Resource Markets

I.   Labor markets vs. other resource markets.

The focus in this part of the course will be almost entirely upon labor markets. However, the discussion of labor markets can be generalized in most instances to markets for other resources.

II.   Why do Individuals supply labor?

1. Labor as a consumption good.

One possible reason explaining why people supply labor is that they do so because they enjoy working. Considering labor as a consumption good, one whose consumption yields utility, allows important insights to be gained about why individuals supply labor. For example, if people gain utility from "consuming" or working at some jobs, they just as surely gain disutility (i.e., don’t enjoy) working at other types of jobs.

It is clear that quite a few jobs have unfavorable job aspects. A job might have an unusually large amount of risk of injury associated with it. Suppose a person works for a power company as a lineman, a person who either installs or repairs electric power lines. This person has risks that other people, say an academic like myself, do not face in their jobs. The power lineman might have a wrench dropped on him by a co-worker from the top of a power pole (something that happened to my own brother-in-law once), not to mention the risk of electrical shock.

Other jobs just have aspects to the job that, while not increasing the risk of death or injury per se, are found by most people to be unappealing. Consider as another example of a job most people would find unappealing the job of garbage pick-up person. Not only would the manual labor associated with this job not be appealing to most people, but the association with smelly garbage all day, tends to make this job an unappealing one.

All of this implies that people must be paid a higher wage for jobs, all else equal, with more unfavorable job aspects than for jobs without these unfavorable aspects. Economists call this higher wage a compensating wage differential – the worker is being compensated for the unfavorable job aspects with the higher wage. Another implication of viewing labor as a consumption good is that jobs with especially favorable aspects would, all else equal, command lower wages.

2. Labor as an investment good.

Rather than viewing labor as a consumption good that provides utility, another method of viewing the labor supply decision is to focus on leisure. Leisure is what an individual does when he is not either supplying labor or in regular daily activities, such as sleeping and showering. Hence, leisure is what an individual chooses to do with his free time. Clearly, there exists an inverse relationship between labor and leisure – as a person engages in more leisure, he must necessarily supply less labor.

From the perspective of labor as an investment good, which yields income to the individual while it is that person’s leisure that yields utility, consider the interpretation of the wage rate. The wage rate has two interpretations:

1. The wage rate equals the price paid for the labor supplied by the individual.
2. The wage rate also equals the price of leisure. That is, the wage is the opportunity cost of time spent in leisure activities that could otherwise have been spent working and earning income.

3. What does an individual’s supply of labor curve look like?

Let us assume that the total amount of time available for either labor or leisure in a given week totals 112 hours. This assumes that 8 hours per day are needed for daily activities. Under these circumstances, is the supply of labor upward sloping as in the graph to the right? That is, when the wage rises do individuals respond by increasing the quantity of labor that they supply?

To answer this question, we must use the two interpretations of the wage rate discussed above. Each yields a separate impact on the quantity supplied of labor as the wage rate rises. Our focus in this analysis will be upon the impact that rising wage rates have upon the quantity of leisure consumed. Recall that an inverse relationship exists between the quantity of leisure consumed and the quantity of labor supplied. Hence, if consumption of leisure increases (decreases) then the quantity supplied of labor will decrease (increase.) The two separate impacts are:

1. As the wage rises, individuals respond by increasing their consumption of leisure because with rising wages individuals obtain additional income. Assuming that leisure is a normal good, individuals will buy more of all normal goods, including leisure, as income rises. Hence, the quantity supplied of labor will decrease as the wage rate rises.

This impact is known as an Income Effect of a wage increase and indicates that an individual’s supply of labor curve is downward sloping.

2. As the wage rises, individuals respond by decreasing their consumption of leisure because leisure has become more costly. In other words, the increased wage also has the impact of increasing the opportunity cost of leisure. As with any consumption good, as its price rises, individuals respond by decreasing the quantity consumed of that good. Hence, the quantity supplied of labor will increase as the wage rate rises.

This impact is known as a Substitution Effect of a wage increase and indicates that an individual’s supply of labor curve is upward sloping. It is a substitution effect because, as we learned in our original discussion of demand and supply, the main reason why individuals buy less of a good like leisure as its price rises is because they substitute lower priced alternatives for the higher priced leisure. The substitution effect indicates that an individual’s supply of labor curve is upward sloping.

Notice that the Substitution Effect and the Income Effect occur simultaneously as the wage rate changes and that they have exactly opposite impacts upon the quantity supplied of labor. Whether the supply of labor curve is upward sloping or downward sloping depends upon which of these two effects is larger. Which effect dominates is, in fact, an empirical question. Studies of real world behavior tend to demonstrate that the Substitution Effect dominates at low wage levels and that the Income Effect dominates at high wage levels for most people. Hence, the supply of labor curve would be backward bending as in the graph to the right.

Although supply of labor curves for individuals have been observed to backward bend, as in the graph above, such backward bending is rare. It has usually only been observed for individuals with very high wages (such as physicians.) Furthermore, it is important to recall that each person is unique. Hence, both the wage level at which the supply curve begins to backward bend and whether the curve will backward bend at all, is unique to each individual.

