Unit 1 The supply side of the macroeconomy: Unemployment and real wages

1.6 Wage setting and unemployment (WS curve)

When describing the labour market, we classify people as employed, unemployed, or inactive. But as we know from our everyday experience, labour markets are in a permanent state of flux. Firms post vacancies and hire new workers; workers quit and search for new opportunities. Workers move from job to job and in and out of unemployment, and even in and out of the labour force. Unit 6 of the microeconomics volume develops a complete model of the labour market; read Section 6.4 for an introduction to the job-finding process. Here we provide a bare-bones description of the model, which in turn provides the foundations for the economy’s WS curve.

Workers and firms search in the labour market for a good match. Both workers and jobs are heterogeneous. Workers have different skills and value different things about a job, such as its location and working hours. Employers’ needs vary depending on what they are producing and the technology they are using. The quality of the match matters to both sides because employment relationships are long term.

matching market

A market for interactions between two distinct groups, in which the members have different characteristics from other members of their own group, and would benefit from matching with particular members of the other group. For example, firms and workers in the labour market, men and women in what is sometimes called the marriage market. Also known as a two-sided market.

The labour market is a matching market because people on each side of the market—jobseekers and recruiters—care about who they match with on the other side. Figure 1.17 illustrates the flows that take place in the labour market as matches are created and later destroyed. The flow model introduces a new variable, V, which is the number of vacant jobs.

The HR department of the firm engages with the labour market to solve two problems it faces when setting the wage: first, how to recruit the desired number of workers (taking account of quits) to maximize the firm’s profits and second, how to motivate them to provide the effort necessary for production to take place.

conflict of interest

The situation that arises in an interaction if, in order for one party to gain more, another party must do less well.

There is a conflict of interest between the employer and the worker in the labour market: the employer wants the worker to work hard and well for the least cost, and the worker wants the highest wage and least onerous working conditions in their job. Jobs involve aspects of behaviour such as effort, attention to detail, diligence, and demeanour that cannot be perfectly observed by the employer and cannot therefore be written into an employment contract which would stand up in a court of law.

If the worker cannot be contractually obliged to exert the effort required by the employer in their production process, another way must be found to prevent shirking on the job. The response by HR departments is to set a wage higher than is necessary to get them to show up to work; the higher wage means they have something to lose if they shirk, are caught, and are fired.

We begin with the wage-setting problem of a single firm and then show how the decisions of firms are aggregated to produce the economy-wide WS curve introduced in the WS–PS model in the previous section. By starting with one firm, we can pick out the factors that ultimately shift the WS curve and that, when combined with the PS curve, affect the supply-side equilibrium in the economy as a whole.

A single firm’s recruitment problem and reservation wage

The HR department of the firm seeks to hire workers from the pool of jobseekers. Remember that we are assuming that all workers are equally productive. We make some additional simplifications: we ignore job-to-job moves and assume that the firm hires only from unemployment; we also assume that the employer makes a ‘take it or leave it’ job offer to the worker and that all workers are paid the same wage.

reservation wage

The reservation wage is the lowest wage a worker is willing to accept to take up a new job. It is the wage available in the worker’s next best job option (the reservation option). For workers whose next best option is unemployment, the reservation wage takes into account the wages they expect to receive when they find a new job as well as any income received while unemployed.

unemployment benefit

A government transfer that is paid to an unemployed person while they are unemployed (or for part of the unemployment period). Also known as: unemployment insurance.

utility

A numerical indicator of the value that one places on an outcome. Outcomes with higher utility will be chosen in preference to lower valued ones when both are feasible.

A jobseeker’s decision about whether to accept the offer depends on their next best alternative option, which is to remain unemployed and seek another job. The overall value of the next best alternative can be summarized as the worker’s reservation wage and depends on:

• income while unemployed, which we will assume to be an unemployment benefit paid by the government
• the additional net benefits of being unemployed (called the ‘net utility of unemployment’)—if the stigma of being unemployed outweighs the benefits that come from not having to commute and being better able to manage care responsibilities, for example, then this is negative; but, depending on tastes and circumstances, it could be positive (this component of the reservation wage, which is called the ‘net utility of unemployment’, will vary across people as their tastes and circumstances differ)
• how many weeks they expect to stay unemployed before receiving another job offer
• how good they expect other job offers to be; that is, the ‘expected value’ of an alternative job.

