Labor Manual
Purpose of the Module
This module is concerned with the operations of a particular resource, or factor, market, a market for labor. In order to permit exploration of the workings of such markets without getting too involved in the entire moral, political, and ethical complexities that make events in labor markets of unusual interest, the market you will be examining exists in the country of Pildia. People in that country have a great love for bread, cake, and other baked goods, so that the first part of the module concerns the market for bakers. In that first part, you will explore the consequences of shifts in the supply and demand for labor in a particular market.
The Pildians are divided into two ethnic groups, the Big Pildians (the dominant group) and the Little Pildians. While they are present in equal numbers they are not equal in power or wealth, and the Bigs often discriminate against the Littles. In the second part we move from the market for bakers to the Pildian national market for all of its labor (not just bakers). In that part you will examine how different degrees of discrimination affect the wages and employment of workers in the labor market, those who were discriminated against and those who were not. Finally, you can try to reduce the burden of discrimination on its victims and on the nation of Pildia as a whole. By the time you have finished this module you should have a better idea of how a labor market works, how it is affected by discriminatory practices, and how well or poorly some anti-discrimination tools work on this problem.
The Basic Model
In markets for labor, the demand for labor comes from businesses which do not hire workers because the boss likes having workers around, but because workers add to production, and the extra products, when sold, get extra revenue for the firm. The more revenue a worker brings in, compared to the cost of hiring the worker, the more profitable it is for the firm to hire the worker. If hiring an extra worker-hour adds $10 to the firm’s revenue, a firm that cares about nothing but profit will hire that worker-hour as long as it costs no more than $10 to hire it. Hiring extra workers means getting less extra product from the added workers due to the law of diminishing marginal returns.
If it is barely worthwhile for the firm to hire a worker-hour for $10 an hour, the firm will not hire another worker-hour unless the cost, or wage, is lower. This is a reason for the downward slope of the firm’s demand for labor. For convenience in this module, the units hired are hours rather than workers, so it doesn’t matter whether the firm hires more people, or more hours per person but the same number of people. In the real world practices such as having to pay time-and-a-half for overtime mean it does matter whether the firm hires more people or just more hours.
There is a difference between the demand by the individual firm and the market demand for labor. As in consumer demand, the market demand for labor is the sum of individual demands for labor by the individual firms. The individual firm in a competitive labor market can determine the extra revenue from an extra worker assuming that the extra production does not affect the market price of the product (since the firm is so small). The overall market demand, however, reflects the fact that the more of the product is produced, the lower of the price of the product. The lower the price of the product, the less worthwhile it is to hire another worker-hour. This is an additional reason why the market demand for labor is downward sloping.
The supply of labor comes from workers who decide that, at a given wage, they are willing to work in this market instead of going to the beach, or working in another market, or going to school, or doing whatever their opportunities offer. The higher the wage, the larger the opportunity cost of doing other things, and the more labor they offer in this market. The market supply of labor is the sum of the labor that all the workers in the market are willing to offer at each given wage.
This module assumes the labor market is a competitive one, with a large number of small bakeries all hiring people with the same skills, and a large number of people with those skills who are interested in working in this field occupation. As a result, the market can be described in terms of the usual supply and demand model. The differences lie in the reasons for “buying” and “selling”, or hiring and accepting a job. “Buyers” are firms who want to hire workers if managers think the workers will make profits for the firm. “Sellers” are individuals who want a job in this industry. In this module the industry is a group of bakeries that make bread.
Demand for Labor
In a competitive market, demand for labor depends on the value of the marginal product of labor, which is the extra output from an extra hour of labor multiplied by the market price of the product. Demand depends on the price of the product and on anything that influences the amount of extra output that the next hour of labor will produce. In this module there are three things that you can use to affect the demand for labor in the Pildian baking industry: the price of bread, the price of ovens used in the industry, and the price of the flour that is a complement to labor in producing bread. For simplicity, in the first part of the module the demand for labor by the industry is presented in a linear form. In reality the product price would multiply the marginal product, which in turn would depend on the other factors in non-linear ways. The number of hours (per week) the industry wants to hire is, that is the demand for labor (DL) is:
DL = a1 + (a2 x Wage) + (a3 x Oven Price) + (a4 x Bread) + (a5 x Price of Flour)
or
DL = a1 + a2 Wage + a3 Oven Price + a4 PBread + a5 PFlour
where a1 = 5.9051; a2 = -0.1; a3 = 0.002; a4 = 2; a5 = -0.04 or
The higher the wage, the lower the number of hours hired so a2 is negative. The use of more capital (ovens) increases the demand for labor by raising the marginal product of labor so a3 is positive. A higher bread price raises labor demand since the marginal product is more valuable so a4 is positive. A higher price for flour lowers demand for labor. The higher flour prices cause firms to buy less flour, which workers use to make bread. Thus fewer workers are hired and a5 is negative.