4. What does the Market supply of labor look like?

The crucial question to address with the market labor supply curve is whether or not such curves can also be backward bending, as for individuals. Clearly, market supply curves could be backward bending because they are the summation of individual labor supply curves. Hence, if individuals’ supply curves can be backward bending, so can market supply curves. However, market supply curves are not observed to be backward bending in actuality. What might cause market supply curves to behave differently than individuals’ supply curves?

To understand why this difference between market and individuals’ labor supply exists, consider carefully what happens in a market when the wage rate rises that does not happen for individuals:

1. With rising wages, markets often experience substitution of labor from other markets with relatively smaller wages. Such substitution may come from markets that are geographically close to the market where the wage is rising. For example, if the wage for nurses in Springfield, MO rises, some nurses may choose to relocate from Kansas City to Springfield to take advantage of the relatively higher wages.

Likewise, such substitution may come from markets that are in the same geographic location but where the individuals have related skills. For example, as the wage for non-academic economists rise some academic economists may choose to enter the non-academic labor market.

2. Over a period of time new labor is trained. As the wage for a particular job rises, relative to other types of jobs then, ceteris paribus, more people will choose to be trained in the for the job whose relative wage rose.

For both of the above reasons, market labor supply curves will tend to remain positively sloped rather than backward bending. In addition, however, it is often the case that many individuals are not allowed to have backward bending labor supply curves. That is, firms often enact policies that reduce the ability of individuals to choose to work fewer hours as their wage rises. Examples of such policies include:

1. Overtime pay. The key component of overtime pay is that a worker will only receive a higher wage if they also work more hours. As a result, while workers may wish to work fewer hours with the higher wage resulting from overtime, they are not allowed to do so and still receive the higher wage.
   
2. Discrete jobs. Firms often have jobs that are discrete, that require a worker to spend a given number of hours in the job per week or to lose the job. This is an all or nothing approach to work, either work a certain number of hours or lose your job. Hence, even though a worker in this type of job might want to work fewer hours as their wage rises, they cannot do so and keep their job.

5. What affects the Market Labor Supply?

This section both summarizes what we learned above and provides some new insights. Since market labor supply is a sum of individual labor supply, the impact of individual decision-making, discussed in C above, must have an impact on the market.

1. Labor/Leisure choices by individuals (see discussion above). The more leisure people consume, the less labor is supplied by each individual. During this century one of the largest impacts in labor markets has been the increase in the leisure that individuals generally consume and the resultant decrease in average labor supplied. For example, after World War II the average worker spent slightly more than 40 hours per week working. By 1997, the average worker had decreased to only 34.6 hours per week working. (Source: Bureau of Labor Statistics, National Employment, Hours and Earnings, Average Weekly Hours of Production Workers.)
   
2. Population. The higher the population the more individuals there are who will choose to work, ceteris paribus.
   
3. The wage rate and its structure (see discussion above).
   
4. The Labor Force Participation Rate (LFPR). The LFPR for a given group of individuals equals the number of individuals in that group working divided by the total number of individuals in that group. Clearly, as the LFPR rises, so will the supply of labor. In the past fifty years, two major changes have occurred in LFPR’s in the U.S. The largest change is the increased labor force participation of women. For example, the LFPR of women age 20 and older rose from 31.8 percent in 1948 to 60.5 percent in 1997. A smaller, but still significant, change is the decrease in male labor force participation over the same time period, from 88.6 percent in 1948 to 77.0 percent in 1997. (Source: Bureau of Labor Statistics, various labor force participation series.)
   
5. Education, Training, and Skills of potential workers. Combined, these three concepts are known in labor economics as Human Capital. Human Capital represents the investments that individuals make in education or different types of training with the intent of increasing their productivity and, hence, their wages. Human Capital has its main impact on Supply of Labor through its impact on the wage rate.

6. Why do individuals invest in Human Capital?

Consider education as one example of the decisions that individuals make with respect to investment in Human Capital. Why do individuals invest in education? One possibility is that individuals view education as a consumption good, one that yields utility. This implies that, all else equal, individuals will tend to choose education in subjects that interest them. Or, conversely, if they are to become educated in a subject that they find less inherently interesting, they must be compensated by a relatively higher wage.

Another possibility is that individuals view education as an investment, one that yields a stream of income. Consider the graph to the right. On the x-axis, a person’s age is measured in years, beginning at age 18, the year most people graduate from high school. On the y-axis, a person’s yearly earnings are measured in dollars. The graph shows two earnings profiles.

1. The earnings profile labeled "College" represents the earnings profile this person would gain if they were to choose to go to college after high school at age 18.
   
2. The earnings profile labeled "No College" represents the earnings profile this person would gain if they were to choose to attend college, thereby putting off job earnings for four years.

