11: Theories of the Labor Market
- Last updated
- Save as PDF
- Page ID
Goals and Objectives:
In this chapter, we will do the following:
- Describe the neoclassical theory of the market for labor
- Explore the neoclassical theory of monopsonistic labor markets
- Consider whether neoclassical monopsony theory represents a theory of exploitation
- Analyze the case of bilateral monopoly in the labor market
- Investigate the Marxian theory of the market for labor-power
- Explain how changes in the character of production influence prices in Marxian theory
Up until this chapter, the focus has been almost exclusively on markets for goods and services sold to the final consumer. Factor markets (also referred to as input markets or resource markets) include the markets for labor, capital, and land. As the reader might expect, different schools of economic thought possess different theories of how these markets function. In this chapter, we will concentrate on the market for labor. We will take a close look at how the labor market operates from a microeconomic perspective, according to neoclassical economists and Marxian economists.
The Neoclassical Theory of the Demand for Labor
In neoclassical economic theory, product markets determine product prices and quantities exchanged. Similarly, neoclassical economists argue that labor markets determine wage rates and employment levels. The theory is essentially a story of supply and demand, much like the one we discussed regarding product markets. A sophisticated analysis underlies this story of supply and demand. This underlying story is developed at length in this section.
We begin with the assumption that the market supply of labor is upward sloping. That is, it is assumed that as the wage rate increases, the quantity supplied of labor rises as well, other factors held constant. Furthermore, it is assumed that the labor market is perfectly competitive such that each employer takes the market wage as given and so is a wage-taker. In other words, no single employer has any power to influence the wage that is paid. In this case, the labor supply curve facing the perfectly competitive firm is completely horizontal. This situation is depicted in Figure 11.1
If an employer reduces the wage paid below the market wage even by a small amount, the quantity supplied of labor will fall to zero. That is, all workers will seek jobs from other employers who are offering the market wage. Similarly, the smallest increase in the wage above the market wage will lead to a sharp (infinite) increase in the quantity supplied of labor. In other words, the wage elasticity of labor supply facing a single employer is infinite in the case of a perfectly competitive labor market.
To understand how much labor an employer will hire to maximize its economic profit, we need to explore the implications of this wage-taking behavior for the firm’s production costs. One concept that is important for this purpose is total resource cost (TRC). The TRC is the total cost of purchasing labor or the total wage bill. It is defined more precisely as follows:
The relationship between the horizontal labor supply curve facing an employer and the employer’s TRC curve is shown in Figure 11.2.
As Figure 11.2 shows clearly, the TRC grows continuously as more labor is hired due to the constant wage rate that must be paid to each worker.
Furthermore, we can define average resource cost (ARC) as the average cost per worker hired. That is, if we were to spread out the total labor cost over the number of workers hired, then we would have the ARC. The ARC is defined precisely as follows, which it turns out can be reduced to the wage:
This result should not be surprising. It simply means that, on average, the cost of a unit of labor is the wage. Because the wage is given, it follows that the wage must be the average cost of this resource.
Additionally, we can define the marginal resource cost (MRC) as the additional resource cost incurred with the purchase of an additional worker hired. Because the TRC grows by a constant amount equal to the wage rate with the purchase of each additional unit of labor, the MRC is the wage rate. It can be defined more exactly as follows:
The reader should notice that the MRC is equal to the slope of the TRC curve. The slope of the TRC curve, of course, is equal to the wage rate. Finally, it should be noted that because the ARC and the MRC are both equal to the wage rate, the ARC and MRC curves will be identical to the horizontal labor supply curve facing an employer. Figure 11.3 adds the ARC and MRC curves to a graph of the horizontal labor supply curve facing one employer.
Table 11.1 provides a numerical example that includes calculations of TRC, ARC, and MRC.
As expected, the MRC and ARC are equal to the wage rate, and the TRC grows continuously with employment due to the constant wage rate.
The employer must consider the effect on revenue of hiring additional labor as well as the effect on cost. As a result, we need to introduce a new concept that neoclassical economists refer to as the marginal revenue product (MRP) of labor. To understand this concept, we need to return to the total product (TP) and marginal product (MP) curves that were first introduced in chapter 7. Figure 11.4 shows the graphs of the total product and marginal product curves.
The reader should recall that marginal product is simply the slope of the total product curve. In the short run, MP rises due to specialization and division of labor at low employment levels and then falls due to diminishing returns to labor at higher employment levels. The MRP refers to the additional revenue earned from the purchase of an additional unit of labor, which can be defined as follows:
The MRP can be further expanded as follows:
In other words, the MRP is the mathematical product of the firm’s marginal revenue and marginal product of labor. Finally, we learned in Chapter 8 that a perfectly competitive firm’s marginal revenue is equal to the given market price. If we assume that this firm is a perfectly competitive producer, then the MRP can be written as follows:
This result is very intuitive. The MRP is the additional revenue that a firm earns from hiring another unit of labor. When the additional unit of labor is purchased, it will produce some additional output. This additional output is the marginal product (MP). The additional output is then sold at the given market price (P) in a perfectly competitive market. The additional revenue generated is the MRP.
A closely related concept is the average revenue product (ARP) of labor. It is simply the total revenue per worker hired, which may be defined as follows:
Figure 11.5 shows the calculation of the MRP and the ARP for a perfectly competitive firm that faces a constant market price of $2 per unit.
As Figure 11.5 shows, the MRP rises and then falls as employment rises. Because the MRP equals the product price times the marginal product of labor and the product price is constant, the MRP will rise due to the specialization of labor, but then it must fall because of the fall in marginal product. That is, the MRP falls due to diminishing returns to labor. A similar argument explains the shape of the ARP curve. Figure 11.6 provides a graph of the MRP and ARP curves.
