Hill – Mankiw 9th Edn Chapter 18 – The Markets for Factors of Production
Mankiw, N. G. (2021) Principles of microeconomics (9th ed.)
Principles of economics (9th ed.)
Mason, OH: South-Western Cengage Learning.
Rod Hill
University of New Brunswick, Saint John campus
Saint John, New Brunswick, Canada
email: rhill@unb.ca
Chapter 18 – The Markets for Factors of Production
Here are some things to consider when reading this chapter.
- Some problems with the concept of the value of the marginal product of a factor
(i) Production requiring fixed proportions of complementary inputs.
The short-run production function (Figure 2, p. 360) shows how the number of apple pickers employed changes the quantity of apples picked, holding all other inputs fixed. The Commentary on Chapter 13 pointed out that most production processes involved combining flows of different inputs, often in fixed proportions, to produce additional output. The inputs are complements, as opposed to substitutes, for each other.
For example, one professor with 50 minutes of lecture hall time can produce one lecture. The marginal product of the professor without the additional services of the lecture hall is zero; so, it only makes sense to speak of the additional output of the combination or bundle of inputs that is used. It’s impossible to separate the marginal product of each of the separate parts of the input bundle.
(ii) Valuing output that has no market price.
Even if this previous issue is set aside, how can the professor’s marginal product be valued? Unlike an apple, it is not sold in a market. The same goes for most of the goods and services produced by government employees and many of those working for nonprofit organizations that provide free services to people. In the National Income accounts, these are valued at their cost, but no one claims that this represents the value of their marginal product.
(iii) Identifying the marginal product of an individual factor.
Let’s just consider work that produces goods and services for sale in markets. Where output consists of many products produced simultaneously by teams of people working in a complex organization, one person’s contribution to overall output is impossible to determine. For example, manufacturing firms employ many office workers not involved directly in the manufacturing process. If such individuals’ marginal productivity can’t be measured, how can the theory be tested?
(iv) The vagueness of the marginal productivity theory.
Even if workers’ marginal products could actually be observed, what exactly is the theory predicting? For example, does the theory say that the workers are paid their actual marginal products every hour or every day? Or will they be paid their average marginal product over some longer period?
What about a group of workers of the same seniority who all get the same wage, even though individual marginal products within the group differ? If pay in such cases reflects the average marginal product of the group, is this consistent with marginal productivity theory?
After asking questions such as these, American economist Lester Thurow concluded that textbook marginal productivity analysis “is so amorphous that I have been unable to say what it is” (1975, p. viii). (He gives a detailed examination in Appendix A of his book).
- Labour productivity and real wages
Mankiw writes (p. 369): “Both theory and history confirm the close connection between productivity and real wages”. The annual growth rate data he reports (in the text and in Figure 7) show labour productivity growing an average of 0.2 percent per year faster than real wages over 1960-2017.
Mankiw’s discussion of productivity is potentially confusing. In the first paragraph he writes that “wages equal productivity as measured by the value of the marginal product of labor”. However, after that, ‘productivity’ refers to average (not marginal) labour productivity. This is an inflation-adjusted estimate of the value of all goods and services produced in the economy, divided by a measure of the labour used to produce it, such as total hours of work.
Mankiw writes that percentage changes in average labour productivity and in the marginal productivity of labour “are thought to move closely together”. If so, according to the theory of wages in the text, average wages would be positively associated with average labour productivity.
Normally, “real wages” describes money (or ‘nominal’) wages’ purchasing power over the goods and services that wage earners buy. Money wages are adjusted by a Consumer Price Index (CPI) to account for inflation. It is real wages measured this way that matter for workers and influence their decisions about how much labour to supply.
However, the description underneath Figure 7 says that real wages there are calculated by dividing an index of money wages by the “price deflator for that sector”. In other words, the percentage change in money wages is compared to the percentage change of the prices of the products that are made in the various sectors where those wage earners are employed. That comparison will be of interest to the firms that pay the wages and sell the goods and services, but not to their employees who obviously don’t spend their wages exclusively on what they produce.