A person who has just graduate from high school at age 18 faces the decision of whether or not to go on to college and must consider both the costs and benefits of the decision. The costs of the decision to attend college are represented by the two areas in the graph, A and B. Notice that during the 4 years of college attendance, the earnings profile is negative indicating that the person must pay direct costs, such as tuition, room and board, and so forth. Area A, below the x-axis and above the negative earnings profile, represents these direct costs. However, when attending college a person also has indirect, or opportunity costs, due to lost earnings. Lost earnings equal the difference between the earnings he could have made in a job out of high school and his actual earnings with a college education. Area B, above the x-axis between age 18 and 22 and above the College earnings profile thereafter and below the No College earnings profile, represents these opportunity costs. Area A and B together represent the cost of the decision to attend college.

Notice that the earnings that a college graduate makes might not, as is shown in the graph, equal the earnings that the non-college graduate would make at age 22. However, the college graduate has the advantage that his earnings rise at a faster rate. Eventually, then, the "College" earnings profile will rise above the "No College" earnings profile. Thereafter, the area between these earnings profiles represents the benefit of college education and is labeled in the graph as area C.

An individual making a decision to invest in education will compare the benefits (area C) to the costs (areas A and B) of education. If the costs outweigh the benefits, then the person will generally choose not to invest in the education. However, if the benefits exceed the costs, then the person will generally choose to invest in education.

There does exist one complicating factor in the decision to invest in education. Notice from the graph above that the costs of education are paid up front while the benefits from the education occur some years later and with some possibility that they will not materialize as expected. The risk that the benefits will not occur as expected can induce people to avoid the investment. Likewise, people have different preferences with respect to time. The fact that the benefits are in the future may induce some people, who may prefer to have their benefits today even though they are smaller, to not invest in college education as well.

The above analysis can be applied to various types of training as well as education.

III.   Why do Firms demand labor?

1. Demand for Labor is a Derived Demand.

Firms do not demand labor for the same reason that consumer demand a good, such as oranges. Consumers demand goods because they gain utility or satisfaction from the consumption of the goods. Firms, however, do not generally gain any utility from providing individuals with jobs. Rather, as profit-maximizing firms, their goal is to earn profits by producing a good and selling the good to consumers. Labor is one of the resources that the firm uses to produce the good. Hence, firms only demand labor in order to produce the good that they sell to consumers. As a result, demand for labor, as with all resources, is ultimately derived from the demand for the good being produced by labor. Without any demand for that good there would exist no demand for labor.

2. A closer examination of derived demand for labor.

Consider the production of a good, such as wheat, whose market is perfectly competitive. In such a market, we know that the market price of the good equals the firm’s marginal revenue. As with all production, we also know that the law of diminishing returns holds, so that the firm’s marginal product of labor (MPP_L) declines as its use of labor increases. These concepts are illustrated in Table 1 below:

Table 1

MPP_L and MR in the Wheat Market

Now define two concepts:

1. Marginal Revenue Product of Labor (MRP_L ). MRP_L equals the extra revenue generated by hiring an additional unit of labor. As a result, MRP_L measures the value to the firm of hiring an additional unit of labor. Hence, demand for labor by the firm equals MRP_L.

According to Table 1, what would be the MRP_L of hiring the first worker? The extra worker produces an additional 10,000 bushels of wheat, which each generates additional revenue (MR) of $5. As a result, an extra $50,000 is generated in revenue. Hence, as can be seen from the example, MRP_L equals MR times MPP_L.

2. Value of the Marginal Product of Labor (VMP_L ). VMP_L equals the extra social (or market) value generated by hiring an additional unit of labor. VMP_L measures the value to society of hiring an additional unit of labor.

What is the value to society of one more unit of output? Recall that price measures the value to individuals of the consumption of a good. In the absence of externalities, price would also measure the value to society.

According to Table 1, what would be the VMP_L of hiring the first worker? The extra worker produces an additional 10,000 bushels of wheat, which can be sold for a price of $5 each. As a result, an extra $50,000 is generated in value to society. Hence, as can be seen from the example, VMP_L equals price times MPP_L.

Table 2

The Demand for Labor in the Wheat Market

Table 2 calculates both MRP_L and VMP_L based upon the numbers first presented in Table 1. According to the above discussion, the demand for labor is given by the MRP_L. Notice that MRP_L and VMP_L are equal for each worker hired. This is because price equals marginal revenue. Second, notice that as expected the demand for labor (MRP_L) is downward sloping. That is, if the wage equaled $50,000 this firm would hire one worker. If the wage fell to $40,000, the firm would hire an additional worker, for a total of two. Thus, the demand for labor appears as in the table to the right.

 

3. Why is the firm’s demand for labor downward sloping?

Recall that a firm’s demand for labor is given by its marginal revenue product of labor curve. As illustrated by Table 2 above, MRP_L equals a firm’s MR times its MPP_L. Thus, for a perfectly competitive firm, as in the current example, a firm’s Demand for labor is downward sloping because of the law of diminishing returns. That is, the law of diminishing returns ensures that the MPP_L will itself be downward sloping. Since the firm’s demand consists of the product of MPP_L and MR, the demand curve will also be downward sloping.