It is easy to see that as the wage rate falls, the quantity of labor demanded increases. In other words, the labor demand curve is downward sloping. Furthermore, because the quantity of labor demanded is determined at points of intersection between the wage rate and the MRP, the MRP curve is the perfectly competitive employer’s labor demand curve.
A second condition is necessary to ensure that economic profits are maximized in the short run. Specifically, it must be proven that the employer cannot earn a larger economic profit by shutting down in the short run. To prove this point, we return to the shut-down rule that we learned when we first discussed how a perfectly competitive firm maximizes economic profits in Chapter 8. In Chapter 8, it was shown that a perfectly competitive firm should only operate when price is at least as great as average variable cost (P ≥ AVC). We may derive a similar shut down rule for a perfectly competitive employer as follows:
In other words, the wage paid must be less than or equal to the ARP. Otherwise, the employer should shut down in the short run. Therefore, when we trace out the labor demand curve, the only relevant portion of the MRP curve is that part that is below the ARP curve, as shown in Figure 11.8. Because the MRP curve intersects the ARP curve at the maximum point on the ARP curve, the highest wage rate at which a positive amount of labor is demanded is the maximum ARP. If the wage rate rises above this point, then the employer will shut down and demand no labor.
Neoclassical economists assert that the demand for labor (or any input) is a derived demand. That is, labor demand is derived from the demand for the product that the labor produces. For example, the demand for engineers depends on the demand for new construction. If firms invest in the construction of more bridges, dams, and skyscrapers, then they will need to hire more engineers. As we learned in Chapter 3, if the demand for a product rises, then the market price will increase, other factors held constant. The rise in the market price will cause the marginal revenue product of labor to increase because the output that workers produce can now be sold at a higher price. This change causes an outward shift of the MRP curve. Because the MRP curve is the employer’s labor demand curve, the labor demand curve shifts outward. Therefore, a rise in the demand for a product causes a rise in the demand for the labor that produces it.
More generally, we can identify two changes that can shift the MRP curve and thus the labor demand curve. Recalling that the MRP is equal to the product price times the MP of labor, we can identify these two changes as follows:
- Any factor that raises the price of the product will increase the MRP of labor and thus the demand for labor.
- A change in production technology, or any other change that increases the marginal product of labor, will increase the MRP of labor and thus the demand for labor.
Now that we have derived the labor demand curve for a perfectly competitive employer, it is a short step to obtain the demand curve for the entire labor market. We simply use horizontal summation to aggregate the individual labor demand (or MRP) curves of many different employers. The downward sloping labor market demand curve that results from this aggregation process is shown in Figure 11.9.
Neoclassical theorists have also developed a theory of labor supply. According to this theory, individual workers allocate their available time between working time and leisure time to maximize utility. In this theory, work is regarded as undesirable for its own sake, but it provides wage income that can be used to purchase commodities. Leisure time, on the other hand, is generally regarded as desirable. Because wage income is desired to acquire consumer goods, the wage rate represents the opportunity cost of one hour of leisure time. That is, by choosing to enjoy an hour of leisure time, a worker sacrifices the wage that could be earned.
We can use the modern theory of utility maximization to represent the problem facing the individual worker. To begin, we consider the time constraint that the worker faces and represent this constraint in much the same way that we represented the budget constraint facing a consumer in Chapter 6. In this theory, the worker has a total amount of time (T) available each day for either work or leisure. T will generally be less than 24 hours because the worker is unavailable for either work or leisure during sleeping hours. The hours spent working (h) and the hours of leisure time (l) add up to the total time available in the day as shown below:
Furthermore, the daily income (Y) is equal to the wage rate (w) times the number of hours spent working (h) as shown below.
If we rearrange the above equation such that h = Y/w, then we can rewrite the total amount of time available in the day in the following way:
Solving this equation for Y, we obtain the following result:
It should be noted that w and T are unknown constants in this equation and Y and l are the only variables. If we graph this result as shown in Figure 11.10, then we obtain a clearer picture of the income/leisure tradeoff facing the individual worker.
Just as the individual consumer’s preferences for goods may be represented using indifference curves, the individual worker’s preferences for income and leisure may be represented using indifference curves as shown in Figure 11.11.
In Chapter 6, we learned that the downward slope of an indifference curve indicates that the consumer is willing to trade off one good for another. Similarly, the downward slope of the indifference curve represented in Figure 11.11 indicates that the worker is willing to trade off income for leisure and vice versa. We also learned in Chapter 6 that the slope of the indifference curve is called the marginal rate of substitution (MRS) and that this slope becomes flatter as the individual moves along the indifference curve. The reason for the change in the slope is that as the worker obtains more leisure, her willingness to trade off additional income for an additional hour of leisure decreases. This diminishing marginal rate of substitution is somewhat like diminishing marginal utility. As explained in Chapter 6, however, diminishing MRS depends entirely on an ordinal notion of utility.
We can also rewrite the MRS as the negative ratio of the marginal utilities of leisure and income. Because the worker’s utility remains the same all along the indifference curve, we can write the following equation:
This equation states that the change in total utility as the worker moves along an indifference curve is equal to the product of the marginal utility of income (MUY) and the change in income (Y) plus the product of the marginal utility of leisure (MUl) and the change in leisure (l). The entire sum is equal to zero because total utility remains constant along the indifference curve. Solving for the MRS generates the following result:
As the worker moves to the right along the indifference curve, the amount of l that is chosen rises and the amount of Y that is chosen declines. As a result, the marginal utility of leisure declines relative to the marginal utility of income, implying diminishing MRS.
We can now represent the utility maximizing choice of the worker. In Figure 11.12, the worker maximizes utility at point A by choosing the amount of leisure (l*) and hours of work (h*) that yields an amount of income, Y*.
