Commuters rushing to work across Reuters Square: Doug Armand
Commuters rushing to work across Reuters Square.

Unit 3 Doing the best you can: Scarcity, wellbeing, and working hours

How individuals do the best they can within the options available, and how they resolve the trade-off between earnings and free time

Before you start

To develop the models in this unit, we will use the economic concepts and modelling principles set out in Section 2.2: Economic decisions: Opportunity costs, economic rents, and incentives, and Section 2.8: Economic models: How to see more by looking at less. You should be familiar with these before beginning work on this unit.

3.1 Would you work fewer hours if your hourly wage doubled?

Imagine that you are working in New York, in a job that is paying you $15 an hour for a 40-hour working week, which gives you earnings of $600 per week. There are 168 hours in a week so, after 40 hours of work, you are left with 128 hours of free time for all your non-work activities, including leisure and sleep.

Suppose, by some happy stroke of luck, you are offered a job at a much higher wage—six times as high. Your new hourly wage is $90. Not only that, but your prospective employer lets you choose how many hours you work each week.

Will you carry on working 40 hours per week? If you do, your weekly pay will be six times as high as before: $3,600. Or will you decide that you are satisfied with the goods you can buy with weekly earnings of $600? You can now earn this by cutting your weekly hours to just 6 hours and 40 minutes (a six-day weekend!), and enjoy about 26% more free time than before. Or would you use this higher hourly wage rate to raise both your weekly earnings and your free time by some intermediate amount?

The idea of suddenly receiving a sixfold increase in your hourly wage and being able to choose your own hours of work might not seem very realistic. But Unit 2 demonstrates that technological progress since the Industrial Revolution has been accompanied by a dramatic rise in wages. In fact, the average real hourly earnings of American workers did increase more than sixfold during the twentieth century. And while employees ordinarily cannot just tell their employer how many hours they want to work, over long time periods the typical hours that we work do change. In part, this is a response to how much we prefer to work. As individuals, we can choose jobs with higher or lower hours, although this may restrict our options. Political parties also respond to the preferences of voters, so changes in typical working hours have occurred in many countries as a result of legislation that imposes maximum working hours.

So, have people used economic progress as a way to consume more goods, enjoy more free time, or both? The answer is both, but in different proportions in different countries. While hourly earnings increased by more than sixfold for twentieth-century Americans, their average annual work time fell by a little more than one-third. People at the end of the century enjoyed a fourfold increase in annual earnings with which they could buy goods and services, and an increase of just under one-fifth in their free time. How does this compare with the choice you made when our hypothetical employer offered you a sixfold increase in your wage?

Figure 3.1 shows trends in income and working hours since 1870 in three countries.

As in Unit 1, income is measured as per capita GDP in US dollars. This is not the same as average earnings from employment, because it includes other forms of income such as profits, and interest on savings. But it gives us a useful indication of employment income for the purposes of comparison across countries and through time. In the late nineteenth and early twentieth century, average income approximately trebled, and hours of work fell substantially.

During the rest of the twentieth century, income per capita rose fourfold. Hours of work levelled off in the US, where there has been little change since 1960, but continued to fall (albeit more slowly) in the Netherlands and France, levelling off around the end of the century.

In this line chart, the horizontal axis shows GDP per capita at PPP 1990 US dollars, and ranges between 1,000 and 57,000 dollars. The vertical axis shows annual hours worked, and ranges between 1,000 and 3,400. Data for different countries and time periods is shown: for the Netherlands, between 1870 and 2018; for France between 1900 an 2018; and for the US, between 1890 and 2018. In the first half of the 20th century, hours of worked for all three countries decreased from approximately 3,000 to 2,000, and GDP per capita increased from 3,000 dollars to 9,000 dollars. From the 1950s until 2018, in the US hours of work stabilised around 2,000 and GDP per capita rose to almost 57,000 dollars; in France, hours of work stabilised around 1,600 and GDP per capita rose to almost 41,000 dollars; and in the Netherlands, hours of work stabilised around 1,400 and GDP per capita rose to almost 49,000 dollars.
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Figure 3.1 Annual hours of work and income (1870–2018).

J. Bolt and J. L. van Zanden. 2020. Maddison Project Database, version 2020. ‘Maddison style estimates of the evolution of the world economy. A new 2020 update’.; M. Huberman and C. Minns. 2007. ‘The times they are not changin’: Days and hours of work in Old and New Worlds, 1870–2000’. Explorations in Economic History 44 (4): pp. 538–567.; OECD. 2021. Average annual hours actually worked per worker. OECD Productivity database.

