Unit 6 The firm and its employees
6.10 Combining recruitment and labour discipline: The wage-setting model
- labour discipline problem, labour discipline model
- Employers face a labour discipline problem when they need to give employees an incentive to ensure that they work hard and well. In the labour discipline model, they do this by setting wages that include an economic rent (employment rent), which will be lost if the job is terminated. See also: employment rent.
The wage affects both the number of workers a firm can employ and how hard its employees will work (the labour discipline problem). How can the firm set the wage to address both of these concerns? In general, the wage required to hire enough workers to achieve a particular level of employment will not be high enough to motivate them to work hard.
- 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.
We will consider the example of the Parisian language school (introduced in Section 6.5), which employs young graduates to teach short courses in French for visiting students. Figure 6.10 shows the school’s reservation wage curve, which tells us the wage required to employ N workers. Potential tutors only accept a job offer if the wage is above their reservation wage, and have different reservation wages according to their individual utility of unemployment. So to recruit and retain more employees, the school has to increase the wage.
For example, if the wage is €650, its potential recruits are limited to those with reservation wages less than or equal to €650, and the maximum number of tutors it can employ is 40. If it raises the wage to €700, it can also attract tutors with reservation wages between €650 and €700, increasing employment to 60.
Figure 6.10 The school’s reservation wage curve.
If the school sets a wage €650 and employs 40 tutors, its employees will have reservation wages between €550 and €650. But it also wants them to work hard—effective teaching requires careful preparation—and it is impossible to monitor and assess the quality of every lesson.
- 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). See also: economic rent.
Consider the case of Marc, a tutor whose reservation wage is equal to €650. He will not choose to work hard if the wage is €650, because he will be indifferent between being employed while exerting no effort, and his next best option, unemployment. To give an employee an incentive to work hard, the wage must be above their reservation wage: firstly to compensate them for the cost of effort, and secondly to ensure that losing the job is costly for them. In other words, they must receive an employment rent, so that they prefer to work rather than risk being caught shirking and 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
The rent required to deter shirking depends on two things: the cost of effort, c, and the number of weeks, s, that a shirker could expect to remain in the job before being caught. For a tutor with reservation wage wr, the no-shirking wage, just sufficient to deter shirking is:
\[w=w_r+c+\text{rent}(s,c)\]Section 6.9 explains how to derive this expression for the no-shirking wage.
We will suppose that for each tutor, the cost of effort amounts to €25 per week, and the required rent is equal to €35 per week. Then the no-shirking wage is:
\[\begin{align*} w&=w_r+25+35 \\ &=w_r+60 \end{align*}\]In Figure 6.11, we have plotted the no-shirking wage curve €60 above the reservation wage curve. If we think of potential tutors as lined up in order of their reservation wages, Marc, with reservation wage €650, is the 40th, and Françoise, whose reservation wage is €600, is the 20th. In each case, their no-shirking wage is €60 above their reservation wage.
Figure 6.11 The no-shirking wage curve.
What can the school do if it wants to employ 40 tutors? A wage of €650 is enough to recruit them, but then Marc, Françoise, and more than half of the others have no incentive to work because the wage is below their no-shirking wage.
Figure 6.11 suggests that to ensure that none of them shirk, the school should set the wage at €710.
But there is one more problem: if the school offered €710, some workers with reservation wages higher than Marc would accept the offer. But they would shirk, because their no-shirking wage is above €710. To overcome this problem, the firm will need to interview its applicants to find out more about them, and make offers only to those it expects to work hard—that is, the ones with reservation wages below €650.
The importance for individual firms and workers of learning more about each other before they commit themselves to an employment contract is one of the reasons that matching in the labour market takes time and effort. In practice, firms hold interviews for most jobs. Assessing who is likely to work hard may be difficult, but in this simple model we will assume that our firm can screen applicants perfectly.
Then, the no-shirking line in Figure 6.11 tells us the lowest wage the school can set if it wants to employ a given number of workers and ensure that they work hard. To employ 40 non-shirking workers, it could set a wage of €710, and screen applicants to recruit only those who will work hard at this wage.
- feasible set
- All of the combinations of goods or outcomes that a decision-maker could choose, given the economic, physical, or other constraints that they face. See also: feasible frontier.
But it could set a higher wage. If the school chose a wage of €730, there would be more applicants for each vacancy, but it could choose only to hire enough to maintain employment at 40. Figure 6.12 shows the school’s feasible set of wages and employment. All the points above the no-shirking wage curve are feasible.
Figure 6.12 The feasible set.
If the school’s owners want to make as much profit as possible, what wage should they set? To answer this question they need to consider how profit depends on N and w.
Profit and isoprofit curves
A firm’s profits are equal to sales revenue minus input costs.
Suppose that each tutor generates revenue of y = €800 per week for the school in student fees. To keep the model simple, assume that wages are the school’s only input cost. Then if N tutors are employed at wage w, the net profit from employing each tutor is 800 – w, and the school’s total profit is:
\[\begin{align*} \text{profit per week}&=(y-w) \times N\\ &=(800-w)N \end{align*}\]As long as the wage is below €800, it will make a profit. The lower the wage, w, and the larger the number, N, of tutors employed, the more profit it will make.
- isoprofit curve
- A curve that joins together the combinations of prices and quantities of a good that provide equal profits to a firm.
We can represent profit in a diagram by finding different combinations of w and N that give the same amount of profit. For example, with N = 10 and w = €650, profit = €1,500. Other ways to obtain profit of €1,500 would be N = 40 and w = €762.50, or N = 75 and w = €780. In Figure 6.13, we have drawn a curve joining these three points with all the other combinations of N and w that give €1,500 of profit. This is called an isoprofit curve (‘iso’ means ‘same’ in Greek). Work through Figure 6.13 to understand how other isoprofit curves can be drawn.
