Unit 2 Technology and incentives

2.8 Economic models: How to see more by looking at less

Economic outcomes—for example, which goods and services are produced and how, or the distribution of incomes—depend on millions of interactions between economic actors. It would be impossible to understand the economy by describing every detail of how they act and interact. We need to be able to stand back and look at the big picture. To do this, we use models.

To create an effective model, we need to distinguish between the essential features of the economy that are relevant to the question we want to answer and should be included, and unimportant details that can be ignored.

Models come in many forms—we have encountered some of them already in Section 1.7, Section 2.2 and Section 2.6. The model of opportunity cost in Section 2.2 is expressed in words and numbers. The Malthusian model in Section 1.7 and the model in Section 2.6 of why firms adopted new technologies in the Industrial Revolution use mathematical representations (graphs), although we could have used equations instead. These models are not realistic—for example, firms face other costs beyond wages and energy prices. But they isolate an important factor (that is, the relative price of labour to coal), and they show how differences in this relative price could explain what happened. The fact that these models omit many details—and in this sense are unrealistic—is a feature, not a bug.

Some economists have used physical models to illustrate and explore how the economy works. For his 1891 PhD thesis at Yale University, Irving Fisher designed a hydraulic apparatus (Figure 2.16) to represent flows in the economy. It consisted of interlinked levers and floating cisterns of water to show how the prices of goods depend on the quantity of each good supplied, the incomes of consumers, and how much they value each good. The whole apparatus stops moving when the water levels in the cisterns are the same as the level in the surrounding tank. When it comes to rest, the position of a partition in each cistern corresponds to the price of each good. For the next 25 years, Fisher would use this contraption to teach students how markets work.

Irving Fisher’s sketch of his hydraulic model of economic equilibrium (1891).
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Figure 2.16 Irving Fisher’s sketch of his hydraulic model of economic equilibrium (1891).

William C. Brainard and Herbert E. Scarf. 2005. ‘How to Compute Equilibrium Prices in 1891’. American Journal of Economics and Sociology 64 (1): pp. 57–83.

How models are used in economics

Fisher’s study of the economy illustrates how all models are used:

  1. First he had a well-defined question: How do the prices of goods depend on the amount of each good supplied, the incomes of consumers, and how much they value each good?
  2. Second, he built a model to capture the elements of the economy that he thought mattered for the determination of prices, and the interactions between them.
  3. Then he used the model to demonstrate the thesis: he showed how the interactions between these elements could result in a set of prices that did not change.
  4. Finally, he conducted experiments with the model to discover the effects of changes in economic conditions: for example, if the supply of one good increased, what would happen to its price? And to the prices of all the other goods?

Irving Fisher’s dissertation represented the economy as a big tank of water, but he wasn’t an eccentric inventor. On the contrary, his machine was described by Paul Samuelson, himself one of the greatest economists of the twentieth century, as the ‘greatest doctoral dissertation in economics ever written’. Fisher became one of the most highly regarded economists of the twentieth century, and his contributions formed the basis of modern theories of borrowing and lending described in Unit 9.

Equilibrium

equilibrium
An equilibrium is a situation or model outcome that is self-perpetuating: if the outcome is reached it does not change, unless an external force disturbs it. By an ‘external force’, we mean something that is determined outside the model.

Fisher’s machine illustrates an important concept in economics. An equilibrium is a situation that is self-perpetuating, meaning that there is no tendency for the situation to change unless an external force for change is introduced. Fisher’s hydraulic apparatus was in equilibrium when water levels were equalized and the apparatus stopped moving, representing a situation in the economy in which the forces determining prices were in balance, so that prices would remain constant.

Malthus’ argument: why technological improvement in farming doesn’t raise living standards.
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Figure 1.9 (reproduction) Malthus’ argument: why technological improvement in farming doesn’t raise living standards.

For a fuller description of the Malthusian model, read Section 1.7.

The concept of equilibrium is important in the Malthusian model, summarized in Figure 1.9. This model is based on a simple description of the relationships between income and population. Specifically, if incomes (living standards) are above subsistence level, population tends to rise. And when population rises, average output (and income) per person falls. In the equilibrium of this model, incomes are at subsistence level. If something outside the model changes to upset the equilibrium—an improvement in technology, for example—the variables within the model (incomes and population) will adjust until eventually the equilibrium is reached with income at subsistence level again.

Endogenous variables and exogenous changes

endogenous
Endogenous means ‘generated by the model’. In an economic model, a variable is endogenous if its value is determined by the workings of the model (rather than being set by the modeller). See also: exogenous.
exogenous
Exogenous means ‘generated outside the model’. In an economic model, a variable is exogenous if its value is set by the modeller, rather than being determined by the workings of the model itself. See also: endogenous.

The Malthusian model focuses on the interactions between two variables: living standards and population. These are endogenous variables: that is to say, their values are determined by relationships built into the model. Other elements of the model are exogenous, meaning that they are determined outside the model: their values are fixed by the modeller. An example is the state of technology. When you apply the model, you can set the level of technology and the model will determine (for example) the size of the population in equilibrium. Then you can conduct experiments, as in step 4 above, to examine the effect of an exogenous change in technology. You set it at a new level, and the model will tell you what happens, as described in Figure 1.9.

Similarly, in Fisher’s hydraulic model, the endogenous variables are the prices of the goods. Fisher examined the effects of changes in the exogenous variables, such as the supply of one of the goods, on the prices prevailing in equilibrium.

