Chapter 4 Labor Demand Elasticity

When wages rise we know that employment declines. What we do not know is how much employment declines by. That is, how responsive is employment to changes in the wage rate.   
Elasticity measures that responsiveness.   

The own wage elasticity (will just call this the wage elasticity for now on) of demand is measured by the percentage change in employment (E) caused by a 1 percent change in the wage rate (W).
h = %D E/%D W.

Remember each point on any given labor demand curve has its own elasticity.

When h >1 then we say it is elastic
When h <1 it is inelastic
When h =1 it is unitary elastic

What is the interpretation of these three elasticities?

We also know that a steep demand curve is more inelastic than a flatter demand curve.
Another way of saying the same thing is a flat demand curve is more elastic than a steep demand curve.

(Insert figure 4.1)

Notice how D1 is flatter (more elastic) than D2 .

How do we know that the flatter demand curve is more elastic?

The change in wage is the same for both curves, moving from W' to W. Thus the percentage change in W is the same on both demand curves. Look at demand curve D1

The change in employment is from E'1 to E1. Now look at the same change in employment on demand curve 2. Notice E'2 E2 is much smaller than the change from E'1 to E1. Thus the percentage change in employment is bigger on demand curve 1 than on demand curve 2. Since the percentage change in wages is the same for both then elasticity must be greater for demand curve 1. Thus the flatter the demand curve the greater the elasticity.

We sometimes get confused when talking about an entire curve being more elastic than another curve. The reason being that we know that on any given demand curve each wage change has a different elasticity. Thus how can an entire curve be more elastic. Again look at figure 4.1. Notice on both curves D1 will always have a bigger percentage change in employment than D2 even though they both might have the same percentage change in wages. Thus the absolute value of the elasticity will always be greater for the same percentage change in wages because the numerator of the elasticity formula is always bigger for D1 than D2.

Let's examine the elasticity of demand on one demand curve and show why each point on the curve has a different elasticity. We will also show that there are ranges on the curve that are elastic and there are ranges that are inelastic.
(Insert Figure 4.2 )

In this diagram low wage type workers tend to be inelastic while higher wage type workers tend to be more elastic. At the midpoint the elasticity = 1. This will be the case for any demand curve. Above the midpoint elasticity >1, below the midpoint elasticity <1 and at the midpoint elasticity =1. Before we explain why go back to figure 4.1. Even though we have two different demand curves, once you pick the midpoint of each above it h >1, below it h <1 at the midpoint h =1. Now you may ask how can that be when D1 is more elastic than D2.

Explain why?

Back to figure 4.2. Explain why above the midpoint h>1.

Notice how wages are going up by the same amount each time $2 and employment is going up by the same amount of 10 workers each time.  So any change in wage will be 2 and any change in employment will be 10.  So any $2 wage change will have a change of 10 in employment no matter where you are on the demand curve.  But the percentage change is very different even though the absolute change is the same.  When taking the percentage change use the formula of percentage change in elasticity.  That would be DQ/(Q1 + Q2)/2 That is divide by the average of the two numbers you are taking the percent change in.(For instance, if wages drop from 12 to 10 (notice by 2) there is a 18.18%  [2/((12+10)/2)] reduction of wages and employment goes from 10 to 20 which is a 66.66% increase.  At wages from 12 to 10 demand is elastic because the percentage change in employment (66.66%) > the percentage change in wages (18.18%) 66.66/18.18 =3.66 which >1.  Now suppose we are at the lower range of the demand curve and the same $2 reduction of wage occurs and the same increase of 10 workers happens.  If at $4 wage and it falls to $2 then we see wages declined by 66.66%.  Employment still went up by 10 from 50 to 60 which is only a 18.18% increase.  Thus the percentage change in employment 18.18 divided by the percentage change in wages 66.6650  18.18/66.66 = .272, which is <1 thus inelastic.

Notice at high wages (low employment) the percentage change in E is large while the percentage change in wages is small thus h >1. At low wages (high employment) the percentage change in E is small while the percentage change in wage is large thus h <1. At the midpoint the percentage change in wages and employment is the same thus h =1.

Hicks-Marshall laws of derived demand

Lets examine the factors that influence the wage elasticity. These factors are summarized by what is called the Hicks-Marshall laws of derived demand.

The wage elasticity of demand for labor is high under these four conditions.

Here we see where the scale and substitution effects come into play. Substitution : when wages rise substitute capital for labor. Scale effect wages rise cost of production rises Price of output rises Quantity of output declines thus need fewer workers.

1. When the price elasticity of demand for the finished product is high then the elasticity for labor is also high. When wages rise, production cost increase the price for the final product goes up. The firm raises the products price and quantity demand declines for the finished product. If the demand for the finished product is elastic then the greater the decrease in output the greater the decline in employment needed to make that product.

There are two implications of this first proposition of Hicks-Marshall law of derived demand.

