Labor Demand - RONGSHENG TANG...

Labor Demand

Rongsheng Tang

Washington U. in St. Louis

July, 2016

Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 1 / 53

Overview

The production functionThe employment decision in the short run and long runThe long run demand curve for laborMarshall’s rules of derived demandFactor demand with many inputsAdjustment costs and labor demand


Theory of labor demand

Firm’s consideration

given wage rate, how many workers to hire

Trade-off

benefit: more worker produce morecost: wage cost


The Production Function

The production function describes the technology that the firm uses toproduce goods and services.For simplicity, we initially assume that there are only two factors ofproduction: the number of employee-hours hired by the firm(E) andcapital(K)

q = f (E,K )

I q is the firm’s output, E is the product of the number of workers hiredtimes the average number of hours worked per person,

I we assume people are homogeneous, meaning that workers have samecontribution to the firm’s output.



Marginal product of labor(MPE ) is defined as the change in outputresulting from hiring an additional worker, holding constant thequantities of all other inputs.Marginal product of capital(MPK ) is defined as the change in outputresulting from a one-unit increase in the capital stock, holdingconstant the quantities of all other inputs.



Figure:


The Production FunctionLaw of diminishing returns: the marginal product of labor eventuallydeclinesThe marginal curve lies above the average curve when the averagecurve is rising, and the marginal curve lies below the average curvewhen the average curve is falling.

Figure:Rongsheng Tang (Washington U. in St. Louis) Labor Demand July, 2016 7 / 53

Profit maximization

firm’s objective is to maximize its profits,

Profit = pq −wE − rK

where p is the price at which the firm can sell its output, w is the wagerate, and r is the price of capital.

In perfect competitive market, firms take prices as given and choose“right” amount of labor and capital.


The Employment Decision in the Short Run

Short run : firm can not increase or reduce the size of its plant or purchaseor sell physical equipment.

How many workers should the firm hire?

Firm will hire employee such that the value of marginal product of laborequals the wage rate and the value of marginal product curve is downwardsloping, i.e.

VMPE = w and VMPE is declining



Short run : firm can not increase or reduce the size of its plant or purchaseor sell physical equipment.

How many workers should the firm hire?

Firm will hire employee such that the value of marginal product of laborequals the wage rate and the value of marginal product curve is downwardsloping, i.e.

VMPE = w and VMPE is declining



value of marginal product: the dollar value of what each additional workerproduces

VMPE = p ×MPE

For convenience, we will restrict our attention to thedownward-sloping segment of the VMPE curve.Here we need law of diminishing returns, if VMPE keep rising, thefirm would maximize profits by expanding indefinitely, it would thenbe difficult to maintain the assumption that the firm’s decisions do notaffect the price of output or the price of labor and capital.



Figure:



demand curve for labor: what happens to the firm’s employment asthe wage changes, holding capital constant.The short-run demand curve for labor is given by the value ofmarginal product curveThe position of the labor demand curve depends on the price of theoutput, stock of capital, productive efficiency or technology.



Figure:



can we get industry’s labor demand curve by adding up horizontally thedemand curves of the individual firms?

No, because the industry level output will affect market price.



can we get industry’s labor demand curve by adding up horizontally thedemand curves of the individual firms?

No, because the industry level output will affect market price.



Figure:



Elasticity of labor demand: percentage change in short runemployment(ESR) resulting from a 1 percent change in the wage:

δSR =percent chage in employmentpercent change in the wage

=4ESR/ESR

4w/w

e.g. the industry hire 30 workers when the wage is $20 and hire 56workers if the wage fall to $10, then the short run elasticity is


=(56− 30)/30(10− 20)/20

= −1.733



Elasticity of labor demand: percentage change in short runemployment(ESR) resulting from a 1 percent change in the wage:


=4ESR/ESR

4w/w

e.g. the industry hire 30 workers when the wage is $20 and hire 56workers if the wage fall to $10, then the short run elasticity is


=(56− 30)/30(10− 20)/20

= −1.733



Firm’s hiring decision can have an alternative interpretation:

firm should produce up to the point where the cost of producing anadditional unit of output equals the revenue obtained from sellingthat output,the marginal cost equals marginal revenue or the unit cost equalsproduct price.



