Unit 6 The firm and its employees

6.11 Putting the wage-setting model to work: Wages, employment, and the rate of unemployment

You can explore trends in world- and country-level unemployment using this chart from Our World in Data.

search unemployment
Since workers differ from each other, and so do jobs, unemployed workers and firms with vacancies spend time searching for an employment match that suits them both. Unemployment caused by the search and matching process is called search unemployment.
involuntary unemployment
A person is involuntarily unemployed if they are seeking work, and willing to accept a job at the going wage for people of their level of skill and experience, but unable to secure employment.

Why is there always unemployment, even when the economy is booming? In most of the last 30 years, the world unemployment rate has been between 5 and 6%, and in some countries it has been persistently above 20%. One reason is the time, effort, and other costs that firms and workers incur in searching for a suitable match. Match formation can bring further costs—such as training, or relocation—so even when they find a potential opportunity, one or other party may prefer to continue searching for a better match. Unemployment resulting from search and matching costs is known as frictional unemployment or search unemployment.

Search unemployment is sometimes labelled ‘voluntary’, on the assumption that it arises because workers’ reservation wages are too high, so they choose to reject available vacancies. But this is misleading: in our model the search and matching process gives labour market power to firms, so we might equally well argue that the wages offered are too low. The two-sided character of search unemployment means it is not voluntary.

The labour discipline problem is another important source of unemployment, and in this case it is clearly ‘involuntary’:

When firms set wages to provide incentives for effort, there must always be involuntary unemployment.

Being unemployed involuntarily means not having a job, although you would be willing to work at the wage that other workers like you are receiving.

Some workers are involuntarily unemployed in our wage-setting model in Figure 6.17. It shows the no-shirking and reservation wage curves for a firm similar to the language school: labour is the only cost and each employee generates revenue y, so the isoprofit curves have the same shape. The employer sets a wage w1 to deter shirking, and only offers jobs to the N1 workers who have reservation wages below r1. All the applicants with reservation wages between r1 and w1 are turned away. They would be willing to accept a job at this wage, but they remain in unemployment. So we can say that these workers are involuntarily unemployed.

In this diagram, the horizontal axis shows employment N. The vertical axis shows wage w. Coordinates are (employment, wage). An upward-sloping, straight line is labelled reservation wage curve, has a vertical intercept of r_0, and passes through points (N_1, r_1) and (N_2, w_1). A parallel, upward-sloping straight line is labelled no-shirking wage curve and lies at all points above the reservation wage curve, and passes through point (N_1, w_1). An upward-sloping, concave curve starts from the horizontal axis at a value between 0 and N_1, and is tangential to the no-shirking wage curve at point (N_1, w_1). The horizontal distance between N_1 and N_2 shows the workers turned away.
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Figure 6.17 Wages and involuntary unemployment.

In contrast, there are other unemployed workers whose reservation wages are higher than w1. These workers would not be willing to accept a job that is acceptable to others. So according to the definition above, they are not involuntarily unemployed. However, as noted earlier, to call them voluntarily unemployed because their reservation wages are higher than offered wages is to ignore the possibility that the wages offered are too low.

What happens when economic conditions change?

Our wage-setting model determines the wage and employment level that firms will choose. But changes in economic conditions can shift the no-shirking wage curve.

An expression for the no-shirking wage curve

The firm’s reservation wage curve corresponds to the reservation wages of the potential employees, lined up in increasing order.

Section 6.8 explains fully how to derive the expression for the reservation wage.

A worker’s reservation wage depends partly on the utility they obtain while unemployed, and partly on the utility they expect to receive when they eventually get another job. While unemployed, they receive an unemployment benefit (b) plus their own individual utility of being unemployed (a), which varies between workers according to their personal and family circumstances. If v is the average utility in other jobs, we can write the reservation wage curve as:

\[w_r=τ(b+a^N)+(1-τ)v\]

where aN is the individual utility of the Nth potential worker. In this equation, τ is the weight that workers put on (b + aN) rather than v. For an unemployed worker considering their planning horizon, τ is the proportion of their time that they expect to spend unemployed rather than employed with utility v. When τ is high, utility while unemployed matters more, so the reservation wage is weighted towards (b + aN).