At point A, the indifference curve passing through point A is tangent to the time line representing the worker’s time constraint. Because the slopes of these curves must be the same, the following condition must hold:It is now possible to derive the individual worker’s labor supply curve using the utility maximizing framework that we have developed. Figure 11.13 shows what happens when the wage rate increases.
In Figure 11.13, the vertical intercept increases because the maximum possible income is now higher. Similarly, the slope increases (in absolute value) because the opportunity cost of leisure has increased with the higher wage rate. Because leisure has become more expensive to consume, the worker chooses to reduce the amount chosen from l1 to l2. The amount of work chosen correspondingly increases from h1 to h2. The quantity supplied of labor thus rises with the wage rate, which implies the upward sloping labor supply curve shown in the graph on the right in Figure 11.13.
On the other hand, it is possible that the worker will stop responding in this manner to the rise in the wage once the wage reaches a very high level. Suppose that the increase in the wage leads the worker to feel richer overall. As a result, the worker purchases more consumer goods but also decides to “purchase” more leisure time by working less. This situation is represented in Figure 11.14.
In Figure 11.14, the wage rises from w1 to w2, and the worker cuts back on leisure time (from l1 to l2) as leisure becomes costlier. Similarly, the hours worked increase from h1 to h2 as before. Once the wage rises to w3, however, the worker increases leisure time from l2 to l3. A corresponding reduction in hours worked from h2 to h3 occurs. This drop in the number of hours worked as the wage increases is represented in the graph on the right in Figure 11.14 as a backward bending labor supply curve.
Our final step is to aggregate the individual labor supply curves of every worker in the labor market. As before, we can use horizontal summation to obtain the labor market supply curve. Figure 11.15 shows two possible examples of the labor market supply curve.
In the graph on the left in Figure 11.15, the labor market supply curve has the usual upward slope that we expect of a supply curve. As the wage rises, workers reduce their leisure time (which is more expensive) and work more to take advantage of the higher wage. The tendency to consume less leisure as the wage rises (other factors held constant) is referred to as the substitution effect in this context in the sense that the worker substitutes away from something that has become relatively more expensive to consume. In the graph on the right, however, workers respond to higher wages by eventually working less and consuming more of all goods, including leisure. The tendency to purchase more of all goods as one’s income rises (other factors held constant) is referred to as the income effect. That is, the worker experiences a rise in real income and so decides to purchase more of everything. Although both effects are typically at work, whether an upward sloping or backward bending supply curve emerges depends on which effect is the stronger of the two. If the substitution effect dominates, then the labor supply curve will be upward sloping. If the income effect dominates, then the labor supply curve will be backward bending.
The Neoclassical Theory of Labor Market Equilibrium
Now that we have developed both the supply and demand sides of the labor market, we can bring them together to show how neoclassical economists explain the movement to equilibrium in these markets. Figure 11.16 shows two possible labor markets.
In the graph on the left, a single equilibrium outcome occurs. The labor market is cleared of shortages as wages increase, and it is cleared of surpluses as wages decrease. Eventually, the market reaches an equilibrium wage rate and employment level. The market will remain at this point unless it is disturbed by a change in an external variable.
In the graph on the right, two different equilibrium outcomes are possible due to the backward bending supply curve, which causes a second intersection with the labor market demand curve. The lower equilibrium at w1 and L1 is the same as the one represented in the graph on the left. It is a stable equilibrium in the sense that a slightly higher or lower wage will lead to a surplus or shortage that will push the wage back in the direction of the equilibrium outcome. The upper equilibrium at w2 and L2, on the other hand, is rather different. If the wage falls below w2 by a small amount, then it will continue to fall due to the surplus that exists. Similarly, if the wage rises above w2 by a small amount, then it will continue to rise due to the shortage that exists. Because the wage tends to move further away from the equilibrium when pushed in either direction by a small amount, the equilibrium is an unstable equilibrium. The presence of an unstable equilibrium creates a risk of considerable market instability.
We have yet to mention the ideological significance of the neoclassical theory of the labor market. The neoclassical model of a perfectly competitive labor market reaches the conclusion that each worker is paid according to that worker’s contribution to production. Earlier in this chapter, it was shown that a perfectly competitive employer achieves maximum economic profits when the MRP is equal to the wage rate (the MRC). This conclusion means that when the labor market reaches equilibrium each worker will receive a wage that is equal to the worker’s contribution to the firm’s revenue. From a purely ideological perspective, this result is a very powerful one. It means that workers are not exploited as Marxian economists assert. They draw from the social product an amount that is exactly equal to what they contribute. The marginal productivity theory of income distribution is implicitly a theory of distributive justice. That is, people receive what they deserve to receive. What they deserve to receive stems from their productive contributions.
The theory has been criticized for a variety of reasons. One objection is that inequality may have its own undesirable social and economic consequences and that payment according to marginal revenue product might lead to extreme levels of inequality. A second objection is that the relationship between social classes (e.g., workers and capitalists) plays no role in the analysis as it does in Marxian economics. Due to the assumption of perfect competition, no employer or worker has any market power. The fact that some own the means of production whiles others lack means of production is given no significance in the model. Finally, the assumption of perfect competition in the labor market is one that opponents of the theory have sharply criticized. As we will see in the next section, when the assumption of perfect competition is dropped, the door to a neoclassical theory of exploitation is suddenly thrown open.
A Neoclassical Theory of Exploitation?
If we drop the assumption of perfect competition in the labor market, then how will the neoclassical analysis of the labor market change? In this section, we consider the case of imperfectly competitive labor markets. We will consider the case of a single employer, also referred to as a monopsony employer. A monopsony exists in a market when only a single buyer exists. In the labor market, the employers are on the buyers’ side of the market. Therefore, a monopsonistic labor market is a market with only a single buyer of labor.
