chapter 3 labor demand

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 deman

d, which is derived from consumer’s demand for final product.


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.


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.


Some analytical concepts –Marginal Product (MP) of laborChange of the output resulting from an a

dditional unit of labor employment, holding capital input constant.

MPL=ΔQ/ΔL=Δf(L,K)/ΔL –Similarly, marginal product of capitalMPK=ΔQ/ΔK=Δf(L,K)/ΔK


–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


Average product (AP) of labor –Defined as average output produced by

one unit of labor input. –APL=Q/L=f(K,L)/LAverage product of capital –Defined as average output produced by

one unit of capital input. –APK=Q/K=f(K,L)/K


Graphical MP and AP


Marginal Expense (ME) or Marginal Cost (MC) –Added cost resulting from employing an additi

onal unit of input. A crucial assumption: The Law of Diminishin

g Marginal Returns –Marginal product of labor will eventually decli

ne as employment increases given a fixed capital.

–Why? Specialization, cooperation, externality, …

–Example of 4S.


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.


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.


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.


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 ca

ses.

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.


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


With the same P, profit maximization rule therefore requires that,

W/MPL=C/MPK –The left-hand side W/MPLdenotes the a

dded 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.


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.


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 producti

on 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.


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


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 increas

e is ambiguous. –See Figure in next slide The long-run story therefore provides further s

upport to the proposition of the downward-sloping labor demand curve.


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 mar

ginalcost of labor –If Wmlie between Wm’ and W0, both w

age 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.

chapter 3 labor demand

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