Figure:



Proposition: The condition equating price and marginal cost is identical tothe condition equating the wage and the value of marginal product oflabor.

By definition

MC = w × 1MPE

ifp = MC

thenp = w × 1

MPE

hencep ×MPE = w


The Employment Decision in the Long Run

In the long run, firm’s capital stock is not fixed, therefore, in the long run,the firm maximizes profits by choosing both how many workers to hire andhow much plant and equipment to invest in.

Isoquants: the possible combination of labor and capital that producethe same level of output.



Figure:



Properties:

Isoquants must be downward slopingIsoquants do no intersectHigher isoquants are associated with higher levels of outputIsoquants are convex to the origin.



Similar to indifference curve, the slope of an isoquant is given by thenegative of the ratio of marginal products, that is,

4K4E

= −MPE

MPK

The absolute value of this slope is called the marginal rate of technicalsubstitution (MRTS).



Isocosts:C = wE + rK

rewriting it as

K =Cr− w

rE



Figure:





At the cost minimizing solution P, the slope of the isocost equals the slopeof the isoquant, that is, marginal rate of technical substitution equal theratio of prices.

MRTS = w/r

Intuition: the last dollar spent on labor yield as much output as the lastdollar spent on capital

MPE

w=

MPK

r



Proposition: a profit maximization conditions imply cost minimization

long run profit maximization requires that labor and capital be hired up tothe point where

w = p ×MPE and r = p ×MPK

henceMPE

MPK= w/r


The Long-Run Demand Curve for LaborWhat happens to the firm’s long run demand for labor when the wagechanges? Will the firm expand if the wage falls?

Figure:


The Long-Run Demand Curve for Labor

scale effect: wage cut reduces the marginal cost of production andencourages the firm to expand, as the firm expands, it want to hiremore workersubstitution effect: the decline in the wage encourages the firm toreadjust its input mix so that it is more labor intensive since the priceof labor relative to that of capital decrease.


The Long-Run Demand Curve for Labor


The Long-Run Demand Curve for Laborboth scale effect and substitution effect induce the firm to hire moreworkers as the wage falls, so the demand curve for labor must bedownward sloping

Figure:


The Elasticity of Substitution

The size of the firm’s substitution effect depends on the curvature of theisoquant.

perfect substitutes: any two inputs in production can be substitutedat a constant rateperfect complements: isoquant between any two inputs is right-angled



Figure:



In between, the more curved the isoquant, the smaller the size of thesubstitution effect, to measure the curvature of the isoquant, we defineelasticity of substitution as

ES =percent chage in(K/E)

percent change in (w/r)

it gives the percentage change in the capital/labor ratio resulting forma 1 percent change in the relative price of labor.The elasticity of substitution is a positive number.

I ES = 0, if two inputs are perfect complementsI ES = ∞, if two inputs are perfect substitute


Policy Application: Affirmative Action andProduction Costs

Affirmative action programs typically “encourage” firms to alter therace, ethnicity, or gender of their workforce by hiring relatively moreof those workers who have been underrepresented in the firm’s hiringin the past.A particular affirmative action plan, for instance, might require thatthe firm hire one black worker for every two workers hired.

I Suppose there are two inputs in the production process: black workersand white workers,

I black and white workers are not perfect substitutes in production,I the market wage rate for black and white workers are wB and wW

respectively



Figure:



when firm discriminates against black workers, it will increase costhence nonprofitable, then the affirmative action program will reducecost for firms.when government force the color-blind firm to adopt an affirmativeaction program that mandates the firm hire relatively more blacks,then it will increase firm’s production cost.


Marshall’s Rules of Derived Demand

Marshall’s rules of derived demand describe the situations that are likelyto generate elastic labor demand curves in a particular industry. Inparticular:

Labor demand is more elastic the greater the elasticity of substitutionLabor demand is more elastic the greater the elasticity of demand forthe outputLabor demand is more elastic the greater labor’s share in total costsLabor demand is more elastic the greater the supply elasticity ofcapital.