Supply of Labor
Households (people) supply labor. How much labor is supplied to this industry depends on how many households there are, how many people per household are willing and able to supply labor to markets, or the labor participation rate, and on the alternatives available (wages in other industries). For simplicity, in this part of the module supply is also linear. In reality the participation rate would appear as a multiplier of the population, both the wage in this industry and in the alternative markets would affect the participation rate, and supply of labor to this industry would be influenced by the ratio between wages in this industry and wages in other markets (e.g. cook’s wage rate.)
The number of hours (per week) that employees want to offer is the supply of labor (SL):
SL = b1 + (b2 x Wage) + (b3 x Population) + (b4 x Participation Rate) + (b5 x Cook’s Wage) or
SL = b1 + b2 Wage + b3 Pop + b4 Prate + b5 Cook’s Wage
where b1 = 7.569; b2 = 0.02; b3 = 0.01; b4 = 0.62; b5 = -0.15
The higher the wage in this market, the more hours are supplied so b2 is positive. The higher the population and the participation rate, the more labor is supplied so b3 and b4 are positive as well. Higher cook’s wages reduce the hours supplied to this market so b5 is negative.
As in any competitive market, equilibrium price and quantity are determined by the equality of supply and demand. The module presumes that the market is always at its equilibrium point, even though that is often untrue for significant periods of time in labor markets. Anything that shifts the demand or supply curves will change the equilibrium wage and hours worked in this market. A change in any of the items listed under demand will shift the demand curve except a change in the wage rate in this market. Similarly, except for a change in the wage in this market, a change in any of the items listed under supply will shift the supply curve.
A shift in demand will change the equilibrium wage and employment in the same direction -- either a higher wage and more employment, or a lower wage and lower employment. A shift in supply will affect the equilibrium wage and employment in the opposite direction -- either a higher wage and lower employment, or a lower wage and higher employment. Figure 1 shows the effects of an increase (shift) in demand; Figure 2 shows the effects of an increase (shift) in supply.
Figure 1 Increase in Labor Demand
Wage ($) SL
We′
We
DL′
DL
Labor (hours per week)
Le Le′
Figure 2 Increase in Labor Supply
Wage (W) SL
SL′
We
We′
Labor (hours per week)
Le Le′
The Discrimination Model
There are a number of different models of how discrimination can work in a job market. The discrimination in this module arises from the behavior of employers. There are two groups of people who can be hired: Big Pildians and Little Pildians. In this module even though members of each group are actually equal in ability, employers prefer to hire Big Pildians and avoid Little Pildians. They will hire Little Pildians only if they are cheaper (accept lower wages) than Big Pildians.
This kind of discrimination effectively reduces the demand for members of the group who are discriminated against. It is as if there are two markets for labor, one for Big Pildians and one for Little Pildians, instead of just one market in which all that matters is the ability to produce. Even if the two markets were separate, however, without the presence of actual discrimination the wages of the two groups would be equal as long as both were equally productive. If the two groups were equal in size, and equal in the demand for their services, employment and wages would be equal. Since there is discrimination, wages and employment will differ between the two. How different they are depends on how strongly employers feel about discriminating. The more strongly employers prefer not to hire Little Pildians, the larger the difference in wages and employment. Whether employers simply dislike Little Pildians, or think their customers are less willing to buy goods baked by Little Pildians, or believe them to be less productive even though that isn’t true, does not matter in this module. The module assumes that all employers act the same way (probably none of them are Little Pildians) so no employers get an advantage (higher profits) by not discriminating.
In this part of the module the formulations of supply and demand are a bit different than they are in the first part. There is no need to look into reasons other than discrimination for shifting the curves, so there is no reason to resort to linear formulas. The module assumes that the supplies of Big Pildians and of Little Pildians are identical (including in quality of potential workers).
The supply of Big Pildians is:
S(Big Pildians) = (Wage(Big Pildians)/b)2
The parameter b incorporates the influences of population size, participation rate, and the wages in other markets. In this module b = 0.28. The diagrams in the module will depict this supply curve as a straight line, but of course it is not.