4. What else affects the Demand for labor (besides the wage rate)?

We’ve already discussed how the wage rate impacts the demand for labor for an individual firm. A change in the wage rate causes a firm to move along an existing demand for labor curve, ceteris paribus. If anything else besides the wage changes that affects the demand curve, then the curve must either shift to the right (D ­ ) or to the left (D ¯ ). These two concepts are illustrated in the graph to the right. A rightward shift in the demand curve is referred to as an increase in demand because, at the same wage, the quantity of labor demanded increases. For example, when D shifts right from D₂ to D₃, the quantity of labor demanded increases from L₂ to L₃. Likewise, a leftward shift in demand is called a decrease in demand because, at the same wage, the quantity demanded of labor decreases. The graph illustrates this as a decrease in quantity demanded, at wage W₁, from L₂ to L₁ when D falls from D₂ to D₁.

What other factors will cause the Demand for Labor to either increase or decrease? Since Demand for Labor equals marginal revenue (MR) times marginal product of labor (MPP_L), obviously anything that increases (decreases) either MR or MPP_L will increase (decrease) the demand curve.

1. Marginal Revenue

The source of marginal revenue is the firm’s output market. For a perfectly competitive firm, as currently being discussed, their MR is determined by the price set in the market. Hence, anything that increases market prices will increase the firm’s MR and, as a result, increase the firm’s demand for labor. Likewise, anything that decreases market prices will have the reverse impact.

What will cause the market price of the good that labor produces to change? Basically the interaction of demand and supply in the market for the good labor produces impacts the market price for that good. Hence, anything that will change either the demand or supply curve for that product will affect the market supply. Our discussion of demand and supply earlier in the semester identifies which factors will shift both curves.

2. Marginal Product of Labor

There exist several factors that can shift the marginal productivity of labor.

• Technology: Recall that the way that we defined an increase in technology was as any change in the production process that allowed the same number of resources to produce a larger output. Such an increase in technology can be focused on labor and, hence, make labor more productive which will, in turn, increase the firm’s demand for labor. Likewise, a decrease in technology will decrease a firm’s demand for labor.

• Human Capital: As discussed above, human capital represents investment in education or training that increases a worker’s productivity. Hence, as workers invest in human capital then the firm’s demand for that labor will increase. The reverse will occur if worker’s allowed their human capital to deteriorate.

3. In addition to the impact of MR or MPP_L, firms will also change their demand for labor based upon the prices of related resources. Demand for labor will change because firms are attempting to minimize the costs of producing a given output by changing their use of inputs based upon the input prices. Resources can be related in two separate manners:

• Complements – two resources are complements if they must be used together in the production process.

If the price of a resource that is a complement to labor rises, then the firm will use less of that resource in the production of the product. Since the two resources are complementary, the firm will also use less labor as well and, hence, demand for labor will fall. If the price of the complementary resource falls, then the demand for labor will rise.

• Substitutes – two resources are substitutes if they can be substituted for each other in the production process.

If the price of a resource that is a substitute for labor rises, then the firm will use less of that resource and more of its substitute, labor. Hence, demand for labor will rise. Likewise, if the price of the substitutable resource falls, then the demand for labor will fall.

5. What factors impact elasticity of the demand for labor?

Recall from our earlier discussion regarding the definition of elasticity. The price elasticity of demand for any demand curve equals:

%D Q_D ¸ %D P

Where Q_D equals the quantity demanded of the good or resource, P equals the price of the good or resource, and D stands for "change in". Given that the price of labor equals the wage rate (W) and the quantity being demanded equals labor (L) we can call this, in the case of demand for labor, the wage elasticity of the demand for labor, which is given by:

%D L_D ¸ %D W

What does wage elasticity measure? We already know that as the wage rate rises, the firm will reduce the amount of labor it hires (L_D will fall). However, we don’t know by how much the firm will reduce its quantity demanded of labor. Wage elasticity allows us to measure how responsive demand for labor is to changes in the wage rate.

Why does an increase in the wage rate cause quantity demanded for labor to decrease? A wage rate increase will cause the firm’s costs of production to increase. An increase in production costs will, in turn, cause supply to rise, thereby increasing price and reducing the quantity demanded for the firm’s output. A reduction in quantity demanded for the firm’s product will force the firm to decrease its production and, therefore, its use of labor. As a result, an increase in the wage rate ultimately results in a decrease in the quantity of labor the firm demands.

Now consider which factors will cause demand for labor to become more or less elastic.

• Price elasticity of demand for the product that labor produces.

As demand for the product labor produces becomes more elastic, quantity demanded for that product will decrease more for a given wage increase. Hence, as demand for the good that labor produces becomes more (less) elastic then the demand for labor will also become more (less) elastic.

• Labor’s share of total production costs.

Compare the impact of a wage change under two different scenarios:

1. Labor’s share of total production costs equals 95 percent. That is, 95 percent of the cost of producing the good by the firm entails payments of wages to labor.
   
2. Labor’s share of total production costs equals 5 percent. Again, only 5 percent of the cost of producing the good consists of wages paid to labor.

Now suppose that the wage rate doubles. In which of the two above scenarios, will costs of production rise more? Obviously, because labor’s share of total costs is larger in number 1, then a doubling of the wage will have a larger impact in the first case, as opposed to the second example, where payments to labor represent such a small portion of total costs.