The reservation wage is the wage at which the current job offer would have exactly the same value as the next best alternative. The worker will accept any offer with a wage greater than or equal to the reservation wage.

Jobseekers will have different reservation wages, because the costs and benefits of unemployment are subjective. So the higher the wage that is offered by the firm, the more workers will accept. This is illustrated in Figure 1.18. If the real wage, w, offered by the firm is equal to \(w_{r}^{1}\), only those workers with reservation wages less than or equal to \(w_{r}^{1}\) will be willing to work there, and the firm’s total employment will be N_low. A firm wanting to employ more workers will have to offer a higher wage such as \(w_{r}^{2}\), so that it can also attract workers with higher reservation wages.

We refer to the upward-sloping line in Figure 1.18 as the reservation wage curve (although in our model it is a straight line). You can think of it in two ways. First, it reflects the distribution of reservation wages among the firm’s potential workers: for example, there are N_low potential workers with reservation wages less than \(w_{r}^{1}\), and (N_high – N_low) potential workers with reservation wages between \(w_{r}^{1}\) and \(w_{r}^{2}\). Secondly, it shows the number of workers the firm could employ at each possible choice of wage.

A single firm’s motivation problem and the no-shirking wage

Getting the desired number of workers to turn up by paying the reservation wage is only part of the solution to the HR department’s problem. It must also ensure that the workers work hard and well. To create an incentive for a new hire to work hard, the HR department will offer a wage above their reservation wage. This implies that the worker has something to lose if they were to shirk on the job. If they were caught and fired, they could not be confident about finding a replacement job at the same wage and conditions.

How much more than the reservation wage the HR department will have to pay will depend on three things:

• The cost of effort: the psychological or other costs for the worker (for example, tiredness or boredom) of working hard enough to meet the standards set by HR.
• The chance of getting caught shirking: how likely it is that if the worker is working below standard, they will be discovered.
• The chance that if discovered shirking, the worker will be fired.

no-shirking wage

The wage that is just sufficient to motivate a worker to provide effort at the level specified by their employer. See also: no-shirking condition

In the economy, each of these will differ from worker to worker and from firm to firm. But to simplify the model, we assume these factors are the same for all workers. The additional amount that has to be paid to get the worker to exert the required effort is then the same for all. As shown in Figure 1.19, this results in a constant vertical distance between the no-shirking wage (NSW) and the reservation wage.

In the last panel of Figure 1.19, the reservation wage (the lowest line) is the wage at which the worker would be indifferent between unemployment and taking the job. At a wage equal to the reservation wage plus the cost of effort (the middle line), the worker would be indifferent between unemployment and working at the required level of effort.

employment rent

The economic rent a worker receives when the net value of their job exceeds the net value of their next best alternative (that is, being unemployed). Also known as: cost of job loss.

But because it may take some time to catch a shirking worker, HR sets a higher wage, the no-shirking wage (top line), to ensure that working hard is not only preferred to unemployment, but also to taking the job and then shirking until caught. This additional payment is called an employment rent.

What shifts the no-shirking wage upward?

Anything that improves the opportunities available to an unemployed jobseeker as they consider taking a job rather than remaining unemployed increases the reservation wage. These include:

• A rise in the unemployment benefit. Because this raises their income when unemployed, the wage offered has to be higher for the worker to accept the job.
• An improvement in the prospective employee’s quality of life without the job relative to the quality of life with the job. For example, if the job they are seeking no longer offers the opportunity to work flexibly or remotely, they would need to be offered a higher wage to accept.
• Other employers increase their demand for labour, reducing the unemployment rate. Because this increases the likelihood that a better job offer will come along soon if the unemployed person turns down the job offer, they need to be offered a higher wage to accept.
• Other employers raise their wages. This makes it more attractive to reject the job offer and to wait for a better offer from another firm.