A. The demand for labor for one individual firm is more elastic than the industries demand for labor in which that firm belongs.

Why do you suppose this is the case?

B. Wage elasticities are higher in the long run than they are in the short run.

Why do you suppose this is the case?


The second factor of Hicks Marshall is

2. When other factors of production can be easily substituted for the category of labor we are talking about then labor elasticity is high. Since there are many substitutes if wages rise firms will just switch to another type of labor and employment of the category we are talking about declines. If there are no substitutes for the category of labor we are using then the wage elasticity will be low.

The third factor of Hicks Marshall is

3. The supply of other factors of production will influence the elasticity of demand for labor. Suppose the wage rate rises capital prices staying the same then the firm would substitute the relatively cheaper capital for labor. But suppose the price of capital also rises when wages go up. Then the firm would not want to substitute as much capital for labor because capital is also more expensive and the elasticity of labor would be smaller.

Why might capital prices rise when wages rise?
If capital price do not rise when wages go up then labor demand will be more elastic.

The fourth Hicks Marshall factor is:

4 When the cost of employing labor is a large share of the total cost of operating the business then the elasticity of labor tends to be large. Thus a small increase in wages will add a significant increase to the total cost and the firm will tend to fire workers to reduce cost. However, if labor is only a small percent of the total operating cost and there is an increase in wages then the total cost does not rise much and the firm can absorb it without firing workers and the demand for labor would be inelastic.

All four of these factors influence the elasticity of demand for labor. Thus when wages rise or fall the corresponding change in employment will depend on these four factors.

Cross Wage Elasticity of Demand

We have discussed how the demand curve for labor shifts when one of the ceteras paribus (holding all things constant ) changes. The question is how much will the employment level change by. To measure this we look at what is called cross elasticities.
For instance, we may have two types of accountants. Class k and Class j. Class k are CPA's while Class j are accounting majors with a 5 year degree. Firms can substitute one for the other in about 70% of the tasks that they need accountants for. Thus the wage change in one class might effect the employment in the other. Cross elasticity tells us what effect a wage change of accountants k will have on the employment of accountants j. (of course you can use labor and capital if that makes this easier to understand)

hjk = %D Ej / %D Wk    
where j is one type of input and k is another type of input

if hjk > 0 then the inputs are gross substitutes for each other.
  W  declines (Qj goes up law of demand) and E declines  or if  W rises and  Ek   rises 

Notice the move in same direction 

if hjk < 0 then the inputs are gross complements for each other.
    W  declines E rises  or if  W rises Ek   declines
 They move in opposite direction. 

Gross Substitutes

If the inputs are substitutes for each other then a decline in the wage of input J (hire more J) causes the employment of input K to fall. Since it is positive they move in the same direction.  Thus if wages fall for J (quantity of J increases) the firm will use more J and the employment of K declines. The wage of J and employment of K both go down. The firm is substituting J for K.

If the  wage of K rises (quantity of k declines) firm use more J. Again they move in the same direction.

Gross Complements

hjk < 0 If wage for J declines (quantity of J rises) the firm will also use more K.

If wages for J rises (quantity of J falls) the firm will also use less K.
The two inputs are gross complements for each other when one goes up the firm also needs more of the other.

Remember whether the inputs are gross complements or substitutes depends on the relative size of the scale and substitution effects.

Go back to our example of accountants. Assume they are both substitutes in production. Now if the wage of 5 year accountants fall then there is a substitution and scale effect for CPA's. The substitution effect tells us for a given level of output the firm will have an incentive to substitute 5 year degree accountants for CPA's. Thus CPA employment declines. On the other hand the scale effect tells us the lower wage of 5 year accountants allows the firm to lower its prices for the output and increase sales thus they need more of both accountants.

If the scale effect is smaller than the substitution effect the two accountants will be gross substitutes. If on the other hand the scale effect is greater then the two inputs are gross complements. The point of this is to remember that even though we know the two types of workers are substitutes in production it does not tell us if they are gross substitutes or gross complements. That depends on whether the scale effect is large or smaller than the substitution effect.

We can examine how the four Hicks Marshall Laws tell us if scale or substitution effect is bigger.

There are some people suggesting that the wage for teenagers should be allowed to fall and perhaps go below the minimum wage.  But for now just think about the wage of teenagers declining. Looking at the four factors of Hicks Marshall provides insights about cross elasticity.  For example if wages of teenagers fall what happens to demand for adults?  It depends on the relative strengths of the scale and substitution effects.  We will look at what determines the strength.

 Scale Effect

If wages for teenagers decline cost of production declines, thus price falls for product and demand for product rises.  With more output the firm needs more workers of all kinds to produce the good including adults. How strong will this scale effect be?  This is where the Hicks Marshal Law comes enters the analysis.

