Download W/MPL=C/MPK

Chapter 3 Labor Demand
The labor is worthy of his hire.
—The Gospel of St.Luke
3.1 The Short-run Labor Demand
What does the term “short-run” mean?
Firm can only change the employment of labor
to maximize profit. That is, the stock of capital
is assumed to be fixed.
 Why do firms hire workers?
–The objective of hiring workers is to produce
product that firm can sell.
–That is, demand for labor is a derived
demand, which is derived from consumer’s
demand for final product.

3.1 The Short-run Labor Demand

How does a firm make decisions on its
production (e.g., whether and how to produce,
increase or decrease output level) ?
–The guide rule is simple: maximizing profit.
 How to realize profit maximization?
–Profits are maximized at the point where
added revenue of one extra unit of input
equals added cost of one extra unit of input.
 For simplicity, still assume two inputs, Kand L.
3.1 The Short-run Labor Demand

Assumptions:
–Both product and labor market are
competitive.
 –Firm’s production
Production technology:Q=f(K,L), Kdenotes
capital input and Ldenotes labor input
Examples: Q=L+K; Q=LK; Q=L1/2K1/2
 –Firms seek profit maximization.
3.1 The Short-run Labor Demand
Some analytical concepts
–Marginal Product (MP) of labor
 Change of the output resulting from an
additional unit of labor employment,
holding capital input constant.
 MPL=ΔQ/ΔL=Δf(L,K)/ΔL
–Similarly, marginal product of capital
 MPK=ΔQ/ΔK=Δf(L,K)/ΔK

3.1 The Short-run Labor Demand
–Marginal Revenue (MR)
Additional revenue generated by an extra unit
of output.
MR depends on the characteristics of the
product market.
e.g., MR=Pin the competitive product market.
 –Marginal Revenue Product (MRP)
Simply combines marginal product and
marginal revenue, i.e., MRP=MP*MR

3.1 The Short-run Labor Demand
Average product (AP) of labor
–Defined as average output produced by
one unit of labor input.
–APL=Q/L=f(K,L)/L
 Average product of capital
–Defined as average output produced by
one unit of capital input.
–APK=Q/K=f(K,L)/K

3.1 The Short-run Labor Demand
Graphical MP and AP
3.1 The Short-run Labor Demand

Marginal Expense (ME) or Marginal Cost (MC)
–Added cost resulting from employing an
additional unit of input.
 A crucial assumption: The Law of
Diminishing Marginal Returns
–Marginal product of labor will eventually
decline as employment increases given a fixed
capital.
–Why? Specialization, cooperation,
externality, …
–Example of 4S.
3.1 The Short-run Labor Demand
3.1 The Short-run Labor Demand
3.1 The Short-run Labor Demand

Profits are maximized at the point where
marginal revenue product of labor equals
marginal cost of labor.
MRPL=MPL*MR=MCL
 In the competitive markets,
MPL*P=W <=> MPL=W/P
 With the equation above, labor demand can be
derived in terms of real money (nominal) wage.
3.1 The Short-run Labor Demand

Labor demand against realwages
–MPL=W/P
–According to the law of diminishing
marginal returns, we expect a negative
relationship between employment and
MP.
–Or a negative slope for the MPL curve.
3.1 The Short-run Labor Demand

Labor demand against moneywage
–MRPL=W
–Again with the law of diminishing marginal
returns, we have a labor demand curve
sloping downward.
–Example of detective hiring. (also, e.g., police
size)
–*The MRPLcurve and the labor demand
curve coincide here.
3.1 The Short-run Labor Demand

One remark
–The term “marginal” is not a function of
individual’s characteristics.
–The size of “margin” depends on the
number of employees that are already
hired.
–The size of “margin” also depends on
the size of other input.
3.2 The Short-run Market Demand curve

Above we show the labor demand curve for a
representative firm, which indicates the level of
firm’s employment at each given wage rate.
 The market demand curve is simply an
aggregation of each firm’s employment at
each wage rate.
 Two objections
–Employers do not know the accurate output of
individual workers, no mention of MRP.
–Additional labor produces nothing in some
cases.
3.3 The Long-run Demand for Labor
In the “long-run”, the size of other inputs
can vary. For example, machines,
materials, energy, and technology.
 We first look at the situation that firm can
only adjust the size of capital used.
 For two variable inputs, profit
maximization will be realized when two
marginal conditions are satisfied.