While many countries have experienced similar trends, there are differences in outcomes. Figure 3.2 illustrates the wide disparities in free time and income between countries in 2020. Here we have calculated free time by subtracting average annual working hours from the number of hours in a year. The higher-income countries seem to have lower working hours and more free time, but there are also some striking differences between them. For example, South Korea and France have similar levels of income, but French workers have much more free time. And Poland and the US have similar amounts of free time, but a large difference in income.

In this scatterplot, the horizontal axis shows average annual hours of free time per worker, and ranges between 6,600 and 7,500. The vertical axis shows GDP per capita in PPP dollars, and ranges between 0 and 100,000. Data for different countries is shown. In general, there is a positive relationship between hours of free time and GDP per capita.
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Figure 3.2 Annual hours of free time per worker and income (2020).

OECD. Average annual hours actually worked per worker.; OECD. Level of GDP per capita and productivity. Accessed January 2022.

In many countries, there has been a huge increase in living standards since 1870. But in some places, people have carried on working just as hard as before but consumed more, while in other countries people now have much more free time. Why has this happened? We will provide some answers to this question by modelling how people choose the hours they would like to work. The model of choice that we apply in this unit has applications to many other economic problems too.

Question 3.1 Choose the correct answer(s)

Currently, you work for 40 hours per week at the wage rate of £20 an hour. Your free hours are defined as the number of hours not spent working per week, which in this case is 24 hours × 7 days − 40 hours = 128 hours per week. Suppose now that your wage rate has increased by 25%. If you are happy to keep your total weekly income constant, then:

  • Your total number of working hours per week will fall by 25%.
  • Your total number of working hours per week will be 30 hours.
  • Your total number of free hours per week will increase by 25%.
  • Your total number of free hours per week will increase by 6.25%.
  • The new wage rate is £20 × 1.25 = £25 per hour. Your original weekly income is £20 × 40 hours = £800. Therefore, your new total number of working hours is £800/£25 per hour = 32 hours. This represents a change of (32 − 40)/40 = −20%.
  • The new wage rate is £20 × 1.25 = £25 per hour. Your original weekly income is £20 × 40 hours = £800. Therefore, your new total number of working hours is £800/£25 per hour = 32 hours.
  • The new wage rate is £20 × 1.25 = £25 per hour. Your original weekly income is £20 × 40 hours = £800. Therefore, your new total number of working hours is £800/£25 per hour = 32 hours. Then your free time is now 24 hours per day × 7 days per week − 32 = 136 hours per week, an increase of (136 − 128)/128 = 6.25%.
  • The new wage rate is £20 × 1.25 = £25 per hour. Your original weekly income is £20 × 40 hours = £800. Therefore, your new total number of working hours is £800/£25 per hour = 32 hours. Then your free time is now 24 × 7 − 32 = 136 hours per week, an increase of (136 − 128)/128 = 6.25%.

Question 3.2 Choose the correct answer(s)

Figure 3.1 depicts the annual number of hours worked against GDP per capita in the US, France, and the Netherlands, between 1870 and 2018. Read the following statements and choose the correct option(s).

  • An increase in GDP per capita causes a reduction in the number of hours worked.
  • The GDP per capita in the Netherlands is lower than that in the US because Dutch people work fewer hours.
  • Between 1870 and 2000, French people have managed to increase their GDP per capita more than tenfold, while more than halving the number of hours worked.
  • Based on the evidence in the figure, the Netherlands will need to increase working hours to levels similar to the US to reach an income per capita of $30,000.
  • The negative relationship between the number of hours worked and GDP per capita does not necessarily imply that one causes the other.
  • While it is true that average annual hours of free time is higher in the Netherlands than in the US, working fewer hours does not necessarily mean GDP per capita must be lower (for example, Switzerland has higher average annual hours of free time than the US and a higher GDP per capita). The lower GDP per capita in the Netherlands may be due to a number of factors, including the possibility that Dutch people may prefer less income but more leisure time for cultural or other reasons.
  • The GDP per capita of France increased from less than $3,000 to more than $30,000 (tenfold) while annual hours worked fell from over 3,000 to under 1,500.
  • The US increased GDP per capita from $25,000 to $30,000 without any increase in working hours. But we cannot tell from the figure whether that is possible at the lower level of working hours in the Netherlands.