But if production costs increase more for scenario 1 than scenario 2, then the price will also increase more in this scenario, reducing quantity demanded for the firm’s product more and, ultimately, decreasing quantity demanded of labor by a larger amount.

Hence, we can conclude that, as labor’s share of total costs increases (decreases) demand for labor will become more (less) elastic.

• Ease of resource substitution.

Consider what happens in the eventual impact of a wage increase on quantity demanded of labor as it becomes easier to substitute other resources for labor. Clearly, in this situation, for a given wage increase, firms will attempt to minimize their costs of production by using less labor and more of the other, substitutable, resources. In other words, for a given wage increase, a firm will decrease their use of labor more as it becomes easier to substitute other resources for labor.

As a result, we can conclude that the demand for labor becomes more (less) elastic as it becomes easier (harder) to substitute other resources for labor.

• The time period.

Consider what can happen as the time period lengthens. In the short-run, for example, firms might find it very difficult to find other resources to substitute for more expensive labor as the wage increases. However, as more time passes, firms will be more likely to be able to find such substitutes, which would then decrease the firm’s use of labor.

Hence, as the time period lengthens (shortens) demand for labor becomes more (less) elastic.

6. Market Demand for Labor.

As with all market demand curves, market demand for labor consists of the summation of all the individual demand curves for individuals consuming in the market. In this case, since it is firms who demand labor, market demand consists of the sum of all the individual firm demand curves.

7. Marginal Factor Cost.

Marginal Factor Cost of Labor (MFC_L) = the extra cost to the firm of hiring an additional unit of labor. The MFC_L is found by the following equation:

D TFC_L ¸ D L

Where TFC_L is the Total Factor Cost of Labor and is given by the wage rate times the amount of labor hired (L).

IV.   Equilibrium Wages and Employment in Different Markets

1. The impact of two markets on equilibrium wages and employment.

• The market for the input (the labor market).

The input market can be either perfectly competitive or a monopsony. A perfectly competitive labor market is one where the firm is so small relative to the market (similar to a perfectly competitive output market) that they take the price of the input as given and hire as much of the input as they wish at that price. In other words, the firms are "wage takers."

Recall that a monopoly occurs when, among other characteristics, there exists a single seller of a good or resource. Conversely, a monopsony occurs when there exists a single buyer of a good or resource. Hence, in a monopsony labor market, in contrast to having many firms hiring labor, only one firm is hiring labor.

We will consider below the impact that both monopsony and perfectly competitive labor markets have upon equilibrium in the market.

• The market for the output.

We will consider below the impact that the level of competition in the output market will have upon equilibrium in the labor market. The equilibrium in the labor market will be examined for the two extremes, either perfectly competitive or monopoly output markets.

The following table describes the four possible scenarios that will be analyzed, based upon the level of competition in both the labor market and the output market.

2. Equilibrium Wages and Employment.

• Quadrant 1 – both the labor market and the output market are perfectly competitive.

We’ve already considered the Demand for Labor for a firm in a perfectly competitive output market in the example used above. There it was shown that demand equaled MRP_L, which was itself equal to VMP_L. The demand curve was downward sloping because of the law of diminishing marginal product (or law of diminishing returns.)

What, then, is the supply of labor for a firm in a perfectly competitive labor market? Recall that we noted above that such a firm would be a "wage taker" because they were so small relative to the market that they could have no impact on the market wage regardless of how much labor they hired. Hence, the following graphs would describe the market and firm situation for Quadrant I.

Every time the firm hires one more unit of labor they must pay the market wage, W_M. Hence, the marginal factor cost of labor equals the market wage for this firm. For the firm in the original example, as re-created below only know with the market wage, market Supply curve, and MFC_L added, the firm will hire how many workers?

Table 3

The Demand for Labor in the Wheat Market

The firm cares about its MRP, for that measures how much extra revenue the firm gains from hiring one more unit of labor and its MFC, for that measures how much extra it costs the firm to hire one more unit of labor. We can conclude that:

1. As long as MRP > MFC, the firm will continue to hire labor. Hence, the firm will hire the first unit of labor from the table above since they will gain $50,000 in revenue but only have to pay $20,000 for that labor.
   
2. As long as MRP < MFC, the firm will reduce its hiring of labor. Hence, the firm will not hire the fifth unit of labor because they will only gain $10,000 in revenue but will be forced to pay an extra $20,000 for that labor.
   
3. Hence, we can conclude that the firm will hire labor where MRP = MFC. In fact, all profit maximizing firms will hire labor where MRP equals MFC. The firm in the above table, therefore, will hire 4 workers and pay them a wage of $20,000.

Notice that even though the firm that is perfectly competitive in both markets hires labor where MRP = MFC, it is also the case that they hire labor where VMP = MFC, MRP = wage, and VMP = wage. This is because, for a firm which faces competition in both markets MRP = VMP and MFC = wage.

• Quadrant II – labor market is competitive while the output market is a monopoly.