Costs and prices will fall more for those firms whose teenage labor cost is a higher proportion of total cost.  (Think Mickey D’s)  The larger this proportion the greater the scale affect thus the higher the chance of more employment including adults. Also the greater the elasticity of product demand the bigger the effect of the cost reductions and price reduction and hence the more output sold.

Substitution effect

If wage for teenagers fall firms will want to use those production techniques that require more teenagers. If adults are complements in production with teenagers then will require more adults to go along with more teenagers and there will be a bigger scale effect.

If they are substitutes then when production changes to teenage intensive methods firms will substitute teenagers for adults.  However, which effect is bigger?

It depends.

The second Hicks Marshall law said if labor (whose price has changed) can easily be substituted for the other product then the substitution effect will be bigger.

However, if adult labor supply was steep and as teenagers are substituted for adults, the demand for adults would decline and with the steep supply curve adult wages would also decline. This would somewhat neutralize the substitution effect because adults are now cheaper to hire.


Insert figure 4.4 from the book here.

Notice in this figure the real wage (which is the demand for labor) is W0/P0and employment is E0.  Thus on demand curve D0 we see the employment level in the year zero.  If in year one minimum wage does not change but money wages and price level rise by the same amount we see that the real wage w1/p1 in year one is the same as in year zero.  However, suppose in year 2 the minimum wage goes up to w2 while at the same time the demand for low skill type workers increase to D1 . Notice how even though the minimum wage increased the employment level also went up.  Some would argue that this is proof that the minimum wage does not have an adverse effect on employment levels.
However, question should be what would have happened to employment levels when demand for labor increased if there was no increase in the minimum wage?
If the min wage did not go up and demand increased we see the employment level at wage w1/p1 would have been E1H.  But since the minimum wage went up to w2/p1 the employment level only goes up to E1  Thus E1H – E1 is the loss represented by the increase in the minimum wage.

Traditional economic theory says that if the minimum wage rises firms will lay off workers thus decreasing the amount of labor and hurting the very group of workers the minimum wage intends to help is not supported by empirical evidence.
 It is very important to note that the minimum wage only effects about 5 to 10% of the entire labor force of the lowest paid workers.  These low paid workers are usually teenagers with no skills, immigrants and untrained poor people.  Thus firms requiring this type of labor can take advantage of the situation by paying these workers low wages.   This group of worker do not have the freedom of mobility to move to areas that pay more, so they are stuck in the lower paying jobs. When the government imposes a minimum wage the argument is these people will lose their jobs  as firms try to reduce the cost imposed on them by the higher minimum wage.

Firm are paying below the equilibrium level and are taking advantage of these peoples unfortunate labor market conditions.  Also they can take advantage of these people because they are not free to move from the lousy area where their jobs exist to areas where better jobs exist.  Thus they have no freedom of mobility.  These poor areas are where new immigrant move into which further increases the supply of labor causing wages to fall.  Those workers earning minimum are usually unskilled.  So economist argue that for the less than 10% of the labor force that earn below the minimum wage the government should step in and protect them from being taken advantage of.  There is no real evidence that the minimum wage displaces workers.

However, recent studies show a different negative effect on workers other than them losing their jobs as a result of the minimum wage rising.  These studies show that while workers are not laid off or fired as traditional theory predicts (but not supported by the data) workers hours and hence income is reduced as a result of an increase in the minimum wage.  Thus employers do not fire workers when the minimum wage rises but instead reduce the hours they work (in order to make up for the higher cost of wages) thus as a result of the minimum wage income for the very workers the minimum wage is suppose to help actually declines.

Another government policy that depends on the elasticity of demand for labor is the use of investment or employment tax credits.

A tax credit is not the same as a tax deduction. If you owe $1000 in taxes and you have a tax credit of $200 then you only owe the government $800 in taxes. A tax deduction just helps determine what you owe in taxes. So if you are in a 30% tax bracket and you get a deduction of $200 then your tax is only reduced by $60 while the credit reduces your tax by $200. Notice there is a big difference.

Often the government has certain types of investment credits to stimulate certain sectors of the economy. They use to have credits for businesses which purchase a new car. This way the cost of the car is reduced.

Lets discuss the investment tax credit.

Since the cost of the investment is reduced (capital prices decline) we want to see what happens to employment.

There is a scale and substitution effect.

Scale effect:

Cost of capital declines firm expands output thus employment will increase and unemployment will decline.

Substitution effect:

Since capital is now cheaper the firm will substitute capital for labor and employment will decline.

The effects of the tax credit on employment depends on whether the substitution effect is greater than the scale effect and the elasticity of employment.

For instance skilled labor is more inelastic than unskilled labor. (It is more difficult to find substitutes for skilled workers than unskilled workers)
When examining the effect of the investment tax credit on employment we must keep in mine that capital and skilled labor are less substitutable than capital and unskilled labor. Thus if a tax credit capital will be substituted for unskilled workers and the total effect will depend a great deal on whether the scale effect is large enough to offset the substitution effect.