An application: Union Behavior

Consider in competitive firm, a union wants to organize the firm’sworkers, and promises the worker that collective bargaining willincrease the wage substantially.Since labor demand curve is downward sloping, the firm may respondto the higher wage by moving up its demand curve and cutting backemployment.Then the union’s organizing drive has a greater chance of beingsuccessful when the demand curve for labor is inelastic.It is the union’s best interests, therefore, to take whatever actions areavailable to lower the firm’s elasticity of demand



Unions often resist technological advances that increase the possibilitiesof substituting between labor and capital.

e.g The typesetters’ unions long objected to the introduction ofcomputerized typesetting equipment in the newspaper industry.

Unions want to limit the availability of goods that compete with theoutput of unionized firms.

e.g. United Auto Workers(UAW) was a strong supporter of policiesthat made it difficult for Japanese cars to crack into the US market.



Unions that organize small groups of workers such as electricians orcarpenters tend to be very successful in getting sizable wage increases.

Unions often attempt to raise the price of other inputs, particularlynonunion labor.

e.g. the Davis-Bacon Act requires that contractors involved in publiclyfinanced projects pay the “prevailing wage” to construction workers.


Factor Demand with Many Inputs

It is easy to extend two inputs model to multi-input model

q = f (x1, x2, ..., xn)

similarly the profit-maximizing firm hires the ith input up to the pointwhere its price equals the value of marginal product of that input:

wi = p ×MPi



We want to know the change of demand for input i when changing theprice of input j, we define the cross-elasticity of factor demand as

Cross-elasticity of factor demand =percent change in xi

percent change in wj

If the cross-elasticity is positive, the two inputs are said to besubstitutes in production.If the cross-elasticity is negative, the two inputs are said to becomplements in production.



Capital-skill complementarity hypothesis:

empirical studies suggest that unskilled labor and capital are substitutesand that skilled labor and capital are complements.

This hypothesis suggests that subsidies to investments in physicalcapital will have a differential impact on different groups of workers.


Adjustment Costs and Labor Demand

Adjustment costs: The expenditures that firms incur as they adjust thesize of their workforce.

Hiring and firing may both induce adjustment costsvariable adjustment costs: depends on number of workersfixed adjustment costs



Figure:



Because of variable adjustment cost, firm will adjust firm size slowly

In term of fixed adjustment cost, firm might as well adjust to the optimallevel immediately as long as it is profitable.



Employment protection legislation:

To enhance the job security of workers, many developed countries haveenacted legislation that imposes substantial costs on firms that initiatelayoffs, for instance, many countries mandate that firms offer severancepay to laid-off workers.

The theory suggests these policies would be expected to slow down therate at which workers are laid off and may prevent layoffs altogether.



These policies may also discourage firms from hiring new workersduring an economic expansion.

I European countries that impose higher costs on layoffs have smallerfluctuations in employment over the business cycle.

I At the same time, mandating that employers pay three months’severance pay to laid-off workers with more than 10 years of seniorityreduces the aggregate employment rate by about 1 percent.

The employment protection legislation affects the amount of effortthat workers supply to their jobs.

I In Italy, it is difficult to fire workers after the 12th week of employment,I a recent study shows that workers are much more likely to be absent

from their jobs after the employment protection kicks in.



The distinction between workers and hours

The firm can adjust the number of employee-hours it wants by eitherchanging the number of workers or changing the length of theworkweek.hiring more workers: induce adjust cost, more health insurancelengthening workweek: overtime premium



The evidence indicates that firms do substitute between workers andhours as the relative costs of the two factors of production change.

It has been estimated that an increase in the overtime premium fromtime-and-a-half to double time may substantially change the numberof full-time workers that the firm wishes to hire.There is also evidence that employers prefer to hire full-timeworkers(rather than part-time workers) when the fixed costs of hiringare substantial.



Job creation and job destruction

The analysis of adjustment cost suggests that small firms would havean advantage in creating jobs if they could respond to favorablechanges in the marketplace much faster than bigger firms.It also might be that small businesses have carved out a niche in thefastest-growing areas of the economy.In manufacture sector in a typical year, nearly 11.3 percent ofmanufacturing jobs disappear, whereas nearly 9.2 percent ofmanufacturing jobs are newly created.


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