Pure monopsonies, just like pure monopolies, are not very common, but sometimes firms approach monopsony status in certain markets. For example, Wal-Mart has been accused of acting as a monopsonist in certain markets in which it buys goods from suppliers. In those cases, Wal-Mart is by far the largest, or may be the only, buyer of a product from its suppliers. In the defense industry, the U.S. government may be the only purchaser of advanced weaponry from firms that produce such products. Monopsony employers, on the other hand, have existed in company towns like General Motors in Flint, Michigan or Carnegie Steel in Homestead, Pennsylvania. In company towns, the people may have limited mobility and so they either work for the dominant employer, or they do not work at all.
As with any neoclassical model, we will start by identifying the model’s main assumptions. We will assume that a single firm exists that is the sole buyer of labor. Furthermore, it is assumed that workers cannot easily move to a new location. Because of these conditions, the monopsonist has the power to set the market wage. That is, the monopsonist has market power, much like the monopolist possessed market power (i.e., the power to set the market price of its product).
Unlike the perfectly competitive employer who faces a horizontal labor supply curve, the monopsonist faces an upward sloping labor supply curve, as shown in Figure 11.17.
As the wage rises from $11 per unit to $12 per unit, the quantity of labor supplied increases from 3 to 4 units. The MRC may be calculated by dividing the change in TRC by the change in L as follows:
It is possible to obtain this result in another way that is more intuitive. When the wage rate is increased from $11 to $12 per unit, an additional worker enters the market. How much does this increase in the wage add to cost? The additional worker is paid $12, but the reader should notice that the three workers, who were receiving $11 each, now receive $1 raises. Therefore, the total resource cost rises by $12 plus $3 or $15. This manner of proceeding is helpful in terms of understanding why the addition to total resource cost exceeds the wage paid. As the reader can observe, in Figure 11.19 the MRC of $15 is above the wage of $12. In general, the MRC will exceed the wage because when the wage rises to encourage another worker to enter the market, the TRC rises both because of the wage paid to the new worker hired but also because each of the existing workers must receive a wage increase. The reader might notice the similarity between this analysis and the analysis of pure monopoly. In the case of pure monopoly, MR falls faster than price because when the price is cut to sell another unit, the price must also be cut on all the other units previously sold at the higher price.
Because the MRC exceeds the wage, the MRC curve will rise more quickly than the labor market supply curve facing the firm. Therefore, we obtain the result shown in Figure 11.20.
Table 11.2 provides an example to demonstrate how to calculate TRC, ARC, and MRC when only given information about the labor market supply curve facing the monopsony employer.
We have now fully developed the cost structure of the monopsonist and can proceed to the profit-maximizing choice of the firm. Figure 11.21 shows how the monopsony employer will set the wage to maximize its economic profit.
It is also possible to compare the monopsonistic equilibrium outcome and the perfectly competitive outcome using the graph in Figure 11.21. Earlier in this chapter, it was explained that the perfectly competitive equilibrium outcome in the labor market occurs where supply and demand intersect. If we assume that the MRP curve of the monopsony employer would be the same as the sum of the MRP curves of many perfectly competitive employers (if this market was perfectly competitive), then we can find the perfectly competitive equilibrium at the intersection of the labor market supply curve and the MRP curve. That is, the MRP curve represents the labor market demand curve and so its intersection with the labor market supply curve represents the competitive equilibrium. In the perfectly competitive equilibrium, wc represents the equilibrium wage rate and Qc represents the quantity of labor that the firm will hire at that wage. Because w* is less than wc, it is easy to see that the monopsony firm reduces the wage to a level that is below what would be paid in a perfectly competitive labor market. Furthermore, because Q* is less than Qc, it is also easy to see that the monopsony firm reduces overall employment below what would exist in a perfectly competitive labor market. The reduction of employment below the perfectly competitive level represents a loss of efficiency brought on by the monopsonist’s pursuit of maximum economic profits.
The Economic Consequences of Labor Union Activity
In Chapter 3, the concept of a price floor was introduced. A price floor establishes a legal minimum price in a market. The price is permitted to rise above a price floor, but the price cannot fall below the price floor. Industrial unions are organizations that attempt to organize all the workers in an industry and then negotiate industry-wide wage floors for their members. Working hours and working conditions are other key points for negotiation. Craft unions have similar aims, but they only organize the workers who share a common skill or trade, such as carpentry, ironworking, or masonry. Unions possess market power on the sellers’ side of the labor market. That is, a union is (sometimes) the sole seller of labor in a market, just as the monopsonist is the sole buyer on the buyers’ side of the market.
A price floor that a labor union might negotiate is just a minimum wage. If the labor market is perfectly competitive, then this situation can be represented as in Figure 11.22.
Figure 11.23 shows the monopsony outcome where the wage is wm and employment is Qm. It also shows the perfectly competitive labor market outcome where the wage is wc and employment is Qc. Let’s assume, however, that a union negotiates a wage of w* with this monopsony employer. In this case, the labor market supply curve becomes perfectly horizontal for every employment level up to the original supply curve. The reason is that the workers who would have entered the labor market at lower wage rates previously are now paid the union wage. Once we reach the original supply curve, however, the wage must rise to encourage more workers to enter the market. The supply curve thus has a kink in it at Q*.
To obtain the MRC curve, it is necessary to use the information given on the supply curve. When the labor supply curve facing the firm is horizontal, as it is in the case of a perfectly competitive market, then the MRC curve is horizontal as well and identical to the supply curve. Therefore, the MRC will be the same as the labor market supply curve up to the kink. For employment levels beyond the kink, however, the MRC corresponding to the upward sloping supply curve applies. As a result, the MRC curve is horizontal up until the kink in the supply curve, then a vertical gap exists until we reach the upward sloping MRC curve, after which point the MRC curve becomes upward sloping as before.