The no-shirking wage curve, w, is above the reservation wage curve because of the cost of effort, c, and the rent that has to be paid to deter shirking.

\[w=w_r+c+\text{ rent}(s,c)\]

(Remember that the rent depends on s, the expected number of weeks before shirkers are caught.) If we put these two expressions together, we can write an equation for the no-shirking wage curve:

\[w= \!\! \underbrace{τ(b+a^N)+(1+τ)v}_{\text{reservation wage of N}^{\text{ th}} \text{ worker}} \!\! +c+\text{rent}(s,c)\]

This equation shows all the things that affect the firm’s no-shirking wage curve.

What shifts the firm’s no-shirking wage curve?

  • If the firm’s ability to detect shirking improves, perhaps because of a new monitoring technology, then s, the time taken to catch shirkers, falls. So the rent required to discourage shirking is lower, and the curve shifts down.
  • If morale among employees falls, they may be more inclined to shirk: effort will feel more costly. The rise in c will shift the curve upward.
  • If the firm’s competitors in the labour market increase their demand for workers—for example because their productivity rises—they will raise wages to recruit more workers: v will increase. This will raise the reservation wages of the firm’s own employees, so its no-shirking wage curve will shift upward.

The effect of a shift in the no-shirking wage curve

Figure 6.18 illustrates the effects of one of these shifts, a rise in the cost of effort, c. Suppose that the firm is maximizing profit at point E, where the no-shirking wage curve reaches the highest possible isoprofit curve. If the employees’ cost of effort increases, perhaps due to a fall in morale, the no-shirking wage curve shifts up, because the employer has to pay higher wages to discourage shirking.

In this diagram, the horizontal axis shows employment N. The vertical axis shows wage w. Coordinates are (employment, wage). The zero-profit line consists of a vertical segment between (0, 0) and (0, y), and a horizontal line starting from (0, y). A series of upward-sloping, concave lines starting from the horizontal axis are isoprofit curves for increasing profits the further away from the origin. An upward-sloping, convex line is tangential to a isoprofit curve at point E (N_1, w_1). When the effort cost c rises, the no-shirking wage curve shifts upwards. This is now tangential to a higher isoprofit curve at point F (N_2, w_2), with N_2 lower than N_1 and w_2 higher than w_1.
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Figure 6.18 A rise in the cost of effort.

The new profit-maximizing point is F. The wage is higher, but because labour is more expensive, the firm lowers employment—and its profit falls.

The firm’s no-shirking wage curve also shifts if economy-wide conditions for unemployed workers change: that is, the unemployment benefit, b, and the rate of unemployment which determines how long workers take to find jobs (τ). But these changes will affect the wages and employment in all firms, and this, in turn, will have further effects on reservation wages and no-shirking wage curves. To fully understand these changes, we need to model the whole economy.

Wages and employment in the whole economy

We can use our model of one firm to build a model of a whole economy. To do this, imagine that there is a fixed number of firms in the economy, and that they are all identical, with the same productivity and the same recruitment and labour discipline problems. The cost of effort and the employment rent will be the same in every firm. All firms will face the same no-shirking wage curve, and will choose the same wage, w, and employment level, N. The net utility that unemployed workers can expect to receive whenever they find a job will be v = wc. So the wage in every firm can be found by putting v = wc in the no-shirking wage curve:

\[\begin{align*} w& = τ(b + a^N) + (1 - τ)(w - c) +c +\text{rent}(s,c) \\ &⇒ τw = τ(b + a^N + c) +\text{rent}(s,c) \\ &⇒ w = b + a^N +c + \frac{\text{rent}(s,c)}{τ(u)} \\ \end{align*}\]

This equation gives us a relationship between wages and the level of unemployment in an equilibrium across the economy as a whole. Note that N is the number of workers employed in each firm, and aN is the individual utility of each firm’s Nth worker (the employee with the highest reservation wage). We have written τ as τ(u) to emphasize that the time taken to find a job increases when unemployment is high.

