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

3.6 Hours of work and technological progress

As Unit 2 explains, new technologies raise the productivity of labour. If workers have sufficient bargaining power to share the benefits with their employers, their wages will rise. Figure 2.18 shows how labour productivity—and subsequently, wages—rose in the centuries following the take-off of the permanent technological revolution. We now have the tools to analyse the effects of increased wages on working hours, and on overall living standards, which depend on both free time and income.

In 1930, John Maynard Keynes, a British economist, published an essay entitled ‘Economic Possibilities for our Grandchildren’, in which he suggested that in the 100 years that would follow, technological improvement would make us, on average, about eight times better off.1 What he called ‘the economic problem, the struggle for subsistence’ would be solved, and we would not need to work more than 15 hours per week to satisfy our economic needs. The question he raised was: how would we cope with all of the additional leisure time?

Keynes’s prediction for the rate of technological progress in countries such as the UK and the US has been approximately right, and Figure 3.1 shows that working hours have indeed fallen, although much less than he expected—it seems unlikely that average working hours in any country will be 15 hours per week by 2030.

To analyse how working people respond to rising wages, we will apply our model of constrained choice. As a first step, we will examine how a higher wage would change Karim’s choice of working hours. Remember, he expects to be able to earn €30 an hour when he moves to Madrid, and at that wage he would like to work for seven hours per day. He would obtain an income of €210 per day to spend on consumption, and have 17 hours free for other activities.

Suppose that when he arrives in Madrid, he finds that workers with his qualifications are much in demand, and there are jobs available at a wage of €45 per hour. How will this change his decision?

When the wage increases from €30 to €45 per hour, Karim’s feasible set expands. Follow the steps in Figure 3.9 to analyse how this change will affect his choice of hours.

In this diagram, the horizontal axis shows hours of free time per day, and ranges from 8 to 24. The vertical axis shows consumption spending in euros, and ranges from 0 to 600. Coordinates are (hours of free time, consumption spending). A straight line connects points (8, 480) and (24, 0). A downward-sloping, convex curve is tangent to the straight line at point E (17, 210). A steeper straight line connects points (8, 720) and (24, 0). Another downward-sloping, convex curve is tangent to this line at point F (17 and a third, 300).
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Figure 3.9 How Karim’s choice changes when the wage rises.

Karim’s utility-maximizing choice at the original wage: In this diagram, the horizontal axis shows hours of free time per day, and ranges from 8 to 24. The vertical axis shows consumption spending in euros, and ranges from 0 to 600. Coordinates are (hours of free time, consumption spending). A straight line connects points (8, 480) and (24, 0). A downward-sloping, convex curve is tangent to the straight line at point E (17, 210).
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Karim’s utility-maximizing choice at the original wage

With a wage of €30 per hour, Karim chooses point E, with 17 hours of free time and consumption of €210 per day.

An increase in the wage: In this diagram, the horizontal axis shows hours of free time per day, and ranges from 8 to 24. The vertical axis shows consumption spending in euros, and ranges from 0 to 600. Coordinates are (hours of free time, consumption spending). A straight line connects points (8, 480) and (24, 0). A downward-sloping, convex curve is tangent to the straight line at point E (17, 210). A steeper straight line connects points (8, 720) and (24, 0).
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An increase in the wage

When the wage rises, the budget constraint changes. If Karim took 24 hours of free time, his consumption would still be zero, as before. But for every hour of free time he gives up to work, his income and consumption will now be higher than before. The budget constraint pivots outwards around the point (24,0).

The budget constraint is steeper: In this diagram, the horizontal axis shows hours of free time per day, and ranges from 8 to 24. The vertical axis shows consumption spending in euros, and ranges from 0 to 600. Coordinates are (hours of free time, consumption spending). A straight line connects points (8, 480) and (24, 0). A downward-sloping, convex curve is tangent to the straight line at point E (17, 210). A steeper straight line connects points (8, 720) and (24, 0).
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The budget constraint is steeper

A rise in the wage from €30 to €45 per hour makes the budget constraint steeper. The slope changes from –30 to –45.

The feasible set is larger: In this diagram, the horizontal axis shows hours of free time per day, and ranges from 8 to 24. The vertical axis shows consumption spending in euros, and ranges from 0 to 600. Coordinates are (hours of free time, consumption spending). A straight line connects points (8, 480) and (24, 0). A downward-sloping, convex curve is tangent to the straight line at point E (17, 210). A steeper straight line connects points (8, 720) and (24, 0). Another downward-sloping, convex curve is tangent to this line. at point F (17 and a third, 300).
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The feasible set is larger

Karim’s feasible set has expanded. Now he has a wider choice of combinations of consumption and free time, and he can reach a higher indifference curve.

The new utility-maximizing choice: In this diagram, the horizontal axis shows hours of free time per day, and ranges from 8 to 24. The vertical axis shows consumption spending in euros, and ranges from 0 to 600. Coordinates are (hours of free time, consumption spending). A straight line connects points (8, 480) and (24, 0). A downward-sloping, convex curve is tangent to the straight line at point E (17, 210). A steeper straight line connects points (8, 720) and (24, 0). Another downward-sloping, convex curve is tangent to this line at point F (17 and a third, 300).
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The new utility-maximizing choice

He will choose the point on the new budget constraint that reaches the highest possible indifference curve. The best choice is point F, where the new budget constraint is tangent to an indifference curve.