To find the profit-maximizing outcome in the bilateral monopoly model, we only need to equate MRP and MRC. In Figure 11.23, the MRP curve intersects MRC somewhere in the gap in the MRC curve. This intersection gives us the profit-maximizing employment level of Q*. It also gives us the profit-maximizing wage. To call forth Q* amount of labor, the wage rate that must be set is w*, which is directly above Q* at the kink in the supply curve.
What we observe in this case is that the wage rate is higher than what the monopsonist would set in the absence of a union. The employment level is higher as well. Furthermore, the gap between the MRP and w is smaller and so the degree of exploitation is lower. On the other hand, it is also the case that the wage rate is lower than the perfectly competitive wage, and the employment level is lower than the perfectly competitive employment level. Still, if the labor union could negotiate an even higher minimum wage, then it would approach or even match the perfectly competitive outcome. If the union negotiates a wage that is higher than wc, however, then unemployment will result as in the perfectly competitive model. The reader might try to verify this result graphically. In general, however, whether the wage that is negotiated is closer to the pure monopsony wage or closer to the perfectly competitive wage will depend on the relative bargaining strength of the monopsonist and the labor union. A relatively strong labor union will negotiate wages that are closer to the perfectly competitive result. A relatively weaker labor union will negotiate wages that are closer to the pure monopsony result.
A situation of bilateral monopoly like the one we have been discussing occurred in 1892 in Homestead, Pennsylvania. In a very famous strike, the Amalgamated Association of Iron and Steel Workers struck against the Carnegie Steel Company. The craft union had a large degree of monopoly power at the time, and Carnegie Steel was the only major employer in the entire town. The union’s goals were to negotiate a minimum wage and to establish a June expiration date (rather than a January expiration date) for the new three-year contract. The union wanted a summer rather than a winter expiration date because if a strike became necessary during contract negotiations, the workers could hold out much better in the summer than in the winter. In this case, the company and the union were not able to arrive at an easy solution. A bitter strike ensued involving a battle between striking steelworkers and Pinkerton guards. Eventually, the Pennsylvania Governor ordered the state guard to force an end to the strike. Abstract models can teach us a great deal, but they often cannot capture the intensity of real life struggles.
The Marxian Theory of the Market for Labor-Power
Now that we have studied the neoclassical theory of the labor market in considerable detail, we can more easily contrast it with the Marxian theory of the market for labor-power. The reader should recall that the commodity that workers sell to capitalists is labor-power as opposed to labor. In Marxian theory, labor refers to the act of working itself, whereas labor-power refers to the ability of a worker to perform labor for a given amount of time, which is sold as a commodity.
In Chapter 4, it was shown how the value of labor-power is determined in Marxian theory. Marx provided a formula for calculating the value of a day’s labor-power. As the reader will recall, that calculation requires adding up all the values of all the means of subsistence that a worker requires in the year to produce and reproduce her labor-power (according to a culturally determined norm) and then dividing that value by the number of days in the year. If the social estimation of what a worker requires for the production and reproduction of labor-power changes, then the value of labor-power will change as well. Additionally, if the values of the required means of subsistence change, then the value of labor-power may change as well. The price of labor-power, which is what is paid for labor-power, may diverge from the value of labor-power at times. In the second part of this book, it is explained why the price of labor-power never diverges very much from the value of labor-power.
Our primary interest in this chapter, however, is to understand how changes in the capitalist production process can be analyzed from a Marxian perspective. This discussion draws heavily upon Marx’s treatment of the subject in chapter 17 of volume 1 of Capital. In the remainder of this chapter, we will consider how productivity changes are treated in Marxian theory. We will also consider two aspects of capitalist production that are not given much attention in neoclassical theory, namely changes in the length of the working day and changes in the intensity of the labor process. As will be shown, the value of labor-power has an important role to play in the analysis.
Changes in the Productivity of Labor
In neoclassical microeconomic theory, an increase in the price of a firm’s product raises the marginal revenue product of labor and thus labor demand. The causal claim is that price increases lead to increases in marginal revenue productivity. In Marxian economic theory, on the other hand, the causal chain runs in the reverse direction. That is, a rise in labor productivity typically leads to a reduction in prices. To see why, we need to return to our working day diagrams from Chapter 4. Figure 11.24 shows the three ways that we may express the value produced in one day in a specific industry.
In this example, the capitalist advances constant capital (c) of $300 for means of production and variable capital (v) of $90 for labor-power. The worker works a 10-hour day. Given a monetary expression of labor time (MELT) of $15 per hour, the $90 of variable capital may be converted into 6 hours of necessary labor (NL). The remainder of the workday then consists of 4 hours of surplus labor (SL), which may be converted into $60 of surplus value (s) using the MELT. The constant capital of $300 may also be converted into its dead labor (DL) equivalent of 20 hours using the MELT. If we assume that the worker produces a total product (TP) 225 lbs. of sugar during the workday, then we can also calculate the individual value of a pound of sugar. All we need to do is divide the total value of the day’s product by the total product. That is, the price (= value) can be calculated as follows:
By dividing c, v, and s by the price of a pound of sugar, we can calculate the dead product (DP) of 150 lbs., the necessary product (NP) of 45 lbs., and the surplus product (SP) of 30 lbs., respectively.
Now that we have reviewed these basic aspects of Marxian economics, we can consider the effects of a change in labor productivity. Unlike in the neoclassical theory we considered earlier in this chapter, it matters a great deal whether the productivity change occurs in an industry that produces means of subsistence for workers (so-called wage goods industries) or in other industries that produce goods that workers do not typically consume. Let’s first assume that a productivity increase occurs in an industry that is not a wage goods industry. This situation is depicted in Figure 11.25.