To understand how wages and unemployment are related, imagine that the economy is experiencing high unemployment. Then:

  • τ(u) is high (it takes a long time to find a new job); this reduces the fourth term in the equation for the wage, rent τ
  • employment, N, must be low in every firm; hence aN, the unemployment utility of the Nth worker, is also low.

Both of these effects lower the equilibrium wage. Conversely, when unemployment is low, wages will be high. For the economy as a whole, this is called the wage-setting or WS curve and represents the supply side of the labour market. In Units 1–4 of the macroeconomics volume, we return to complete the model of the economy as a whole and analyse real wages, unemployment and inflation. But there is one question we can answer now: is full employment possible? When the wage is set on a firm’s no-shirking wage curve in Figure 6.17, there is involuntary unemployment.

Why full employment is impossible

The economy-wide relationship between wages and employment tells us that it is impossible to eliminate unemployment completely. If no-one were unemployed, that would mean workers who lost their jobs must be able to find new jobs immediately. So τ, the time taken to find a job, would be zero.

Think about what happens to the wage as τ gets closer to zero. The fourth term, rent τ, becomes infinitely large. The wage that is required to ensure that workers do not shirk therefore exceeds their productivity: no firm would offer such a wage.

So there cannot be an equilibrium in the economy with no unemployment. The threat of losing one’s job and remaining unemployed, at least for a short time, plays an essential role in labour discipline.

Exercise 6.10 The ‘Great Resignation’

Since the 2020 COVID-19 pandemic, many workers in several countries, including China, Australia, and the US, have decided to quit their jobs. Use these articles to help you answer the following questions:

  1. What are some of the main reasons why workers have been quitting their jobs, and how has the pandemic contributed to these reasons?
  2. Choose one of the reasons given in the articles and use a diagram like Figure 6.18 to illustrate how it could affect the various curves and labour market equilibrium.
  3. How do you think firms could effectively retain their workers?

How economists learn from facts Workers speed up when the economy slows down

The incentives provided by employment rents are illustrated in a study by Edward Lazear (an economic adviser to former US President, George W. Bush) and his co-authors. They investigated a single firm during the global financial crisis, to investigate how the managers and workers reacted to the turbulent economic conditions. The firm specializes in technology-based services such as insurance claims processing, computer-based test grading, and technical call centres, and operates in 12 US states. Lazear and his colleagues used the firm’s data from 2006 to 2010 to analyse the effect on labour productivity of the worst recession since the Great Depression.

They found that the firm’s productivity increased dramatically as unemployment rose during the financial crisis. One possible explanation is that average productivity increased because the least productive workers were fired. But Lazear found that it was more due to workers putting in extra effort. The severity of the recession raised the workers’ employment rent for any given wage, and they responded by working harder.1

Our model predicts that employers would have cut wages, while sustaining an employment rent sufficient to motivate hard work. But wages were not cut. An earlier recession provides another insight that helps to explain firms’ reluctance to reduce wages in the crisis. Truman Bewley, an economist, was puzzled when he saw only a handful of firms in the northeast of the US cutting wages during the recession of the early 1990s. Most firms, like the one Lazear’s team studied, did not cut their wages at all.

Bewley interviewed more than 300 employers, labour leaders, business consultants, and careers advisers in the north-east of the US. He found that employers chose not to cut wages because they thought it would hurt employee morale, reducing productivity and leading to problems of hiring and retention. They thought it would ultimately cost the employer more than the money they would save in wages.2

Exercise 6.11 Lazear’s results

Use the findings of Lazear and co-authors (from the ‘How economists learn from facts’ box) to answer the following questions.

Assuming that the employer did not adjust wages, draw a diagram like Figure 6.18 for each of the following years, and explain what it illustrates:

  1. the pre-crisis period (2006)
  2. the crisis years (2007–8)
  3. the post-crisis year (2009).
  1. Edward P. Lazear, Kathryn L. Shaw, and Christopher Stanton. 2016. ‘Making Do With Less: Working Harder During Recessions’. Journal of Labor Economics 34 (1/2): pp. 333–360. 

  2. Truman F. Bewley. 1999. Why Wages Don’t Fall During a Recession. Cambridge, MA: Harvard University Press.