A higher wage raises Karim’s living standards: In this diagram, the horizontal axis shows hours of free time per day, and ranges from 8 to 24. The vertical axis shows consumption spending in euros, and ranges from 0 to 600. Coordinates are (hours of free time, consumption spending). A straight line connects points (8, 480) and (24, 0). A downward-sloping, convex curve is tangent to the straight line at point E (17, 210). A steeper straight line connects points (8, 720) and (24, 0). Another downward-sloping, convex curve is tangent to this line at point F (17 and a third, 300).
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A higher wage raises Karim’s living standards

Karim will choose point F, increasing his utility (living standards). Here he will have more free time (17 hours and 20 minutes per day) and higher consumption (€300). As a result of the wage rise, he wants to reduce his work hours by 20 minutes per day.

With the higher wage, Karim will choose point F, where the new budget constraint is tangent to indifference curve IC4, giving him more utility than at point E. Because the feasible set has expanded, he can achieve a higher standard of living. To obtain the highest possible utility, he chooses the point on his new budget constraint where \(\text{MRS} = w\), so that his two trade-offs are in balance. His marginal rate of substitution between free time and consumption is equal to the marginal rate of transformation between them—which is now higher, because it is given by the wage.

In Figure 3.9, the effect of the wage rise is that Karim chooses to have more of both goods: not only higher consumption but also more free time. It is important to realize that this is just one possible result. Had we drawn the shape of the indifference curves differently, the tangency point would have been different. The higher wage definitely makes it feasible to have both more consumption and more free time, but whether Karim will choose to have more of both depends on his preferences between the two goods.

The reason why is that the increase in wage affects Karim in two ways.

income effect
The effect that an increase in income has on an individual’s demand for a good (the amount that the person chooses to buy) because it expands the feasible set of purchases. When the price of a good changes, this has an income effect because it expands or shrinks the feasible set, and it also has a substitution effect. See also: substitution effect.
substitution effect
When the price of a good changes, the substitution effect is the change in the consumption of the good that occurs because of the change in the good’s relative price. The price change also has an income effect, because it expands or shrinks the feasible set. See also: income effect.

First, it moves the budget constraint outwards, expanding his feasible set. He is better off: he can now choose combinations of consumption and free time that he couldn’t afford before. This is called the income effect: in general, if we can afford to have more of the goods we value—including free time—we will want to do so.

The income effect of a wage rise makes Karim want to take more free time.

Secondly, the wage rise increases the opportunity cost of free time, giving him a greater incentive to work. Taking an extra hour of free time now costs more in lost consumption. This tips the balance towards consumption rather than free time, encouraging him to work more. This is called the substitution effect: if one good (free time in this case) becomes more expensive relative to the other, we will use our resources to obtain less of it, and more of the other. We will want to substitute some of one good for the other.

The substitution effect of a wage rise makes Karim want to take less free time.

So these two effects of a wage rise work in opposite directions. In Figure 3.9, the income effect dominates. At any level of free time, Karim can obtain higher consumption than before. He takes advantage of the additional income to have more free time. But it is also possible for the extra incentive to work to dominate, in which case workers respond to rising wages by working longer hours.

Keynes, in considering what might happen over the course of a century, correctly predicted that hours of work would fall. He argued that with much higher wages, his grandchildren’s generation would easily be able to satisfy their material needs and live a comfortable life. He was assuming that as their incomes rose, they would attach relatively less value to increasing income further. Interpreting his argument using our model, we could say that he thought that the income effect would outweigh the increased incentive to work.

But in predicting that working time would fall to 15 hours a week, he seems to have underestimated the strength of the preference for working and consuming that would affect the decisions of future workers as prosperity rose. Later in this unit, we will discuss some reasons why preferences may have changed.

Question 3.8 Choose the correct answer(s)

Starting from a diagram like Figure 3.9, consider what would happen to Karim’s utility-maximizing choice of consumption and working time if his wage increased further, to €60 an hour. Based on this information, read the following statements and choose the correct option(s).

  • The opportunity cost of free time would fall, so he would take more free time.
  • He may choose to work longer hours and consume less.
  • He may decide to work 9 hours a day, as he did when the wage was €30.
  • His living standards may fall, if hours of work are high at the utility-maximizing point.
  • The opportunity cost of free time is equal to the wage. So the opportunity cost of free time would rise to €60 an hour. But he may take more free time.
  • He would not reduce both free time and consumption, because that would give him lower utility than he has at point F.
  • Working hours at the new utility-maximizing choice could be the same as at points E or F—or higher, or lower, depending on the shape of his indifference curves.
  • After the wage rise, F would still be feasible. But Karim will choose a point with higher utility, or in other words, higher living standards.

Exercise 3.6 Why do people still work long hours?

An article by Tim Harford in the Undercover Economist column of the Financial Times considers why we have not reduced working hours as much as Keynes expected.2

  1. What are the main reasons he suggests for this observation? Would these reasons affect some groups of workers more than others?
  2. If Tim Harford is right, what has happened to our marginal rate of substitution between consumption and free time as prosperity has increased?
  1. John Maynard Keynes. 1963. ‘Economic Possibilities for our Grandchildren’. In Essays in Persuasion, New York, NY: W. W. Norton & Co. 

  2. Tim Harford. 2015. ‘The rewards for working hard are too big for Keynes’s vision’. The Undercover Economist. First published by The Financial Times. Updated 3 August 2015.