In Figure 11.25, a 30% productivity increase is assumed. What this change means is that a worker can transform 30% more means of production (as reflected in a 30% rise in constant capital) into 30% more finished product in the same 10-hour workday as previously. That is, it is assumed that the worker produces more in the same 10 hours while working at the same level of intensity as previously. Indeed, this change represents a pure productivity increase. In this example, the additional $90 of constant capital (∆c) is used to purchase means of production representing 6 hours of additional dead labor (∆DL). Similarly, the additional sugar produced may be considered an addition to the total product (∆TP) of 67.5 lbs., which is a 30% increase. The new value of labor-power and the newly created value are not affected at all in this case. The price of sugar, however, is affected as can be observed in the following calculation:
By dividing each monetary magnitude in Figure 11.25, we can calculate the new values for the surplus product, the necessary product, the dead product, and the change in dead product, as shown in Figure 11.25. To carry out these calculations, the exact figure for the price was used. As a result, when we add together each product figure, we obtain the new total product for the day of 292.5 lbs., which represents a 30% increase in production. The price of sugar, therefore, falls when labor productivity rises. By contrast, we would expect a productivity decline to increase the price of sugar.
The other possibility we should consider is a productivity change that occurs in a wage goods industry but not in the industry that we are considering. If productivity rises in a wage goods industry, then this change will have a direct impact on the value of labor-power. By reducing the value of the means of subsistence that the worker requires, the commodity labor-power becomes less valuable. If the price of labor-power falls in line with the drop in the value of labor-power, then this change will lead to a re-division of the workday in the industry that we are considering. This situation is depicted in Figure 11.26.
Figure 11.26 represents a situation in which the labor embodied in the required means of subsistence for the day falls to 5 hours of SNALT. With the necessary labor at 5 hours, the variable capital declines to $75 (given the MELT of $15/hour). In a similar fashion, the surplus labor rises from 4 hours to 5 hours (given the 10-hour workday), and the surplus value produced rises from $60 to $75. The constant capital advanced remains unaffected by this change in labor productivity in the wage goods sector. Because the total value of the day’s product remains at the same level of $450 and the total amount of sugar produced remains unchanged at 225 lbs. of sugar, the price of sugar is not affected at all.
In Figure 11.26, the fall in the value of labor-power simply leads to a change in the distribution of the new value created. Aside from that change, production levels in this industry remain the same. Notice that workers receive a smaller money wage, but they can purchase the same quantity of means of subsistence as previously. Their absolute standard of living remains the same. Capitalists are the sole beneficiaries of the productivity increase in this case. It is possible that a struggle may develop between capitalists and workers over the division of the new value created. If labor unions are relatively strong, then the price of labor-power might rise above its new value (but perhaps not as high as the previous value of labor-power). In that case, the workers enjoy a higher standard of living, as they can purchase more means of subsistence than previously. At the same time, the capitalists extract more surplus value from the workers, and workers become poorer relative to capitalists. This possibility is interesting because it reveals that Marx’s theory is consistent with rising real standards of living for workers even as inequality worsens.
Of course, the one situation we have not considered is a productivity increase in a wage goods industry and the consequences of that change for the wage goods industry itself. This case would combine the two examples we have considered. That is, prices would fall in the wage goods industry and a part of the new value created would be redistributed from workers to capitalists as the value of labor-power declines. Although it is possible, it is not necessary to create a diagram for this case since it would simply reproduce the results we have already obtained in the previous two cases.
Changes in the Length of the Working Day
The next change we need to consider is a change in the length of the working day. Unlike in neoclassical theory where the worker decides how to allocate her time between work and leisure to maximize utility, in Marxian theory, capitalists tell workers what the length of the working day is. In the absence of a union, they either accept those terms or they seek work elsewhere.
Figure 11.27 represents a situation in which the working day has been extended.
In Figure 11.27, the working day is extended by 30% or 3 hours. Because workers must have means of production with which to work, this extension necessitates a 30% increase of $90 in the amount of constant capital advanced. The total product produced in the day subsequently rises by 30% or 67.5 lbs. The consequence of this increase in the length of the workday is an increase in the surplus value produced, but it has no effect on the price of sugar. The new (unchanged) price of sugar may be calculated as follows:
The new dead product of 45 lbs. may be calculated simply by dividing the new constant capital advanced of $90 by this price.
The main consequence of an extension of the working day is an increase in the degree of exploitation. The value of labor-power is typically unaffected by such a change. Marx, however, did argue that the additional wear and tear that labor-power experiences due to this extension may increase the value of labor-power. That is, the means of subsistence necessary to make the production and reproduction of labor-power each day may rise due to, for example, an increased need for medical care. Beyond a certain point, however, no increase in the means of subsistence can compensate for the deterioration of the worker’s health due to endless drudgery.
Additionally, if the value of labor-power remains unchanged even with a lengthening of the workday, it is possible that its price may increase above its value. That is, a struggle between workers and capitalists over the new value created might occur. Depending on the relative strength of the one versus the other, workers or capitalists may end up appropriating a larger portion of the newly created value as wages or surplus value, respectively.
Changes in the Intensity of Labor
The final change that we will consider is a change in the intensity of labor that occurs in a single industry but not across all industries simultaneously. For example, suppose that the intensity of the labor process increases above the social norm that exists in other industries. In this case, even with the same number of hours in the workday, the worker will create an even larger amount of new value than previously. The reason is that one hour of SNALT is not necessarily the same as one hour of clock time. If the intensity of labor rises above what is considered the social norm in a specific society, then one hour of clock time might be consistent with more than one hour of SNALT. This situation is depicted in Figure 11.28.