Ceteris paribus

Designing a model involves choosing which elements of the economy matter for addressing the question you want to answer, and specifying the relationships between them (step 2 above). The model provides a simplified representation of reality that focuses attention on these elements, and sets aside others.

In the Malthusian model, we assume that what matters for determining the size of the labour force is the size of the population. If the population increases, the number of people working the land rises in proportion, and that determines how much output they produce.

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’.

There are other things that might affect the labour force: for example, social conventions or laws affecting the age at which children can work. When we use the model, we set this factor aside—not because we think it has no effect, but because we want to understand the links between population and living standards, and changing other things at the same time may stop us from seeing them clearly. So we specify that the size of the labour force is proportional to the population: we are assuming that other things affecting it remain constant. We say that the labour force is proportional to the population ceteris paribus: a Latin expression often translated as ‘holding other things constant’, or more literally, ‘other things equal’.

Setting aside other factors, or holding them constant, does not mean ignoring them altogether. When you interpret the results of a model, it can be important to remember which factors have been held constant: they might be part of the explanation for the evidence we observe.

Mathematics

Economic models often use mathematical relationships in the form of equations and graphs.

Mathematics is part of the language of economics. Combined with clear descriptions, using standard definitions of terms, it can help us to communicate statements precisely to others.

We will use mathematics as well as words and pictures to describe models, usually in the form of graphs. Some of the Extension sections contain some of the equations behind the graphs.

What makes a good model?

This book contains many examples of models. An effective model helps us to understand and explain some aspect of the economy, and is consistent with the evidence we observe.

Model-building

When we build a model, the process follows these steps:

  1. We begin with a well-defined question.
  2. We construct a simplified description of the conditions under which people take actions.
  3. We describe in simple terms what determines the actions that people take.
  4. We determine how each of their actions affects each other.
  5. We determine the outcome of these actions. This is often an equilibrium (something is constant).
  6. Finally, we try to get more insight by studying what happens to certain variables when conditions change.

When you encounter a model, think critically about the assumptions underlying it, and what it does and doesn’t explain. This will help you to understand how to apply it. To assess whether it is a ‘good’ model, you should keep in mind the question that it is designed to answer. Since a model never gives a complete picture of the economy, it can do a good job of answering one question, but be inadequate for addressing others. We use the Malthusian model in Section 1.7 to give insight into the question: ‘Why didn’t living standards rise for hundreds of years, despite improvements in technology?’ But it doesn’t help explain why agricultural technology improved in the seventeenth century.

To develop your skills as an economist further, you can try to develop models for yourself: simplified descriptions using words, diagrams, and (if you like) equations, that help you to understand the essential elements of a problem.

A model starts with some assumptions or hypotheses about how people behave, and often gives us predictions about what will happen in the economy in different situations. Gathering data and comparing it with what a model predicts helps us to decide whether the assumptions we made when we built the model (what to include, and what to leave out) were justified.

To have confidence in a model, we need to know whether it is consistent with evidence. We apply this test to the Malthusian model in Section 1.7, and to the model of technology choice in Section 2.7. As well as interpreting the past, models are used by governments, central banks, corporations, trade unions, and others who make policies or forecasts. Bad models can result in disastrous policies, and we will discuss this idea in other parts of this book.

Exercise 2.9 Designing a model

For a country (or city) of your choice, find a map of the railway or public transport network.

Much like economic models, maps are simplified representations of reality. They include relevant information, while abstracting from irrelevant details.

  1. How do you think the designer selected which features of reality to include in the map you have selected?
  2. In which way is a map not like an economic model?

Exercise 2.10 Using ceteris paribus

Suppose you build a model of the market for umbrellas, in which the predicted number of umbrellas sold by a shop depends on their colour and price, ceteris paribus.

  1. The colour and the price are the variables that are used to predict sales. Which other variables are being held constant?
  2. Which of the following questions do you think this model might be able to answer? In each case, suggest improvements to the model that might help you to answer the question.
    1. Why are annual umbrella sales higher in the capital city than in other towns?
    2. Why are annual umbrella sales higher in some shops in the capital city than others?
    3. Why have weekly umbrella sales in the capital city risen over the last six months?

Exercise 2.11 Ceteris paribus assumptions: Study time and grades

A group of educational psychologists looked at the study behaviour of 84 students at Florida State University to identify the factors that affected their performance. The two tables below show how grade point average (GPA) varies with study time, where students are either split into two groups according to their study time (top table) or four groups according to their study time and study environment (bottom table).1

  High study time (42 students) Low study time (42 students)
Average GPA 3.43 3.36
  High study time (42 students) Low study time (42 students)
Good environment 3.63 (11 students) 3.43 (31 students)
Poor environment 3.36 (31 students) 3.17 (11 students)
  1. By comparing the information in the two tables above, explain why it is important to think about which variables are ‘held constant’ (or assumed identical between students) when examining the relationship between study hours and exam performance.
  2. In addition to the study environment, which factors do you think should ideally be considered or included when analysing the relationship between study hours and GPA?
  3. What information about the students would you want to collect beyond GPA, hours of study, and study environment?
  1. Elizabeth Ashby Plant, Karl Anders Ericsson, Len Hill, and Kia Asberg. 2005. ‘Why study time does not predict grade point average across college students: Implications of deliberate practice for academic performance.’ Contemporary Educational Psychology 30 (1): pp. 96–116.