**Unit 6** The firm and its employees

## 6.8 Counting the cost of job loss: Rents and reservation wages

In this section, we calculate the employment rent received by Maria, an employee earning $12 an hour for a 35-hour working week, when she exerts the amount of effort her employer requires. In the next section, we will show how her employer can use rents to motivate her to work hard.

To determine Maria’s rent, we need to think how she would evaluate two aspects of her job:

*her pay:*something she values*how hard she works:*effort is costly for her.

- 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.

We can weigh these elements against each other using the concept of **utility**: her utility is increased by the goods and services she can buy with her wage, but reduced by the unpleasantness of going to work and working hard all day—the disutility of work.

Suppose that the required effort costs her the equivalent of $2 per hour. Then while she remains in her job she receives:

\[\begin{align*} \text{net utility per hour} &= \text{wage} − \text{disutility of effort per hour} \\ &= \$10 \end{align*}\]To calculate her economic rent, we compare the value of staying in her job with the value of her next best alternative option, which is to be unemployed, and search for a new job.

### Building block

For more about calculating rents, read Section 2.2.

- 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.*

People who lose their jobs can typically expect some help from others while they are out of work if their family and friends have jobs. And in many economies, they receive an **unemployment benefit** or financial assistance from the government. Suppose that for each hour Maria spends unemployed rather than working, her net utility—allowing for both income from these sources and the disutility of being unemployed—is $6.

It might be many weeks before she finds another job. The overall cost of job loss depends on how long she expects to be unemployed, and how much she expects to earn when she finds a new job. Maria estimates it will take her 44 weeks to find a new job, and that the average net utility she can expect in a new job is $9 (the wage minus effort costs).

To compare the value of her job with the next best option, we will suppose that Maria’s planning horizon is three years (156 weeks). In other words, what matters to her is how she will support herself and her family over the next three years. She cannot foresee what might happen after that. Figure 6.8 compares her current job with the next best alternative of becoming unemployed, over the planning period.

The two lines in Figure 6.8a show Maria’s net hourly utility in her current job, and in her next best alternative, which is to become an unemployed job-searcher. The total value of the reservation option is $10,080 less than the value of her current job. Her total employment rent, $10,080, corresponds to the area between the two lines.

\[\text{total cost of job loss} = \text{total employment rent} = \text{\$10,080}\]It is often more convenient to think about the value of different employment options, and hence employment rents, in hourly or weekly terms, rather than calculating the total value over a long period. That is easy for Maria’s current job: it is worth $10 per hour for the whole period.

But what about her reservation option of unemployment? To evaluate this, we need to take into account not only that she will receive $6 per hour while unemployed, but that it gives her the opportunity to search for a new job. On average, over the whole period, her reservation option is worth:

\[\frac{\text{\$44,520}}{156 \times 35 \text{ hours}} = $8.15 \text{ per hour}\]Then we can say that Maria’s employment rent per hour is the difference between her net utility in the current job, and the average net utility of her reservation option:

\[\text{employment rent} = $10.00-$8.15 = $1.85 \text{ per hour}\]### Maria’s reservation wage

Using average values is also helpful because it allows us to think of the option ‘unemployment plus job search’ as equivalent, for Maria, to having a different job with net utility $8.15. She would be indifferent between an offer of a job worth $8.15 to her, and becoming unemployed and searching for a better job.

- 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.

So we can say that $8.15 is Maria’s **reservation wage**. It is a measure of how she ‘values’ unemployment, her reservation option. Rather than being an unemployed job-searcher, she would accept any job at a wage (or net utility if effort was required) greater than $8.15. Figure 6.8b illustrates this way of thinking about unemployment.

It is important to understand why Maria’s reservation wage is above the net utility of $6 she receives while unemployed. She would not accept a wage offer of $6, because she would do better to wait, and search for an offer closer to the average that other firms are offering. Her reservation wage, $8.15, represents the value to her of being unemployed and waiting for such an offer. While unemployed, she makes decisions as she would if she had a permanent job paying $8.15 per week.