3.3 The Long-run Demand for Labor

In formula,
MPL*P=MCL=W
MPK*P=MCK=C
C denotes the cost of capital (e.g., interest)
 Rearrange the two equations,
P=W/MPL
P=C/MPK
3.3 The Long-run Demand for Labor

With the same P, profit maximization rule
therefore requires that,
W/MPL=C/MPK
–The left-hand side W/MPLdenotes the
added cost of producing one additional
unit of output using labor.
–The right-hand side C/MPKdenotes the
added cost of producing one additional
unit of output using capital.
3.3 The Long-run Demand for Labor
What does the equation mean for a
representative firm seeking profit
maximization?
 The firm must adjust the sizes of labor
and capital so that the marginal cost of
producing one additional output using
labor is equal to the marginal cost of
producing one additional output using
capital.

3.3 The Long-run Demand for Labor

So, how is the long-run labor demand of a
representative firm if wage increases (or
decreases)?
–Equation W/MPL=C/MPKis disturbed.
–In the short-run, the marginal cost of
production using labor exceedsthe marginal
cost using capital.
•First the firm will cut the size of employment
as before, which leads to raise MPL.
•Less labor also results in falling MPK, which
will lead to reduction of its capital input.
3.3 The Long-run Demand for Labor

In the long-run, the firm can substitute
capital for labor since capital is more
cheaper than labor. The substitution also
leads to
–Increase of MPLdue to higher capital
per worker
–Decrease of MPK due to the Law of
Diminishing Marginal Return
3.3 The Long-run Demand for Labor

In the end, a rise of wage rate will cause a
decline of employment level.
–Falling output level (scale effect)
–More capital input (substitution effect)
–However, whether the sizes of capital
increase is ambiguous.
–See Figure in next slide
 The long-run story therefore provides further
support to the proposition of the downwardsloping labor demand curve.
3.3 The Long-run Demand for Labor
3.3 The Long-run Demand for Labor

The case of more than two types of inputs
–Labor demand is now a function of wage rate
and the prices of all other inputs.
–Inputs are substitutes,
•Scale effect
•Substitution effect
–Inputs are complements
•Only scale effect
3.4 Monopoly in the markets
Up to now, we are assuming that the
representative firm is not only a price
taker but also a wage taker.
 We now turn to the situations in the
noncompetitive markets.
–Monopolistic product market
–Monopolistic labor market

3.5 Monopolistic Labor Market

What if a mandated wage is imposed?
–Change the market supply curve
–Change the firm’s MEcurve
–Change both the average cost and
marginalcost of labor
–If Wmlie between Wm’ and W0, both
wage and employment rise.
–If Wmis higher than Wm’, then ?
3.5 Monopolistic Labor Market

In the long-run, if the mandated wage is
not too high, or reduce the MEof labor,
–Substitution effect more labor, less
capital
–Scale effect:less output lower
employment level
–Uncertain gross effect
Summary

In the short run, a profit-maximizing firm hires
workers up to the point where the wage equals
the value of marginal product of labor.
 In the long run, a profit-maximizing hires each
input up to the point where the price of the
input equals the value of marginal product of
the input. This condition implies that the
optimal input mix is one in which the ratio of
marginal products of labor and capital equals
the ratio of input prices.
Summary

In the long run, a decrease in the wage
generates both substitution and scale effects.
Both of these effects spur the firm to hire more
workers.
 Both the short-run and long-run demand
curves for labor are downward sloping, but the
long-run demand curve is more elastic than
the short-run curve.
 The short-run labor demand elasticity may be
on the order of -0.4to –0.5.The long-run
elasticity is on the order of -1.
Summary


Capital and skilled workers are complements in the
sense that an increase in the price of capital reduces
the demand for skilled workers. Capital and unskilled
workers are substitutes in the sense that an increase
in the price of capital increases the demand for
unskilled workers.
The imposition of a minimum wage on a competitive
labor market creates unemployment because some
workers are displaced from their jobs and because
new workers enter the labor market hoping to find one
of the high-paying (but scarce) jobs.
Summary



The elasticity of teenage employment with respect to
the minimum wage is on the order of -0.1 to -0.3.
The presence of variable adjustment costs implies that
firms adjust their employment slowly when the wage
changes. If fixed adjustment costs are important,
employment changes in the firm are large and sudden,
if they occur at all.
An instrument is a variable that shifts either the supply
or demand curve. The variation caused by this shock
can be used to estimate the labor demand or labor
supply elasticity.