From the discussion of Quadrant I it is clear that when the labor market is perfectly competitive then the firm is a wage taker and S_L (wage) is equal to the MFC_L. However, what is the impact of monopoly on the labor market? Recall from our discussion of monopoly power earlier in the semester that monopolists have (a) downward sloping demand curves and (b) their MR curves are less than their demand curves, that is, MR is less than the price in the market.

Table 4 below derives demand for labor (MRP_L) for a monopolist. First, notice that MPP_L is downward sloping in accordance with the law of diminishing returns. From the MPP_L one can calculate total output (Q). Notice that for the first worker, who produces 10 thousand units of output, total output must also equal 10 thousand. The second worker produces an additional 9 thousand, making total output 19 thousand, the 10 thousand produced by the first worker and the 9 thousand produced by the second worker.

Table 4

The Demand for Labor in a Monopoly Output Market

The demand curve for the output produced by labor is represented by the relationship between price (P) and total output (Q). Notice that as must be the case for a monopolist, as the price falls, total output falls. That is, the demand curve is downward sloping for this monopolist.

The next step in the table is to derive the MRP_L. This is done by first calculating total revenue, which equals price times quantity. Then, total revenue is used to calculate marginal revenue, which is given by D TR ¸ D Q. Thus, to obtain the $5.63 for the third worker one takes the change in total revenue (which equals $45,000) and divides it by the change in quantity (which equals 8,000). Finally, MRP_L equals marginal revenue times the marginal product. Likewise, VMP_L equals the price times marginal product. Notice that since the marginal revenue does not equal price that, unlike a perfectly competitive output market, the two measures are not equal. We will end up with the graph to the right.

The above graph shows only the representative firm; the market is as shown in the graph for quadrant I. There exists one important difference between the graphs for Quadrants I and II. When the output market is perfectly competitive as in Quadrant I, D_L equals MRP_L, which equals VMP_L because price equals marginal revenue. However, when the output market is a monopoly, as in Quadrant II, the VMP_L is greater than MRP_L because for a monopolist marginal revenue is less than price. Hence, one can always tell whether a firm is perfectly competitive or a monopolist in the output market by checking to see whether or not MRP equals VMP; if MRP_L = VMP_L then the output market is competitive; if .MRP_L < VMP_L then the output market is a monopoly.

The above difference notwithstanding, the firm will still hire labor as did the firm in Quadrant I, where MRP_L equals MFC_L. Hence, the firm in the table will hire 4 workers, where the MFC of $22,000 equals the MRP of $22,000. In the above diagram the firm hires labor at L₁ and pays a wage of W_M.

Notice that the fourth worker’s value to society, given by his VMP, equals $49,000 but this worker is only paid $22,000. The difference between the two, VMP minus the wage, equals exploitation. The monopoly firm makes a profit by paying the worker less than his value to society. Since this exploitation results from monopoly power, this type of exploitation is called monopoly exploitation. In the graph above, monopoly exploitation equals the difference between W₁ and W_M. Efficiency requires that the monopolist hire workers where society’s marginal value (VMP) equals society's marginal cost (the wage rate). As a result, we can see that the monopolist hires too few workers (L₁ instead of L₂).

Finally, we ask again why the monopolist’s demand for labor curve is downward sloping. As with the perfectly competitive firm in Quadrant I, the monopolist’s demand for labor curve equals his MRP_L. Similar to the perfectly competitive firm, then, obviously his MRP_L also is downward sloping because his MPP_L is downward sloping. However, unlike the perfectly competitive firm in Quadrant I, the monopolist’s marginal revenue curve is also downward sloping, which will also contribute to his downward sloping demand for labor curve.

• Quadrant III – labor market is a monopsony while the output market is perfectly competitive.

Based upon our discussion of Quadrant’s I and II it is clear that when the output market is perfectly competitive that a firm’s demand for labor equals its MRP_L which also equals the VMP_L. The main question to be answered in this section deals with the firm’s supply curve and its MFC curve.

Because the firm is a monopsony, the only firm hiring labor in the market, they must face the entire market supply. Market supply is determined, not by the firm, but by the individuals supplying labor in the market. As discussed in section II above, market labor supply curves are generally upward sloping. Hence, the monopsonist firm faces an upward sloping supply of labor while a firm that is competitive in the labor market faces a perfectly elastic supply curve.

A competitive firm in the labor market not only has a perfectly elastic supply curve but also is a wage taker, resulting in its MFC equalling its supply of labor curve and, finally, equalling the wage rate (MFC = S_L = W). Is this also true for a monopsonist? Consider the example Table 5 below to answer this question

Table 5

The Supply of Labor in a Monopsony Labor Market

Recall, that the firm is perfectly competitive in the output market and, hence, its MRP_L equals its VMP_L just as was true in Quadrant I. The relationship between labor (L) and the wage (W) represent the supply of labor curve. Recall that the monopsonist firm must have an upward sloping supply of labor curve. This is shown in the table by having the wage rate rise as the quantity of labor hired rises. Hence, the firm only has to pay $5,000 to hire one worker but must pay $10,000 to hire two workers. Each time the firm wants to hire more workers it must pay a higher wage.