The supply curve of Little Pildians is the same, except that the wage that affects the quantity supplied is the one Little Pildians can get:
S(Little Pildians) = (Wage(Little Pildians)/b)2
The demand for Big Pildians depends on the same things as before. Since employers don’t dislike hiring from this group, and don’t hire Big Pildians just because they like them -- they hire them if they will create profits -- only the variables discussed before would be relevant. However, since all these variables will now be constant, the value of the marginal product can be described simply, and without making believe everything is linear. The production function which describes the relationship between the amount of labor hired and the amount produced is:
Output = c1 + c2 x (Labor hired)0.5
wherec1 = 6000; c2 = 1120
The fact that this function allows for a positive output when the amount of labor hired is zero is, of course, very unrealistic, but it makes the calculations simpler and does not affect the conclusions of the module.
The marginal product of labor (MPL) for either Big or Little Pildians is therefore:
MPL = 0.5 x c2 x (Labor hired)-0.5
However, the value of the marginal product for the two groups differs, from the perspective of a prejudiced employer. When considering hiring a Big Pildian, the marginal value to the firm of hiring, the marginal value product of labor (MPL) is:
MVPL(Big Pildian) = Product Price x MPL
If a prospective employee is a Little Pildian the prejudiced employer discounts the value by a factor reflecting the degree of prejudice held by the employer, or the employer’s reflection of perceived customer prejudice. There are a number of ways this could be incorporated into this module. The way it is put in is by having the employer act as if the price of the product were lower than it actually is. In effect, the MVPL becomes:
MVPL(Little Pildian) = (Product Price - ∆) x MPL
The new factor ∆ is a measure of how much the employer dislikes hiring Little Pildians. If the employer didn’t dislike hiring them, but thought the Little Pildians were less productive, the exact reason for the difference would change, but the overall effect would be the same -- hiring the same number of each group, the true MVPL for each would be the same, but the employer would act as if the MVPL(Little Pildians) was smaller. Since the MVPLis the demand curve for labor, that means the demand for Little Pildians will be smaller than that for Big Pildians. Figure 3 below shows the differences between the two markets. The D′ line in the diagram for Little Pildians is demand as it would be if there is discrimination. The D line is the one that applies with no discrimination. The thick horizontal line on the left part of Figure 3 is the unemployment observed at the no-discrimination wage (see below for analysis).
Figure 3 Labor Market Discrimination
WageS Wage S
We We
We′
D′
Labor Labor
Le Le′Le
The cost of having labor market discrimination to those who are discriminated against is clear -- they get lower wages and less employment. The cost to society as whole can be measured in terms of the value of the products that would have been produced if there were no discrimination (a lower real GDP). The existence of such costs is the economic justification for society to take legal measures to reduce or eliminate this type of discrimination. (There are non-economic justifications for such measures that will not be covered here.)
Fighting Discrimination
In the real world there are a variety of methods used to combat discrimination. This module incorporates two such methods and allows you to use one method at a time to eliminate discrimination. Note: Many economists think that the kind of discrimination featured in this module will disappear in the long run. That is because if some employers do not discriminate they can hire productive workers for less than their competitors, become more profitable, and drive the discriminators out of business. Even if that is true in the long run it need not be true in the short run, which is the focus of this module. Also, in this module it is assumed that all employers discriminate so there is no one to drive discrimination out. (Presumably Little Pildians are making such small incomes they never save enough to start their own businesses and hire their own people.)
Equal Pay
One method is to pass and enforce a law requiring “equal pay for equal work.” In this module, that requires employers who hire Little Pildians to pay them the wage that is already being paid to Big Pildians. Since employers still prefer to hire Big Pildians, they will only hire Little Pildians to the point where they are so much more productive than Big Pildians that the extra value created makes up for the dislike they have of hiring from this group. That was already true (before this policy was applied) -- but the lower wage for Little Pildians made it easier to get employers to overlook their preferences. With this policy in place, there is no lower wage and there are even fewer jobs for Little Pildians.
In Figure 3, the amount of equilibrium employment for Little Pildians with discrimination is at the intersection of the supply curve and the D′ curve. If the equal pay rule is enforced, employment for Little Pildians can be found at the intersection of the D curve and wage with no discrimination, or W. You might notice that that point is not on the supply line for Little Pildians, so at that wage the quantity of labor offered to the market by members of this group is larger than the quantity demanded. In terms of the usual market analysis that means there is a surplus, in the context of a labor market we say there is unemployment (people willing to work at the given wage who can’t find a job at that wage).