The reservation wage depends both on her individual characteristics, which determine her own utility of unemployment, and on economy-wide things such as unemployment benefit and how easy it is to find a new job. To understand this more clearly, it is helpful to write a general expression for the reservation wage. Working in weeks rather than hours as above, suppose that:

- Her planning horizon is
*h*weeks. - Weekly unemployment benefit is
*b*. - Her additional net utility of being unemployed is
*a*per week. We label it^{M}*M*for Maria as a reminder that it depends on things that are specific to her, such as her family responsibilities, and whether she has any savings she can use. - The average net utility in other jobs (the wage minus the cost of effort) is
*v*per week. - She expects that it will take
*j*weeks to find another job.

Then if Maria enters unemployment, she expects to receive: *b* + *a ^{M}* for

*j*weeks, and net utility of

*v*for the remaining

*h*–

*j*weeks of her planning period. Maria’s reservation wage is the average value of her reservation option—that is, the total value divided by the number of weeks,

*h*:

We can rearrange this equation to write it as:

\[w_r=τ(b+a^M)+(1−τ)v\]In this expression, *τ* is equal to *j/h.* For an unemployed worker considering their planning horizon, *τ* is the proportion of time for which they can expect to remain unemployed. This will depend on the rate of unemployment in the economy. When there are many other unemployed people searching for jobs, the time taken to find a new job will be higher.

So Maria’s reservation wage is a weighted average of her utility while she is unemployed (*b* + *a ^{M}*), and the net utility

*v*that she expects to receive when she finds a new job. When labour market conditions are bad for workers, finding a job takes a long time: she will put more weight on her utility while unemployed. But when she can find a job quickly, her reservation wage will be higher: it will be weighted towards the average value,

*v*, of the job offers she expects to receive.

We have calculated Maria’s reservation wage using the ‘expected’ or ‘average’ length of unemployment. In practice, finding a job is uncertain: it may take less time, or more. Similarly, when she finds one the pay may be above or below average. Since she doesn’t know exactly what will happen, she bases the decision on the average values.

**Exercise 6.5** Assumptions of the model

As in all economic models, our simplified representation of Maria’s employment rent has deliberately omitted some aspects of the problem that might be important. For example, we have assumed that:

- Maria finds a job with a lower wage after her spell of unemployment.
- Maria continues to receive unemployment benefits as long as she remains unemployed.

Redraw Figure 6.8b to show how relaxing each of these assumptions would alter the employment rent. Specifically, assume:

- Maria finds a job with the same wage of $12 per hour after her spell of unemployment.
- Maria’s eligibility for unemployment benefits lasts for only 13 weeks.

**Question 6.10** Choose the correct answer(s)

Maria earns $12 per hour in her current job and works 35 hours a week. Her disutility of effort is equivalent to a cost of $2 per hour of work. If she loses her job, she will receive unemployment benefits equivalent to $4 per hour. Additionally, being unemployed has psychological and social costs equivalent to $1 per hour. Suppose that Maria’s planning horizon is 156 weeks, and that, if Maria were to become unemployed, she expects to find another job at the same wage and cost of effort after 44 weeks. Then:

- Maria’s net hourly benefit of being employed compared with unemployment is $7 for the first 44 weeks, but she receives a net hourly benefit of $0 for the remaining 112 weeks, so her employment rent will be less than $7 per hour. (Calculation: the total value of the next best alternative is ((10 − 3) × 35 × 44) + (10 × 35 × 112) = $43,820, and her employment rent per hour is 10 − (43,820 / (156 × 35)) = $1.97.)
- From the reservation wage equation, Maria’s reservation wage does not just depend on the size of the unemployment benefits and the costs of being unemployed; it also depends on the net utility of being unemployed, her planning horizon, and how long she expects to wait to find another job. Maria’s reservation wage is the total value of the next best alternative divided by the number of hours = ((7 × 35 × 44) + (10 × 35 × 112)) / (156 × 35) = 43,820 / 5,460 = $8.03.
- Maria’s employment rent = $7 (employment rent per hour) × 35 hours per week × 44 weeks = $10,780.
- If she could get a job at the same wage after 44 weeks, Maria’s total employment rent = $7 (employment rent per hour) × 35 hours per week × 44 weeks = $10,780. If the new job were to have a lower wage, her total employment rent in the current job (cost of job loss) would be higher than $10,780.