The chart here shows an index of labour productivity for 1960-2017 and these two alternative measures of real wages. (All indices are scaled to have a value of 100 in 1970.)
The data illustrated in the chart show that before the early 1970s increases in real wages, measured both ways, did follow changes in labour productivity. But, in a break with the pattern of the past, changes in average labour productivity and in both measures of real wages began to diverge in the early 1970s. This appears to conflict with Mankiw’s contention that they are closely connected. The definition of the real wage that Mankiw chooses diverges less that the standard one, at least up until 2000. (The data underlying the graph are available here.)
From 1960-2017, average labour productivity grew an average of 2.0 percent annually, while real wages, measured in Mankiw’s favoured way grew by 1.6 percent annually – hence the significant gap between the two in 2017, as seen in Figure 1. Real wages calculated using the consumer price index grew by 1.05 percent annually in these years, half the rate of labour productivity growth.
This apparent decoupling between overall labour productivity growth and this standard measure of real wage growth is not unique to the United States and has generated considerable debate concerning its causes. In effect, Mankiw denies that this debate exists when he writes: “The bottom line: Both theory and history confirm the close connection between productivity and real wages” (p. 369).
A key point is that wages (or more broadly ‘compensation’, which includes the value of ‘fringe benefits’) depend on more than labour productivity. As Lawrence Summers and Anna Stansbury (2018) explain
just as two time series apparently growing in tandem does not mean that one causes the other, two series diverging may not mean that the causal link between the two has broken down. Rather, other factors may have come into play which appear to have severed the connection between productivity and typical compensation.
In a short essay, Robert Solow (2015) explains why changes in productivity and in real wages were roughly the same in the quarter century before they began to diverge. He writes:
In the years after the Second World War, … [t]his rough balance was made explicit in what came to be called the Treaty of Detroit: the agreement between the United Auto Workers and General Motors (followed by Ford and Chrysler) that the average annual rate of wage increase would be the percentage increase in productivity plus the percentage increase in consumer prices. This norm spread beyond the auto industry.
His explanation of what was happening during this time and after it is based on the view that a significant amount of national income consists of what Mankiw calls economic or monopoly profits. Solow terms it “monopoly rent” or just “rent”.
This contrasts with Mankiw’s claim that “we will not go far wrong assuming that firms operate in competitive markets, even if that is not precisely the case” (p. 312). If that were so, monopoly profits (or rents) would be small, not the 10 and 30 percent of the economy that Solow says is the range of current estimates.
Solow writes that rents are “a return to the special position of the firm” as a result of it being “at least partly protected from competition. … The division of rent among the stakeholders of a firm is something to be bargained over, formally or informally. … It is essential to understand that what we measure as wages and profits [i.e. the income of capital owners] both contain an element of rent.”
He explains that the Treaty of Detroit, and the social norm that followed from it, was a way of fixing the division of monopoly rents between labour and capital owners. But that division “depends on bargaining power, business attitudes and practices, social norms and public opinion.” Those are the factors which, if they shift, can sever the apparently close connection between labour productivity and typical wages, as Summers and Stansbury wrote.
Labour has been getting an increasingly smaller share of rent as its “social bargaining power” has weakened. Solow points to “the decay of unions and collective bargaining, the explicit hardening of business attitudes, [and] the popularity of right-to-work laws” as contributing to this. International competition and technological change, which could put downward pressure on the typical worker’s wage can also play a role. Solow also notes the increasing importance in the labour force of part-time work, temporary workers, independent contractors, and workers with fixed-term contracts. Such workers “have little or no affective claim to the rent component of the firm’s value added.”
To sum up: Mankiw’s presentation of the data on labour productivity and real wages effectively obscures their divergence in recent decades. This allows him to claim, incorrectly, that the perfectly competitive model of labour markets adequately explain the relationship between the two. Instead, the extensive debate among economists about the changing productivity-wage relationship is based on a different story. It’s about pervasive imperfect competition giving rise to significant monopoly rents. Relative bargaining power over the distribution of those rents is affected by, among other things, labour market regulations and institutions and social norms.
