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

3.2 A problem of choice and scarcity

scarcity
A good is scarce if it is valued, and there is an opportunity cost of acquiring more of it.
income, disposable income
Income, also known as disposable income, is the amount of profit, interest, rent, labour earnings, and other payments (including transfers from the government) received, net of taxes paid, measured over a period of time such as a year. Your income is the maximum amount that you could consume per period and leave your wealth unchanged.

To help us understand how and why working hours differ between countries and change over time, we will study a basic problem of economics—scarcity—and how people make choices when they cannot have all of everything that they want, such as goods and free time. Study the model of decision-making that we use carefully! It is used repeatedly throughout this book, because it provides insight into a wide range of economic problems.

We will build a model of how an individual worker decides how much time to spend working. One of the important factors in the decision will be the available wage, but individuals will make different decisions, even if they can earn the same wage, depending on their own preferences and circumstances.

Consider the situation of Karim, who has just completed an online Business Studies course, and has decided to move to Madrid to find work. Newly qualified Business Studies graduates can expect to earn €30 an hour. Karim wants to earn enough to cover day-to-day living costs in Madrid, but also to have enough time to enjoy getting to know the city and making new friends. How many hours should he work each week? Should he find a part-time job, to have plenty of time for his social life? Or is it more important to find a job with longer hours, to increase his income so that he can afford a more comfortable apartment?

Together, the wage and the hours of work will determine his total income. If we write \(w\) for the wage, and he works for an average of \(h\) hours per day, then his daily income, \(y\), is given by:

\[y = wh\]

Figure 3.3 shows graphically how his income depends on hours of work, when his hourly wage is €30. For example, if he works for four hours he is at point A with an income of €120 per day. We will assume that he cannot work more than 16 hours per day on average—he needs time to sleep, eat, and travel to work.

In this diagram, the horizontal axis shows hours of work per day, and ranges between 0 and 16. The vertical axis shows income in euros, and ranges between 0 and 600. Coordinates are (hours of work, income). An upward sloping straight line starting from the origin passes through point A with coordinates (4, 120) and point B with coordinates (10, 300).
Fullscreen
Hours of work 0 2 4 6 8 10 12 14 16
Income (€) 0 60 120 180 240 300 360 420 480

Figure 3.3 Karim’s income depends on his working hours.

Figure 3.3 is a bit like a production function, such as the one in Unit 1 for farmers producing grain. Karim’s total income increases with his hours of work, so it is an upward-sloping line. But since, unlike the farmers, he receives the same amount for every hour he works, it is a straight line. The slope of the line is constant, and equal to the wage, because at every point, an increase of one hour of working time leads to an increase of €30 in income. Alternatively, you can work out the slope by taking any two points, such as A and B in the figure, and calculating:

\[\begin{align} \text{slope} &= \frac{\text{vertical change}}{\text{horizontal change}} \\ &= \frac{180}{6} \\ &= 30 \end{align}\]
consumption
Expenditure on consumer goods. Consumer goods include both short-lived goods and services and long-lived goods, which are called consumer durables.

If Karim’s income depends on his hours according to the function shown in Figure 3.3, how many hours per day will he choose to work? The decision depends on the things that he cares about. If he cared only about money, he should work for 16 hours a day to maximize his income. But, like other people, Karim also cares about his free time—he wants to be able to relax, meet friends, and explore the city. And he is concerned about income not for itself, but for what it enables him to spend on food, accommodation, and other goods and services including leisure activities—in other words, his consumption.

scarcity
A good is scarce if it is valued, and there is an opportunity cost of acquiring more of it.

Karim faces a problem of scarcity: he would like to enjoy both a high level of consumption and plenty of free time, but his choice is constrained by the relationship between hours and income. In the next section, we will introduce a way of describing his objective more precisely.

Question 3.3 Choose the correct answer(s)

Based on the information in Figure 3.3, read the following statements and choose the correct option(s).

  • Karim will always choose to work 16 hours because doing so maximizes his total income.
  • If Karim’s maximum working hours per day increased by two hours, under the same hourly wage, his maximum income would be €540.
  • If Karim had ten hours of free time per day and spent the rest of his time working, his daily income would be €300.
  • If Karim’s hourly wage were instead €20, the slope of the line relating his income to working hours would be less steep than that shown in Figure 3.3.
  • If Karim also cares about free time, he may not choose to work 16 hours. He may prefer to have less income and more free time.
  • Karim’s maximum total income would now be 30 × 18 = €540.
  • If Karim had ten hours of free time per day, he would be working 14 hours, so his daily income would be €420.
  • The slope of the line is equal to his hourly wage, so when his hourly wage is €20, the line will be less steep compared to when his hourly wage is €30.