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

3.8 Is this a good model?

We have modelled the way people decide how long to spend working by assuming that they will make the best choice they can from the available combinations of two goods: consumption spending and free time. We have described their preferences using indifference curves, and their feasible set by working out their budget constraint. The model tells us that their best (utility-maximizing) choice is the level of working hours at which the feasible frontier is tangent to the indifference curve: in other words, where MRT = MRS.

You may have been thinking: this is not what people do!

Billions of people organize their working lives without knowing anything about MRS and MRT. (If they did make decisions that way, perhaps we would have to subtract the hours they would spend on calculations). And even if they did make their choice using mathematics, most people can’t just start and leave work whenever they want. So how can this model be useful?

As we explain in Section 2.8, models help us ‘see more by looking at less’. Lack of realism is an intentional feature of this model, not a shortcoming.

Trial and error replaces calculations

Can a model that ignores how we think possibly be a good model of how we choose?

Milton Friedman, an economist, explained that when economists use models in this way, they do not claim that we actually think through these calculations (such as equating MRS to MRT) each time we make a decision. Instead, we each try various choices (sometimes not even intentionally) and we tend to adopt habits or rules of thumb that make us feel satisfied and not regret our decisions.

In his book, Essays in Positive Economics, he described it as similar to playing billiards.

Consider the problem of predicting the shots made by an expert billiard player. It seems not at all unreasonable that excellent predictions would be yielded by the hypothesis that the billiard player made his shots as if he knew the complicated mathematical formulas that would give the optimum directions of travel, could estimate accurately by eye the angles, etc., describing the location of the balls, could make lightning calculations from the formulas, and could then make the balls travel in the direction indicated by the formulas.

Our confidence in this hypothesis is not based on the belief that billiard players, even expert ones, can or do go through the process described. It derives rather from the belief that, unless in some way or other they were capable of reaching essentially the same result, they would not in fact be expert billiard players.¹

Milton Friedman. 1953. Essays in Positive Economics (7th ed.). Chicago: University of Chicago Press. Close footnote

Similarly, if we see a person regularly choosing to go to the library after lectures instead of going out, or not putting in much work on their farm, or asking for longer shifts after a pay rise, we do not need to suppose that this person has done the calculations we set out. If that person later regretted the choice, next time they might go out a bit more, work harder on the farm, or cut their hours back. Eventually, we could speculate that they might end up with a decision on work time that is close to the result of our calculations.

That is why economic theory can help to explain, and sometimes even predict, what people do—even though those people are not performing the mathematical calculations that economists make in their models.

Ceteris paribus

Another objection might be that we have left out important factors that influence decisions about working hours. We have assumed that workers only care about two goods, free time and consumption. But they may also care—for example—about their future career, and work longer hours to gain valuable experience and opportunities for promotion. And their decision may depend on the other demands on their time: for example on how many children they have and the availability of childcare. Does it matter that we have left these things out of the model?

ceteris paribus

Economists often simplify analysis by setting aside things that are thought to be of less importance to the question of interest. The literal meaning of the expression is ‘other things equal’. In an economic model, it means an analysis ‘holds other things constant’.

The answer is that it may not matter, as long as we are aware of the factors that we are ‘holding constant’. We can use the model to make statements about how people will respond to a rise in wages, ceteris paribus⁠ceteris paribus Economists often simplify analysis by setting aside things that are thought to be of less importance to the question of interest. The literal meaning of the expression is ‘other things equal’. In an economic model, it means an analysis ‘holds other things constant’.close (holding other things constant). But we need to be aware that the statements would no longer be valid if those other things did change. So it might be the case that if an employer raised wages, the employees would like to increase their hours ceteris paribus, but if the employer closed the workplace nursery at the same time, the wage rise would not have the same effect.

The ceteris paribus assumptions can make it difficult to apply a model to changes that happen over a long period of time: the longer the period, the more likely it is that other things will change too.

The representative worker

We have developed a model of the choice made by a single worker, and we have analysed how the decision depends on the worker’s preferences and feasible set. How can we use it to explain the behaviour of large groups of workers—for example, all the workers in a particular country at a particular time?

In a large group, each individual will make a different decision, depending on their own preferences and feasible set. But we can use the model to understand their average behaviour if we think of it as representing the decision of a typical, or ‘representative’ worker: a worker whose preferences are typical of those in the group, and whose feasible set is determined by the average wage.

In later sections of this unit, we will apply our model of wages and working hours to help us understand data for average wages in different countries and how they have changed over time. We will interpret the data as resulting from the decisions of representative workers. But again, we will need to be careful: the typical worker that Keynes was thinking about in Britain in 1930 may be very different from typical workers in Britain, or China, in the twenty-first century.

The influence of culture and politics

Another unrealistic aspect of the model is that employers, rather than individual workers, typically choose working hours, and employers often impose a longer working day than workers prefer. And as a result, the hours that many people work are regulated by law, so that beyond some maximum amount, neither the employee nor the employer can choose hours. In this case, the government has limited the feasible set of hours and goods.

Although individual workers often have little freedom to choose their hours, it may nevertheless be the case that changes in working hours over time, and differences between countries, partly reflect the preferences of workers. If many individual workers in a democracy wish to lower their hours, they may ‘choose’ this indirectly as voters, if not individually as workers. Or they may bargain as members of a trade union for contracts requiring employers to pay higher overtime rates for longer hours.

This explanation stresses the influence of culture (leading to preferences that are shared by people within a society or country, and different from those in other societies) and politics (meaning the effects of laws, or trade union strength and objectives). They certainly help to explain differences in working hours between countries.

Cultures seem to differ. Some northern European cultures value their vacations highly, while South Korea is famous for the long hours that employees put in. Legal limits on working time differ. In Belgium and France, the normal work week is limited to 35 to 39 hours, while in Mexico the limit is 48 hours and in Kenya even longer.

But, even on an individual level, we may influence the hours we work. For example, employers who advertise jobs with the working hours that most people prefer may find they have more applicants than other employers who offer too many (or too few) hours.

In summary, our model of working hours omits many things that influence what people do in practice, and it is important to think about whether the omissions matter for any conclusions that we draw. But we judge the quality of a model by whether it provides insight into something that we want to understand. In the next section, we will explore whether our simplified model of the choice of hours of work can help us understand why working hours have changed over time.