Figure 11.28 is almost identical to Figure 11.27, which depicted an increase in the length of the working day. The only difference is that the 3 hours of additional surplus labor do not occur because of an increase in the length of the workday. Instead, it is the result of 30% more work being performed within the span of the 10-hour workday. For this reason, the portion of the timeline that shows an extension of 3 hours is a dashed line rather than a whole line, as was the case in Figure 11.27. That is, the increase in labor intensity leads to the incorporation of more SNALT in the final product and a greater value of the final product, but these additions are like the 30% increase in dead labor and constant capital advanced in that they are not part of the working day proper. On the other hand, these changes do represent new value created, and in that sense, they are very different from the contribution that the additional constant capital makes to the final product. In this case, because the value of the final product and the physical product both rise by 30%, the price of sugar remains unchanged. This result is to be expected because the numerical changes are identical to those obtained from an extension of the workday.
As in the case of an extension of the working day, the value of labor-power may rise due to its more rapid deterioration. Workers are not working longer hours, but they are working harder, which may impact their health. The same limits to compensating workers with a higher wage that apply in the case of the extension of the working day should also be expected to apply in this case. As before, even if the value of labor-power does not rise, workers might push for an increase in the price of labor-power as they struggle to win a portion of the newly produced value that their more intense labor has made possible.
The amount of new value created due to the intensification of the labor process is directly related to the extent of the divergence between the intensity of labor in this industry and the social norm. A general change in the intensity of labor across all industries, however, that alters the social norm will have no effect on the new value produced during a 10-hour workday. Such a change would instead act more like an increase in labor productivity in that more means of production will be transformed into final products and prices can be expected to fall.
Simple Labor v ersus Complex Labor
Throughout this entire discussion, it has been assumed that the labor that is being performed is of a very simple variety. That is, no special skill or training is required to perform this specific type of labor, which we will call simple labor. Of course, most types of labor require at least some basic training and many types of labor require years of prior education and training if they are to be performed well. These more skilled types of labor we will refer to as complex labor.
The existence of complex labor appears to create a difficulty for Marxian economics. If one hour of simple labor (e.g., sweeping floors) creates the same amount of value as one hour of complex labor (e.g., surgical labor), then this theory appears to be flawed. Recall, however, that SNALT is not the same as clock time, and so it is possible that one hour of surgical labor might create 100 times as much value as one hour of unskilled labor.
To understand how Marxian value theory can address these issues, let’s consider a numerical example. Suppose that a person goes to a technical school for four years and learns to produce a specialized commodity. The number of hours spent in school during these four years might be 8,320 hours, which may be calculated as follows:
Suppose the worker then works for 40 years producing the specialized commodity. During this 40-year period, the number of hours worked may be calculated in a similar way:
The total value created during the working life of this person may be expressed in SNALT as the sum of the hours spent in training plus the hours spent working. This calculation is as follows:
Further suppose that the worker produces 9,152 use values during her entire working life. To keep the example simple, let’s ignore the value of the means of production by assuming that the constant capital advanced is equal to zero. We can use this information to calculate the value (or price) per unit of the commodity produced in terms of SNALT as follows:
If we assume a MELT of $6 per hour, then the price of the commodity will be $60 per unit (=$6/hour times 10 hours/use value), and the total value of the worker’s lifetime product will be $549,120 (=$60/unit times 9,152 use values).
If we next consider an unskilled worker who works for 40 years performing simple labor and producing a similar, albeit unspecialized commodity, then we can see what contribution the first worker’s training makes to the production of value. Let’s assume that the unskilled worker also produces 9,152 units of the unspecialized commodity. Since the worker works for 40 years, she has performed 83,200 hours of work, just like the skilled worker. The value of each unit of the unspecialized commodity may be calculated in terms of SNALT as follows:
Using the same MELT of $6 per hour, the price of the unspecialized commodity will be about $54.54 (=$6/hour times 9.09 hours per use value), and the total value of the worker’s lifetime product will be about $499,150 (≈ $54.54/unit times 9,152 use values), ignoring some rounding error here.
This example shows rather clearly that the skilled worker produces a more valuable product than the unskilled worker. The difference in the value created occurs because the skilled worker creates more value in the same 40-year period. This enhanced value-creating potential is not the result of a more intense labor process or a longer working day. The superior ability of the skilled worker to create value exists because the hours the worker has spent acquiring specialized knowledge are labor hours that were necessary for the worker to produce and reproduce her labor-power. Just as work is required to produce the means of subsistence the worker needs to perform labor each day, work is also required to produce the knowledge that the worker uses to produce commodities each day. In summary, the value-creating potential of complex labor increases with the educational requirements of the specialized labor process that requires that special type of labor.
Following the Economic News 
The Asia News Monitor recently reported on a publication of the European Union Agency for Fundamental Rights (FRA) that relates to the subject of severe labor exploitation of migrant workers. The FRA report urges “European governments to do more to tackle severe labour exploitation in firms, factories and farms across the EU.” According to the report, migrant workers have experienced exploitation in numerous industries that include “agriculture, construction, domestic work, hospitality, manufacturing and transport.” As we learned in Chapter 4, migrant workers are often subjected to harsher forms of exploitation because they lack recourse to the legal system. The lack of access to legal solutions stems from lack of language skills, political rights, and financial resources. In the case of migrant workers in the EU, many find themselves in “concentration camp conditions.” The report explains that migrant workers in the EU are paid very little, must repay debts to traffickers before they receive earnings, work long, 92-hour weeks, sleep in shipping containers, are beaten and verbally abused, are given no protective gear when working with dangerous chemicals, are coerced into drug trafficking, and are threatened with deportation. The tremendous power that employers have over migrant workers allows employers to greatly increase the intensity of the labor process. The low pay and long hours raise the rate of exploitation of migrant workers, but the intensification of the labor process also leads to the creation of more value within the same working time. The result is an expansion of the surplus value produced, which raises the rate of exploitation as well. Fortunately, the FRA report ends with some positive steps that EU institutions and EU nations may take to address the problem of exploitation of migrant workers. Although the most extreme forms of labor exploitation might be halted, absent a revolutionary transformation of the economic system, the capitalist exploitation of wage workers cannot be entirely abolished.