The next step is to determine whether, as with a firm that is competitive in the labor market, the monopsonist has a MFC curve that equals its supply of labor. Recall from section III-G above that before being able to calculate marginal factor cost, one must first calculate the total factor cost of that resource. The total factor cost of labor just equals total dollar payments for labor, the wage bill, which is found by multiplying the wage by the number of workers hired. Hence, the cost of hiring one worker equals $5,000 ($5,000 times 1) while the cost of hiring two workers equals $20,000 ($10,000 times 2), and so forth.

The marginal factor cost equals the additional cost of hiring an additional worker (D TFC ¸ D L.) Thus, it costs an extra $5,000 to hire the first worker, an extra $15,000 to hire the second worker, and so forth. It becomes immediately clear that, unlike a competitive firm in the labor market, a monopsonist firm does not have a supply of labor curve (wage) which equals its marginal factor cost. In fact, as Table 5 demonstrates the monopsonist firm has a MFC curve which exceeds the firm’s supply of labor (wage) curve.

The firm that is perfectly competitive in the output market and a monopsonist in the labor market appears as in the graph to the right.

The graph shows only the firm, but recall that for a monopsonist the firm equals the entire labor market. There exist several crucial differences between the above graph and the graph for Quadrant I, graph 6, where the labor market is perfectly competitive. Not only is the supply of labor upward sloping, rather than perfectly elastic, but the MFC_L curve is greater than the supply of labor (the wage) for a given amount of labor.

The supply curve is upward sloping because the monopsonist faces the market supply curve. MFC is greater than the wage (S_L) because, as shown in Table 5, each time the firm wants to hire additional labor it must pay a higher wage. However, it must pay the higher wage to, not only the additional worker, but also workers who were previously working for a lower wage. Thus, in Table 5, the MFC of the second worker equals $15,000 even though the firm only pays the second worker $10,000. The extra $15,000 in costs comes from two sources: (1) the extra $10,000 the firm pays to hire the second worker and (2) the extra $5,000 the firm pays the first worker when it raises his wage from the original $5,000 to $10,000.

Hence, one can always tell whether a firm is perfectly competitive or a monopsonist in the labor market by checking these two differences.

1. Is the supply of labor curve perfectly elastic (competitive) or upward sloping (monopsonist)?
2. Does the MFC equal the supply of labor (competitive) or does the MFC exceeds the supply of labor (monopsonist).

One similarity that all profit-maximizing firms have, as noted above, is that they hire workers where MRP_L equals MFC_L. Hence, the firm in Table 5 above will hire 4 workers where both MRP and MFC equal $35,000. Likewise, in the graph above, the monopsonist will hire L₁ workers.

One of the crucial questions to address is that of the wage paid by the firm. In Quadrants I and II, this question was moot, as the firm always paid the wage determined by the market. However, students often make mistakes when answering this question for monopsonist firms, where the wage is not determined by the market. The wage is determined by the supply of labor curve at the profit maximizing level of labor (where MRP equals MFC). Thus, while it is tempting for students to conclude in the above graph that the wage will equal W₃, this is incorrect. The firm can hire L₁ workers at a wage of W₁, given by the supply curve. In the table, the firm will pay a wage of $20,000 to hire 4 workers.

Finally, consider whether or not exploitation exists. As discussed above, exploitation exists if the last worker hired is paid less (wage) than his value to society (VMP). We’ve already determined that in the graph (table) above the profit maximizing firm will hire L₁ (4) workers and pay them a wage of W₁ ($20,000). According to the graph (table), the last worker hired is paid a wage of W₁ ($20,000) but his value to society (VMP_L) equals W₃ ($35,000). The difference between the two, W₃ - W₁ ($15,000), equals the exploitation. The monopsony firm makes a profit by paying the worker less than his value to society. Since this type of exploitation results from monopsony power, it is called monopsony exploitation. Efficiency requires that the monopsonist hire workers where society’s marginal value (VMP) equals society's marginal cost (the wage rate). As a result, we can see that the monopsonist hires too few workers (L₁ instead of L₂).

• Quadrant IV – labor market is a monopsony while the output market is a monopoly.

Recall that in our discussion of Quadrant’s I through III above, we have already determined the impact that both monopoly and monopsony power have upon the labor market. These impacts are as follows:

1. Monopoly power.

A perfectly competitive firm in the output market has its demand for labor equalling its MRP_L which is also equal to its VMP_L (D_L = MRP_L = VMP_L).

While a monopolist’s demand for labor, as is true for all firms, still equals MRP_L, its VMP_L is greater than MRP_L (D_L = MRP_L < VMP_L).

2. Monopsony power.

A perfectly competitive firm in the labor market has its supply of labor equalling the market wage which is also equal to its MFC_L (S_L = Wage = MFC_L). The supply of labor curve is perfectly elastic at the market wage.

While a monopsonist’s supply of labor still equals the wage, as is true for all firms, its MFC_L is greater than the supply curve (S_L = Wage < MFC_L). Both the supply of labor curve and the MFC curve are upward sloping.