- indifference curve
- A curve that joins together all the combinations of goods that provide a given level of utility to the individual.
We could describe the isoprofit curves as the firm’s indifference curves: the firm is indifferent between combinations of w and N giving the same level of profit. Isoprofit curves have the following characteristics:
- They slope upward: If you start at point A, for example, and then increase the number of workers, you do not need as much profit per worker to keep total profit constant. Therefore you can raise the wage.
- They have higher levels of profit towards the bottom right of the diagram, where N is high and w is low.
- They all have a similar curved shape: They are steep when N and w are both low, and quite flat when N and w are both high.
To understand the last property, consider what happens when you increase the number of workers, N, by one. How much do you have to change the wage to stay on the same isoprofit curve—that is, to make the same profit as before? Figure 6.14 shows this calculation for two points on the 1,500 isoprofit curve. When w and N are low, you make a lot of profit on the additional worker, and you have to increase w a lot to offset this extra profit: the slope of the curve is high. When w and N are high, profit on the extra worker is low and you don’t have to adjust the wage as much.
Compare two points on the 1,500 isoprofit curve | If you increase N by 1, how much do you have to raise the wage to stay on the same curve? | |||||||
---|---|---|---|---|---|---|---|---|
N | w | Profit | Profit per worker | N + 1 | Profit goes up by: | To keep profit constant, raise the wage by: | Slope | |
Low w and N | 5 | 500 | 1,500 | 300 | 6 | 300 | 300/6 = 50 | High |
High w and N | 75 | 780 | 1,500 | 20 | 76 | 20 | 20/76 = 0.26 | Low |
Figure 6.14 Calculating the slope at two points on an isoprofit curve.
Maximizing profit
Profit is high when N is high and w is low. But not all combinations of N and w are feasible. The best the school can do is to find the most profitable combination in the feasible set. Figure 6.15 brings together the isoprofit curves and the feasible set of (N, w) combinations—the points on or above the no-shirking wage curve—so that we can find the one that gives maximum profit.
Figure 6.15 Where is the highest profit in the feasible set?
There are no feasible points with profit as high as €5,000: the firm cannot reach the €5,000 isoprofit curve. But there are feasible points with profit of €3,000, and other points with higher profit than that.
Profit is always higher at a point on the no-shirking wage curve than at any point vertically above it. So the school will always choose a point on this curve: it tells us the wage that the school will set for any given level of employment.
In Figure 6.16, we have drawn the highest isoprofit curve that the firm can reach—the one where profit is €3,610, which just touches the no-shirking wage curve.
Figure 6.16 Maximum profit of €3,610 is achieved at point E, where w = €705 and N = 38.
The firm makes the maximum feasible amount of profit at point E, employing 38 tutors at a wage of €705.
Profit is maximized at the tangency point of the reservation curve and the isoprofit curves—just as, in Unit 3, utility is maximized where the budget constraint is tangent to an indifference curve.
To understand why, imagine yourself moving along the no-shirking wage curve. Start where N is small, near the vertical axis: profit there will be low. As you move along the line, you cross the €1,500 isoprofit curve, then the €3,000 one—profit is rising until you reach point E, where profit is €3,610. But if you keep going, profit starts to fall; you hit the €3,000 curve again, then €1,500. Point E is the best you can do.
Our model of wage setting tells us the following:
- The number of workers a firm can employ depends on its wage, and the reservation wages of potential employees (the reservation wage curve). To increase employment it needs to raise the wage, in order to recruit employees with higher reservation wages.
- The firm chooses a wage on the no-shirking wage curve, which lies above the reservation wage curve. The difference between the two is the cost of effort, and the employment rent required to deter shirking.
- It chooses the point where the no-shirking wage curve touches the highest possible isoprofit curve.
- labour market power
- A firm has labour market power (sometimes called monopsony power) if it can reduce the wage it needs to pay its workers by lowering the number of workers that it employs. See also: monopsony power.
In this model, the firm faces a trade-off: to employ more workers it has to raise wages. As long as the wage is less than €800, the language school makes a profit on each tutor employed—so it would like to employ more. But then it would have to raise the wage, reducing the profit on every tutor. Restraining employment keeps the wage down, enabling it to make a high profit on each employee. The firm’s ability to control wages in this way is called labour market power.
Our model of wage setting demonstrates how firms can set wages both to recruit and retain workers, and to provide them with an incentive to work hard. In the next section, we will examine the implications: how wages and employment are affected when economic conditions change.
Question 6.11 Choose the correct answer(s)
Read the following statements about Figure 6.16 and choose the correct option(s).
- (30, €700) is above the no-shirking wage curve, so it is a feasible choice for the firm (though it gives lower profits of €3,000).
- (19, €610) is on the same isoprofit (€3,610) as point E, but (16, €550) gives a higher profit of (800 – 550) × 16 = €4,000.
- The firm’s profit is always maximized at the tangency point of the no-shirking wage curve and the isoprofit curves. The isoprofit curves have steeper slopes at lower levels of employment, so the tangency point would be at a lower level of employment than point E.
- The firm’s profit is always maximized at the tangency point of the no-shirking wage curve and the isoprofit curves, so the profit-maximizing point will be on the no-shirking wage curve even if the firm has labour market power.
Exercise 6.9 Competition and profits
Suppose that the language school in Figure 6.16 now faces more competition from other schools. Explain, using a diagram like Figure 6.16, how increased competition would affect:
- the no-shirking wage curve
- the firm’s profit maximizing choice
- the firm’s profits.