Summary of Key Points
- For a perfectly competitive employer, the total resource cost (TRC) curve grows continuously with employment, but the average resource cost (ARC) and the marginal resource cost (MRC) curves are identical to the labor supply curve facing the firm due to the constant wage rate.
- The marginal revenue product (MRP) curve of a perfectly competitive employer may be calculated by multiplying the product price by the marginal product of labor.
- The profit-maximizing rules (MRP = MRC and only operate when w ≤ ARP) leads to the conclusion that the MRP curve below the maximum ARP is the perfectly competitive employer’s labor demand curve.
- A shift of the labor demand curve may result from either a change in the product price or a change in the marginal product of labor.
- The individual worker’s labor supply curve is determined by utility maximization as the worker considers the tradeoff between income and leisure while faced with a time constraint.
- When a backward bending labor market supply curve exists, both a stable equilibrium and an unstable equilibrium may exist.
- In a monopsony labor market, the MRC rises more quickly than the ARC because the monopsonist must pay all workers a higher wage when an additional worker is hired.
- In a monopsony labor market, economic exploitation exists because the MRP exceeds the wage paid, but in a bilateral monopoly labor market, the degree of exploitation depends on the relative strength of the employer and the union.
- In Marxian theory, an increase in productivity in industries that produce workers’ means of subsistence lowers the prices of those commodities and increases the production of relative surplus value, but when the productivity increase occurs in other industries, it only causes a reduction in commodity prices.
- In Marxian theory, an increase in the length of the working day increases the amount of absolute surplus value produced, but it leaves commodity prices unchanged.
- In Marxian theory, an increase in the intensity of labor increases the amount of surplus value produced during a working day of a given length, but leaves commodity prices unchanged.
- In Marxian theory, complex labor creates a larger amount of value in a specific period than simple labor in the same amount of time.
List of Key Terms
Factor markets (input markets or resource markets)
Wage elasticity of labor supply
Total resource cost (TRC)
Average resource cost (ARC)
Marginal resource cost (MRC)
Marginal revenue product (MRP)
Average revenue product (ARP)
Labor market demand curve
Marginal productivity theory of income distribution
Problems for Review
1.Complete the missing information for the perfectly competitive employer represented in the table below. Assume the product price is $2 per unit. Then determine the profit-maximizing employment level.
2. Suppose T = 20 and w = $3 per unit of labor. Derive the equation of the time constraint beginning with the fact that T = h+l and Y = wh. When utility is maximized, what will the slope of the indifference curve be that is just tangent to the time line?
3. Complete the missing information for the monopsony employer represented in the table below. Assume the product price is $2 per unit. Then determine the profit-maximizing employment level and wage rate.
4. Suppose the working day is 11 hours, the variable capital is $32, the constant capital is $124, and the MELT is $4 per hour of SNALT. Also, assume that 50 pounds of the product are produced in one day, and this sector does not produce wage commodities.
- What is the current price per pound of the product?
- Suppose labor productivity rises in the wage commodities sector causing the variable capital to fall to $24. What will happen to the surplus value, the necessary labor, and the product price as a result?
- Returning to the original conditions, suppose that a 20% increase in labor productivity occurs in this industry alone. What will happen to the product price, the surplus value, and the necessary labor in this case? Be sure to account for the change in the amount of use values produced and the change in the constant capital advanced.
- Returning to the original conditions, suppose that the working day is extended from 11 hours to 12 hours. What percentage increase in the length of the workday is this change? What will happen to the surplus value, the constant capital, and the product price as a result?
- Returning to the original conditions, suppose that the intensity of labor increases by 10%. This change is equivalent to how much of a change in the length of the workday? What is the new surplus value, the new constant capital, and the price of the commodity?
5. Suppose a worker spends 2 years in technical school. The training involves a 7-hour workday for 6 days each week during the 52 weeks in the year. The worker then works 8 hours per day and 7 days per week for 30 years. If the constant capital advanced during those 30 years equals $200,000 and the MELT is $9 per hour, then what is the total value produced? Also, if 80,000 use values are produced during the 30 years, then what is the value (price) of the product?
- Prof. David Ruccio’s presentation of the neoclassical theory of labor supply in his introductory economics class at the University of Notre Dame in the early 2000s inspired the presentation in this section. I served as Prof. Ruccio’s teaching assistant at the time. ↵
- Chiang and Stone (2014), p. 305-306, represent an exception to the usual rule. They refer to the “monopsonistic exploitation of labor” and even include a box devoted to Marx’s critique of capitalism. They do not emphasize, however, that Marx’s condemnation of capitalism applies equally to intensely competitive market conditions. They refer to the term “exploitation” as loaded, which seems to imply that it should be used with caution. The caveat is not surprising. The authors are one step away from entering a competing discourse that neoclassical economists generally refuse to acknowledge. ↵
- For an excellent account of the Homestead strike, see Wolff, Leon (1965). ↵
- In this example, we have ignored the labor embodied in school supplies and equipment. The intensity of schooling is another difficult aspect of the problem, but it would need to be considered as well. ↵
- “European Union: Severe labour exploitation of migrant workers: FRA report calls for ‘zero’ tolerance of severe labour exploitation.” Asia News Monitor. Bangkok. 01 July 2019. ↵