buec 280 lecture 4 - sfu.cafriesen/buec_280_lecture_8.pdf · mpl=10 when a second worker is hired,...
TRANSCRIPT
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BUEC 280 LECTURE 8
Introduction to Labour Demand
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Last few weeks …
We developed two simple models of labour supply
Consumption-leisure choice model
Household production model
The goal was to understand the decisions that people
make to determine their labour supply
Now, we’ll do the same for firms
Where does the labour demand curve come from?
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Profit maximization
Our basic assumption is that firms maximize profits
They continually ask “what changes can we make to improve profits?”
Firms can only control certain things
Usually assume that firms cannot choose prices (they are determined in a
market)
Firms can choose how much output to produce, and how to produce it
(technology, mix of inputs, etc.)
Focus on marginal changes – small changes in one dimension, holding
other things constant
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Inputs to production
Assume there are two factors of production (inputs): labour and capital
Assume that firms expand/contract production by varying the quantity of one or both factors, holding constant their production technology
What do I mean by technology? It is how firms combine labour and capital to produce output.
How are these decisions made?
If income (revenue) generated by using 1 more unit of an input exceedsthe extra expense, then use more of that input
If revenue generated by using 1 more unit of an input is less than the expense, use less of that input
If revenue generated by adding 1 more unit of an input is equal to the expense, no change necessary
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Marginal product, marginal revenue, and marginal
revenue product
So the basis of the decision to use more/less of an input is based on the extra revenue generated by using 1 more unit of an input – we call this the marginal revenue product
It is the product of two quantities: the extra output produced by using 1 more unit of the input (the input’s marginal product) and the extra revenue from producing one more unit of output (marginal revenue)
Example: Imagine a tennis tournament. Suppose that if a famous tennis player plays in the tournament, 2000 extra spectators will come. Tickets are $25 each.
The player’s marginal product is 2000 spectators
Marginal revenue is $25 per spectator
Maria’s marginal revenue product is $25 x 2000 = $50,000
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Formal definitions
The marginal product of labour (MPL) is the change in physical output (ΔQ) due to a change in the units of labour input (ΔL), holding capital (K) constant:
MPL = ΔQ / ΔL (holding K constant)
Similarly, the marginal product of capital isMPK = ΔQ / ΔK (holding L constant)
The firm’s marginal revenue (MR) is the extra income generated by producing an additional unit of output. In a competitive output market, firms take prices as given, and MR is just the equilibrium price of the good they produce:
MR = p
The marginal revenue product of labour (MRPL) is the extra revenue generated by employing an extra unit of labour:
MRPL = MR x MPL = p x MPL (competitive market)
Similarly, the marginal revenue product of capital (MRPK) is:MRPK = MR x MPK = p x MPK (competitive market)
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What about costs?
Hiring an additional unit of labour or capital isn’t free …
For now, assume firms take all prices (including input prices) as given
i.e., decisions made by the firm do not affect prices
The worker’s wage W is the marginal expense of hiring one more unit of labour
The rental rate of capital r is the marginal expense of hiring one more unit of capital
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Short-run labour demand with perfectly competitive input
and output markets
We’ll focus first on the short run – a period of time that is short enough so that firms can vary L but notK
Assumption: Declining MPL
We will assume that (eventually) each additional unit of labour hired by the firm is less productive than the previous unit
MPL can rise at first (maybe because of cooperation), but eventually it must fall
Why? Because one factor (capital) is fixed
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Example of declining MPL
Consider a hypothetical car dealership
The first worker hired sells 10 cars
MPL=10
When a second worker is hired, total sales are 21 cars
MPL=11>10 because the two salespeople can help one another
# Salespeople # Cars Sold
MPL
0 0
1 10 10
2 21 11
3 26 5
4 29 3
When a third is hired, total sales increase to 26 MPL=5<11 because a fixed building can only contain so many
cars and customers (diminishing marginal product)
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The profit maximization conditions
Before, we said that to maximize profits:
If MRPL exceeds the marginal expense of labour, then hire 1 more unit to increase profit
If MRPL is less than the marginal expense, reduce labour input to increase profit
If MRPL is equal to the marginal expense, no change necessary because profit cannot be increased by changing labour input
The marginal expense of labour is W
Profits are maximized when MPRL = W
MPL x p = W
MPL = W/p
What’s W/p? The real wage, in units of output.
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The firm’s short run labour demand
L
MPL,Real Wage (W/p)
MPL
W3/p
W2/p
W1/p
L3 L2 L1
W3
W2
W1
L3 L2 L1
Labour Demand
Nominal Wage (W)
L
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Where does market labour demand come from?
We just add up all the individual firms’ labour demand
curves
E.g., suppose there are 2 firms in the economy. If firm 1 demands
2 units of labour when W=10 and firm 2 demands 3 units, then
total labour demand is 5 units at this wage
Because MPL is downward sloping for each firm, we know
labour demand is downward sloping for each firm
⇒ market labour demand is also downward sloping
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Going a step further …
We can use a graphical model to analyze the firm’s demand for labour Looks like the consumption-leisure choice model
Decision maker is the firm
Decides how many units of labour to hire at given input prices
It is a cost minimization problem
The firm cannot maximize profits without minimizing costs.