Hence, putting these together with the graphs done above, we know that the firm that is both a monopsonist and a monopolist appears as in the graph below. Notice that this firm contains both aspects from graphs above described for Quadrants II and III. The demand side is similar to firms in Quadrant II while the supply side is similar to firms in Quadrant III.

Where does the monopsonist and monopolist firm hire labor? As with all profit maximizing firms, this firm will hire labor where MRP equals MFC. Hence, the firm will hire L₁ workers.

What wage does the firm pay? Recall that the supply curve determines, for a given number of workers hired by the firm, the wage. Hence, at L₁ workers the wage, given by the supply curve, equals W₁.

Finally consider the issues of exploitation and efficiency. Clearly, since the last worker hired (L₁) is paid a wage (W₁) that is less than his value to society (VMP_L = W₄), exploitation exists. The total exploitation equals the difference between these two values, W₄ - W₁. This exploitation arises because of both monopoly and monopsony power. By comparing the graphs describing Quadrant II and III, Graphs 7 and 8, we can determine which portion of this total exploitation results from the firm’s monopoly power and which portion results from the firm’s monopsony power.

As shown in Graph 7, monopoly exploitation arises because of the difference between a firm’s VMP curve and its MRP curve. Hence, in Graph 9 above, monopoly exploitation will also arise because of the difference between these two curves, VMP and MRP, at the profit maximizing level of labor (L₁). Thus, when the firm hires L₁ units of labor, monopoly exploitation will equal the difference between the firm’s VMP (W₄) and the firm’s MRP (W₃), W₄ - W₃.

As shown in graph 8, monopsony exploitation arises because of the difference between a firm’s supply of labor curve (wage) and its MFC curve. Hence, in Graph 9 above, monopsony exploitation will also arise because of the difference between these two curves, S_L and MFC_L, at the profit maximizing level of labor (L₁). Thus, when the firm hires L₁ units of labor, monopsony exploitation will equal the difference between the firm’s MFC (W₄) and the firm’s supply of labor curve (W₁), W₃ - W₁. Notice that, as should be the case, monopoly exploitation and monopsony exploitation add up to total exploitation as defined above.

3. Summary of the section.

There exist a number of issues that each student should be able to address for each of the four types of market structures discussed in this section.

1. What is the firm in both the labor market and the output market?

Each student should be able to determine whether a firm is (a) a monopolist or (b) perfectly competitive in the output market. Likewise, students should be able to determine whether a firm is (a) a monopsonist or (b) perfectly competitive in the labor market. Students should be able to make this determination from the graph, from tables, or from other relevant information. The general rule is that:

• Output Market

A perfectly competitive firm in the output market has price equal to marginal revenue and, hence, its MRP_L curve equals its VMP_L curve. Both will be downward sloping, as discussed above, because of the law of diminishing returns.

A monopoly firm in the output market has a price that exceeds its marginal revenue and, hence, its VMP_L curve will exceeds its MRP_L curve. Both will be downward sloping, as discussed above, partially because of diminishing returns but also because a monopolist’s marginal revenue curve and demand curve (price) are downward sloping.

• Labor Market

A perfectly competitive firm in the labor market is a wage taker and, hence, its S_L curve is perfectly elastic at the market wage and equal to its MFC_L curve.

A monopsony firm in the labor market faces the entire market supply of labor curve and, hence, its S_L is upward sloping. The S_L curve determines the wage the firm can pay to a obtain a given amount of labor. However, the firm’s MFC_L curve exceeds the firm’s S_L curve, although it is also upward sloping.

2. How much labor will the profit-maximizing firm hire?

All profit-maximizing firms hire labor where MFC_L equals MRP_L.

Be careful, however, because for other types of firms other conditions can also be met. For example, if a firm is perfectly competitive in both the output market and the labor market then:

MRP_L = VMP_L = Wage = MFC_L

meaning that it would correct to note that such a firm hires labor where its VMP_L equals its MFC_L. Obviously other variations would also be correct.

3. What wage will the profit-maximizing firm pay the labor that it hires?

The wage is determined by the firm’s supply of labor curve at the profit-maximizing level of labor hired. This is true for all types of firms. However, if the firm is perfectly competitive in the labor market the wage will always equal the wage set by the market as a whole.

4. Does exploitation exist? If so, what type of exploitation is it?

Exploitation exists whenever the last worker hired is paid less than his value to society (VMP_L). As discussed above, exploitation occurs in all four scenarios except when both the labor and output market are perfect competitive. Hence, both monopoly and monopsony power leads to exploitation.

Because monopoly power results in a firm’s VMP_L curve exceeding its MRP_L curve, monopoly exploitation equals the difference between these two curves.

Because monopsony power results in a firm’s MFC_L curve exceeding its S_L (wage) curve, monopsony exploitation equals the difference between these two curves.

5. Is the market efficient?

In labor markets, the allocatively efficient level of labor to hire is that level where society’s value (VMP_L) equals society's marginal cost (the wage rate.) A profit-maximizing firm will only hire the efficient level of labor when both markets are perfectly competitive. Otherwise, both monopoly and monopsony power results in the firm hiring fewer workers than is efficient, and paying them a lower wage, in order to increase the firm’s profits.

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