- Employer power in the labour market
Mankiw gives a brief discussion of monopsony, giving little detail “because monopsonies are rare” (p. 370). Like all mainstream introductory texts, Mankiw considers only the case of pure monopsony – a market with just one buyer – giving the example of a company town.
The model of monopsony, like the model of monopoly, serves to illustrate the general idea of the ability of buyers to set prices rather than take them as given by a perfectly competitive market. So, in the chapter on monopoly, Mankiw used the phrase “monopoly power” to mean the ability of any noncompetitive firms (not just pure monopolies) to set prices. In the same way, “monopsony power” refers to buyers’ ability to set prices. in labour markets, employers set the wages they will offer.
(i) The ubiquity of monopsony power in the labour market
Mankiw maintains that the perfectly competitive model of supply and demand is the best one to use except in the rare case of pure monopsony (p. 370). However, the perfectly competitive model misses many important features of real labour markets that give employers market power.
To illustrate these features, British labour economist Alan Manning (2003: p.4) points out a prediction made by the perfectly competitive model. Because employers are price takers, if an employer reduces its wage by one cent, all of its workers will quit and immediately be employed elsewhere. That’s what it means to have no market power.
Applied to real labour markets, this prediction is obviously incorrect, but why? If you’re reading this, no doubt you can easily come up with a list of several reasons. These are called ‘frictions’. Your list might include things like the cost of searching out wages available elsewhere, uncertainties about what other jobs and workplaces would be like, disruption of social ties with current coworkers, and possible increases in commuting costs or even moving costs if an alternative job requires it. (These ideas were mentioned in Part 5 of the Commentary on Chapter 6 that considered the analysis of the minimum wage there.)
As well, employees may have firm-specific skills or knowledge, which enhances their productivity, and therefore their wage, with their current employer compared with alternative employers. Quitting is costly because this wage premium would be lost; by definition, such firm-specific skills would have no value elsewhere. This contrasts with general skills that can be widely applied. These include literacy, numeracy, and knowledge and skills acquired through formal education and training. The perfectly competitive model of the labour market, in which everyone receives the same wage, implicitly assumes that all skills are general skills.
As a result, if a firm reduced wages, workers would quit at a greater rate than before and recruitment would become more difficult, while the reverse would happen if the firm increased wages. In short, real-world firms face upward sloping labour supply curves and have a choice about what wage to offer.
Many principles texts present a simple monopsony model, as illustrated in Figure 1. Since the monopsonistic employer faces an upward-sloping labour supply curve, hiring an extra worker increases the wage for all workers hired. As a result, the marginal cost of an additional worker is not just the wage paid to that worker, but also the additional cost of all the other workers it previously employed at a lower wage. Except for the first worker, the marginal labour cost exceeds the daily wage that is shown by the Supply curve.
In the model, the employer hires workers up to the point where their marginal revenue product just equals the marginal cost of hiring an additional worker. The wage is shown by the labour supply curve. Note that workers are paid less than the value of their marginal product. If some degree of monopsony power is the rule rather than the exception, the marginal productivity theory’s general claim that wages equal the value of the marginal product in each labour market is not correct.
(ii) Monopsony and the minimum wage.
Some principles texts go one step further and examine the result of legislating a minimum wage in this model. In the earlier example, what happens if the government sets a minimum wage of $70/day? As seen in Figure 2, this minimum wage becomes the marginal cost of labour, at least up to the point where the labour supply curve shows that a wage higher than $70/day is needed to induce a greater supply of labour. (Then the marginal cost of labour becomes discontinuous, jumping up to the part of the line originally seen in Figure 1.)
The $70/day minimum wage happens to be what the wage would be if the labour market were competitive. The effect is to increase employment and to offset the employment effect of employers’ market power. This contrasts with a predicted decline in employment if a minimum wage is set in a perfectly competitive labour market, as Mankiw describes in detail (pp. 116-117).
