRPN (long run, K varies)
MRPN (K=K0)
MRPN (K=K1)
SR
LR
N
Exercise: Suppose you have a firm that wishes to produce Q0. Even though wage changes to w1,
the firm still wishes to produce Q0. How much labour will this firm employ, relative to the above
example, if it stays on Q0 but faces a wage of w1?
12
Elasticity of Demand for Labour
The elasticity of labour demand tells us how sensitive labour demand is to a change in price.
Specifically, elasticity of demand for labour = % change in labour demand
% change in wage
How does elasticity of demand affect employment?
A very inelastic demand implies that as wage increases, the decrease in employment will be small.
A very elastic demand implies that as wage increases, the decrease in employment will be large.
Inelastic
Elastic
w
w
Nd
Nd
N
N
What factor affect the elasticity of demand?
1. Availability of Substitute Inputs
If a firm can substitute other inputs for labour (i.e. inexpensive robots), then the demand for labour
will be relatively elastic. That is, a change in wage will result in a large change in labour
demanded. (substitutable: assembly line industries, etc. ; not very substitutable: construction
workers, trades workers, etc) (substitution effect)
2. Elasticity of Supply of Substitute Inputs
If the supply of substitutes is inelastic (a change in demand results in a large change in price), then
these substitutes will be less appealing to the firm. In this case, labour demand will be relatively
inelastic. (substitution effect)
3. Elasticity of Demand for Output
The elasticity of the product demand determines the size of the scale effect.
If demand for the product is elastic, a price increase will yield a large reduction in quantity
demanded. Thus, if the product demand is elastic, an increase in wage will lead to a large
decrease in labour demand primarily due to the scale effect. This is particularly the case in highly
13
competitive industries where substitutes are readily available and as such product demand highly
elastic.
4. Ratio of Labour Cost to Total Cost
If the cost of labour is small relative to the cost of capital, and hence to the total cost of production,
A change in the wage will represent a small change in total cost. In this case, the scale effect
would be small because the shift of the MC curve would be slight. (examples: pilots, architects,
etc.)
Global Competition
Labour demand also affected by changes in the product market such as global competition, free
trade, industrial restructuring, technological change, privatization and subcontracting.
International competition is a particular concern of many nations. Firms wish to remain
competitive in a global economy, and are often concerned by changing trade regulations (such as
NAFTA). Countries with high wages are uncertain that they can compete with low wage
countries. (fear that low wage firms will go to Mexico and high wage brain drain from Canada to
U.S.)
We can use the analysis we have learned so far to analyze the impact of free trade on Canadian
labour demand in the short run.
14
Ex/
With trade liberalization, firms will experience increased competition. Some foreign companies,
in some industries, will be able to produce equivalent goods at a lower cost and hence lower prices.
This means that Canadian firms must lower their prices in order to sell.
Trade liberalization, will, therefore, lead to a decline in the value of the marginal product of
domestic labour, VMPN, for these industries. Recall VMPN = P*MPPN .
Lower VMPN will imply a shift left of the demand curve for Canadian labour. If wage remains
constant, then labour demand will fall. If wages were to decline, this decreased demand might be
small, and/or non-existent.
Wage
W1
W2
N2
d
N1d
N
Alternatively, we could think of Canadian labour as one of several inputs into global production.
Trade liberalization will allow some Canadian firms to substitute away from Canadian labour to
cheaper labour from other countries (by moving factories there, etc). They will do this in order to
maximize profits, where again, the optimum condition characterized by the ratio of marginal
products set equal to the ratio of input prices:
MPNC = WC
MPNF
WF
This suggests that production (& jobs) will move toward the lower-wage country. The assumption
is that the workers from different countries are perfect substitutes. That is, we assume workers in
Canada and abroad have the same skills and productivity.
Would Canadian firms still wish to hire foreign workers if the workers in Canada were twice as
productive? Not unless Canadian wages were more than twice the price (depends on production
function).
H-O
Suppose some industries would move their factories to lower wage countries, why would freer
trade be a good thing?
By looking at one industry or one market, we ignore the benefits that can come from trade via
specialization.
15
Recall from ecn104 the production possibilities curve, also called the production possibilities
frontier. This curve shows the various combinations of two goods which a country is able to
produce.
Suppose we have two countries, each with different production possibilities. Country G is best at
producing beer, country F is best at producing wine. Below we see the PPF for country G:
Country G
Beer
Wine
If country G produced only Beer, it could produce quite a lot (ex/100), compared to if it produced
only wine (ex/30). However, country G wants to consume both Beer and Wine, so if it doesn’t
trade with other countries, it must produce both itself. Depending on the preferences of the
country, the point of production may be somewhere in the middle, like point A (ex/ 70 beer and 25
wine).
Country G
Beer
100
A
Slope = PW/PB = -5
70
UA
25 30
Wine
At this point, the implicit ratio of price of beer to wine is given by the slope of the dashed line.
That is, five cases of beer trade for one case of wine. That is how much beer must be foregone in
order to produce one more case of wine, that is also how much beer country G is willing to give up
for one case of wine and remain equally happy.
16
Now suppose this country, G, looked over and noticed that the price ratio of wine to beer in
country F was lower (ex/-2). Suppose country F was willing to trade with country G: 3 cases of
beer for 1 case of wine. G could improve their utility by accepting this offer.
Country G
Beer
100
Slope = PW/PB = -5
70
UA2
UA1
25
30
Slope = PW/PB = -3
Wine
Country G could improve utility even further by specializing in Beer.
Country G
Beer
B
100
Slope = PW/PB = -5
UA3
UA2
UA1
70
25
30
Slope = PW/PB = -3
Wine
Here, country G produces at point B, almost completely specializing in Beer, and trades with
country F to obtain more wine and beer than it could have produced on its own.
Therefore, even though some sectors might suffer (ex/ layoffs in the wine labour market in country
G), the total gains from trade make the country as a whole better off. It’s becomes, here, a
question of allocation of goods.
17