And anything that raises the reservation wage of each worker will also shift the firm’s no-shirking wage curve upward. In addition, the no-shirking wage curve is also shifted up if one of the following situations occur:

• It becomes more difficult for the employer to monitor the effort of workers. With less chance of being caught shirking, the worker requires a higher wage to motivate them to work hard.
• It becomes more costly for the employer to fire a worker caught shirking (in terms of worker morale or in hiring and training a replacement). If the worker knows that they are unlikely to be fired even if caught shirking, they will have to be paid a higher wage to get them to work up to the HR standard. Unit 2 will discuss how labour market regulations and trade union behaviour can influence the cost of firing.
• Employees find it more unpleasant to meet HR’s work standard either because it has been raised, or due to a deterioration in the relationship between the firm and its employees. The worker requires a higher wage to comply with the effort required.

ceteris paribus

Economists often simplify analysis by setting aside things that are thought to be of less importance to the question of interest. The literal meaning of the expression is ‘other things equal’. In an economic model, it means an analysis ‘holds other things constant’.

When we describe the effect of one of these changes on the wage set by one firm, we assume that nothing else in the economy changes. This assumption, called ceteris paribus, helps us to isolate each effect from the others. But some of the changes above will affect all firms; and if other firms change their wages, this in turn will change the situation facing each one. Next, we show how this model of wage setting in the firm feeds through to the aggregate economy.

The economy as a whole: The unemployment rate and the WS curve

To return to the aggregate economy, we need to add up the decisions of all the firms, taking account of their interdependence. We already have a hint about interdependence: every firm sets its wage to recruit and motivate their desired number of workers, but the collective decisions affect the overall demand for labour in the economy, and hence, the economy’s unemployment rate. And the unemployment rate in turn affects the no-shirking wage for the firm.

Figure 1.20 shows the situation for a firm in the upper panel and for the aggregate economy in the lower one. Since all firms in the economy are identical, they will make identical choices. Suppose that aggregate employment is N₁, and the corresponding employment in each firm is \(N^f_1\). What is the aggregate wage?

The lower panel shows that aggregate employment is low (compared with the labour force), so unemployment is high. The firm’s no-shirking wage (NSW) for a high level of unemployment is shown by the line in the upper panel. To employ \(N^f_1\) workers, each firm sets a wage, w₁ (point A on the NSW). So w₁ is the aggregate wage, and point A in the lower panel must be on the wage-setting (WS) curve for the whole economy. Work through the steps in the figure to find other points on the WS curve.

The WS curve in Figure 1.20 curves upward increasingly steeply as unemployment falls. Why does it have this shape?

Think about what happens in an individual firm when the unemployment rate falls. We know from the previous section that if nothing else changes (ceteris paribus), this means that jobseekers have a better chance of getting a job if they just wait a bit more, so the wage required to get a worker to accept an offer increases. Therefore the NSW for the firm shifts up.

But something else does then change: other firms’ NSW curves shift up too. Now that other firms are willing to pay higher wages, workers’ reservation wages will rise further. So each firm’s NSW shifts further. And the effect of the extra wage competition from other firms is greater when unemployment is low, because workers can find these good jobs elsewhere more quickly.

This explains why, in the upper panel of Figure 1.20, the NSW shifts more when unemployment falls from medium to low, than when it falls from high to medium. And that means that the aggregate wage rises more, so the WS curve in the lower panel is steeper.

What shifts the WS curve?

Above, we identified seven factors that shift firms’ NSW curves upwards. Two of these—the unemployment rate and the wages offered by other firms—are built into the aggregate wage-setting curve. But the following five factors will shift the WS curve upwards:

• a rise in the unemployment benefit
• an improvement in the prospective employee’s quality of life without the job relative to the quality of life with the job
• it becomes more difficult for the employer to monitor the effort of workers
• it becomes more costly for the employer to fire a worker caught shirking
• employees find it more unpleasant to meet HR’s work standard, which increases the disutility of work.

The wage-setting curve for the US economy

To find an example of an empirical wage-setting curve, we show in Figure 1.21 a curve estimated from data for the US. Note that the horizontal axis shows the unemployment rate explicitly, falling from left to right. On the vertical axis is the real wage, measured by real annual earnings. Economists use the fact that unemployment rates and wages vary across local areas to estimate an empirical wage curve for the economy as a whole. To do this, they use the detailed information on wages and other characteristics of individuals that is collected in surveys. Each point in the chart is the estimated real wage (in 2019 prices) at the particular unemployment rate shown on the horizontal axis.

Wage-setting curves have been estimated for many economies. David Blanchflower and Andrew Oswald explain in more detail how it is done in their paper ‘The Wage Curve’.