If employers have monopsonistic power, a minimum wage can potentially offset that in the same way that price regulation in monopoly can offset the monopolist’s market power. In this case, the minimum wage eliminates the inefficiency caused by the gap between the value of what an extra worker could produce (the MRP) and what a worker would be willing to accept to produce it, as shown by the supply curve.
As briefly reviewed in the Commentary on Chapter 6, the empirical evidence in recent decades about the effects of minimum wages on employment has undermined support for the perfectly competitive model in favour of models that recognize employers’ monopsonistic power. A survey of members of the American Economic Association found that agreement with the statement “A minimum wage increases unemployment among young and unskilled workers” has “steadily eroded” between 1990 and 2020. Only 30 percent agreed unconditionally in 2020, compared with 63 percent in 1990. 35 percent now disagree with the statement compared with only 18 percent in 1990. 35 percent agreed “with proviso”, meaning that certain conditions would have to apply (Geide-Stevenson and La Parra-Perez 2021).
The provisos are not described. Perhaps some respondents think that relatively small increases in the minimum wage don’t decrease employment, but large increases would. Another possibility: measured unemployment would increase if more people are searching for work at the current wage. If a higher minimum wage makes work harder to find, some might leave the labour force (or postpone entering it) to undertake education or training to improve their chances of getting a job. Because they are not looking for work, they do not count as unemployed.
- Does marginal productivity theory explain how the value of total production is divided among factor owners?
As presented by Mankiw, marginal productivity theory seemingly explains the prices of all factors. If so, then the incomes of factor owners must add up to the value of total production. Otherwise, there would either be something left over or there would not be enough to make those payments. This is the so-called ‘adding-up problem’ that concerned some economists in the 1890s as the marginal productivity theory was being developed.
They discovered that, in the theoretical model, the incomes of factors do indeed add up to the value of the goods produced, but only if the economy consists of perfectly competitive factor and product markets in equilibrium. There must be constant returns to scale in production because economies of scale would lead to large firms and imperfect competition.
It can be shown that if factors are paid their marginal products by imperfectly competitive firms, those payments would more than use up total output (Steedman 1987). As a result, such firms cannot “pay the factors they hire their marginal products. If economies of scale characterise much of modern manufacturing, marginal productivity theory is simply irrelevant”, as Mark Blaug explained (1996, p. 438).
The adding up problem can be avoided by including an additional factor, often termed ‘entrepreneurship’, as some textbook authors do. That factor gets the residual – whatever is left over once the other factors have been paid. That residual can be thought of as ‘pure economic profits’. Marginal productivity theory has nothing to say about it (Steedman 1987).
REFERENCES
Bhaskar, V., Alan Manning and Ted To (2002) “Oligopsony and Monopsonistic Competition in Labor Markets”, Journal of Economic Perspectives, 16(2): 155-74.
Blaug, Mark (1996) Economic Theory in Retrospect, Cambridge University Press.
Economic Policy Institute (2022) “The Productivity-Pay Gap”, October.
Federal Reserve Bank of St. Louis (2023) “When comparing wages and worker productivity, the price measure matters”, The FRED Blog, March 23, available here.
Geide-Stevenson, Doris and Alvaro La Parra-Perez (2021) “Consensus among economists 2020: A sharpening of the picture”, manuscript.
Manning, Alan (2003) Monopsony in Motion: Imperfect Competition in Labor Markets, Princeton University Press.
Solow, Robert M. (2015) “The future of work: Why wages aren’t keeping up”, Pacific Standard Magazine, August 11.
Stansbury, Anna and Lawrence H. Summers (2018) “On the link between US pay and productivity”, VOXEU, Centre for Economic Policy Research, February 20.
Steedman, Ian (1987) ‘Adding-up problem’, in Palgrave Macmillan (eds), The New Palgrave Dictionary of Economics, Palgrave Macmillan. doi.org/10.1057/978-1-349-95121-5_507-1.
Thurow, Lester (1975) Generating Inequality: Mechanisms of distribution in the US economy, Basic Books.