That is, to maximize profit, the firm must minimize the cost of producing a given level of output
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The production function
We’ll continue to assume there are two inputs to production: labour (L) and capital (K)
We will describe a firm’s technology by a function:
Q = f(L,K)
Here, Q is the output produced by the firm, and f is the name of the function
We call this a production function, and it tells us how many units of output Q the firm can produce if it uses K units of capital and L units of labour
The production function describes the firm’s production technology
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Isoquants
We represent the production function graphically with an
isoquant
A curve that tells us all the different combinations of L,K that can
be used to produce a given level of output, Q
Think of it like an indifference curve
Instead of measuring different combinations of leisure &
consumption that yield the same level of U, it measures
combinations of L,K that can be used to produce the same level of
output Q
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Properties of Isoquants
Negative slope
L,K are substitutes
Convex
Mixtures of L,K are more productive than extremes
Diminishing marginal returns
Don’t cross
The bundles (L1,K3), (L2,K2), and (L3,K1) all produce the same level of output Q=100.
If we fix capital at K3, changing the quantity of labour changes output: f(L1,K3) = 100f(L2,K3) = 150f(L3,K3) = 200 L
K
Q=100
Q=150
Q=200
L1L2 L3
K1
K2
K3
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The Marginal Rate of Technical Substitution
In the leisure-consumption choice model, the slope of the indifference curve was called the marginal rate of substitution (MRS)
Rate at which individual was willing to trade off consumption and leisure to hold utility constant
We call the slope of the firm’s isoquant the marginal rate of technical substitution (MRTS)
Rate at which the firm can trade off capital and labour and hold output constant
It is negative because if we increase L, we must decrease K to hold output constant
QQL
KMRTS
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Short-run Labour Demand
In the short run K is fixed, say at K*
Profit max: MPL = W / p
This defines short run labour demand
Recall we assumed MPL declining (need this for the MPL = W/p condition to have meaning)
We can see that MPL declines in the figure at right:L3 - L2 > L2 – L1
L
K
Q=100
Q=150
Q=200
L1L2 L3
K*
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The Long Run
In the long run, firms can vary both L and K
Just like before, the firm maximizes profits only if the extra revenue from hiring one more unit of an input equals the extra cost
i.e., marginal revenue = marginal cost
In the short run, this was just MRPL = W
In the long run, this condition must hold for L and K:
MRPL = W p x MPL = W p = W / MPL
MRPK = r p x MPK = r p = r / MPK
W / MPL = r / MPK
Since MPL = ΔQ / ΔL and MPK = ΔQ / ΔK, we see that
WΔL / ΔQ = rΔK / ΔQ
Extra cost of producing 1 more unit of output using L = Extra cost of producing 1 more unit of output using K
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Why is this profit maximizing?
Our conditions is: W / MPL = r / MPK
Extra cost of producing 1 more unit of output using L = Extra cost of producing 1 more unit of output using K
Suppose this equality didn’t hold, so that W / MPL > r / MPK. This means Extra cost of producing 1 more unit of output using L >
Extra cost of producing 1 more unit of output using K
The firm could reduce its use of labour and increase its use of capital, save money, and produce the same level of output TO MAXIMIZE PROFITS, THE FIRM MUST MINIMIZE COSTS
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A Graphical Treatment
We can show this graphically
Need to introduce the analog to the budget line: called an isocost line
The isocost line represents combinations of L,K that cost the same amount
just like a budget line, except the firm can choose their level of expenditure, i.e., which isocost line they are on
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The isocost line
Suppose W = $10 r = $20
Here are three isocost lines. They give combinations of L,K that cost $1000, $1500, and $2000 respectively
In each case,Slope = – W / r
= - 1 / 2L
K
100 150 200
50
75
100
Cost=$1000
Cost=$1500
Cost=$2000
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The cost minimization problem
Recall our profit max (or cost min)
condition:
W / MPL = r / MPK
WΔL / ΔQ = rΔK / ΔQ
W / r=(ΔK / ΔQ) / (ΔL / ΔQ)
W / r = ΔK / ΔL
Slope of isocost = MRTS!!
The cost-minimizing way to produce
output level Q* is (L*,K*), which costs
C*
Is this profit maximizing?L
K
Q=Q*
Cost = C*
L*
K*
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Scale and Substitution Effects
How do firms respond to changes in input prices?
Suppose W increases
Because labour is now more expensive relative to capital, and because labour and capital are substitutes in production, firms will change their input mix to use less labour and more capital to produce any level of output
This is a substitution effect
Because it is now more expensive to produce any level of output, the firm will reduce output (and hence reduce use of labour (and probably capital too)
This is a scale effect (like an income effect in the leisure consumption choice model)
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Scale and Substitution Effects Graphically
L
K
Q=Q0
Cost = C0, slope = -r/W0
L0
K0
Cost > C0, slope = -r/W1
1. Wage is W0, and firmchooses (L0,K0) to produceQ0 units at cost C0
2. Wage increases to W1
Substitution effect:(L0,K0) to (Ls,Ks)[change in input mix due to higher wage, holding outputconstant]
Scale effect:(Ls,Ks) to (L1,K1)[change in inputs due toreduced output Q1, becauseproduction is more expensive]Note: we don’t know Q1
Ls
Ks
Q=Q1
L1
K1