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

## 3.3 Goods and preferences

- goods
- Economists sometimes use this word in a very general way, to mean anything an individual cares about and would like to have more of. As well as goods that are sold in a market, it can include (for example) ‘free time’ or ‘clean air’.
- preferences
- A description of the relative values a person places on each possible outcome of a choice or decision they have to make.

We can think of both free time and total consumption spending as **goods** for Karim. Economists use the word ‘good’ to refer to anything that people care about, and would like to have more of. We will simplify the model by assuming he doesn’t care about anything else; in particular, he doesn’t care about the future, so is not interested in saving any of his income. We will also assume that his average spending cannot exceed his earnings (for example, he cannot borrow to increase his consumption).

Since Karim cares about both goods, his choice of working hours involves thinking about a trade-off: how much consumption is he willing to give up, in order to have more free time? To understand the decision Karim will make, we need to know his **preferences**—how much he values the two goods, relative to each other.

We illustrate his preferences using Figure 3.4, with free time on the horizontal axis and consumption on the vertical axis. Free time is defined as all the time that he does not spend working. Every point in the diagram represents a different combination of free time and consumption spending. Given his wage, many of these combinations will not be possible for Karim. But for the moment we will focus on which combinations he would prefer if he could have them.

We can assume that:

- For a given amount of consumption, he prefers a combination with more free time to one with less free time. Therefore, even though both A and B in Figure 3.4 correspond to €540 of consumption, Karim prefers A because it gives him more free time.
- Similarly, if two combinations both have 20 hours of free time, he prefers the one with a higher consumption.
- But compare points A and D in the table. Would Karim prefer D (low consumption, plenty of time) or A (higher consumption, less time)? One way to find out would be to ask him.

- utility
- A numerical indicator of the value that one places on an outcome. Outcomes with higher utility will be chosen in preference to lower valued ones when both are feasible.

Suppose he says he is indifferent between A and D, meaning he would feel equally satisfied with either outcome. We say that these two outcomes would give Karim the same **utility**. And we know that he prefers A to B, so B provides lower utility than A or D.

In this model, we can think of utility as a measure of Karim’s overall living standards, taking into account that he cares about free time as well as consumption.

A systematic way to graph Karim’s preferences would be to start by plotting all of the combinations that give him the same utility as A and D. We could ask Karim another question: ‘Imagine that you could have the combination at A (15 hours of free time, €540). How much consumption, in euros, would you be willing to sacrifice for an extra hour of free time?’ Suppose that after due consideration, he answers ‘€94’. Then we know that he is indifferent between A and E (16 hours, €446). Then we could ask the same question about combination E, and so on until point D. Eventually we could draw up a table like the one in Figure 3.4. Karim is indifferent between A and E, between E and F, and so on, which means he is indifferent between all of the combinations from A to D.

- indifference curve
- A curve that joins together all the combinations of goods that provide a given level of utility to the individual.
- consumer good
- Any good that can be bought by consumers, including both short-lived goods and long-lived goods, which are called consumer durables.

The combinations in the table are plotted in Figure 3.4, and joined together to form a downward-sloping curve, called an **indifference curve**, which shows all of the combinations that provide equal utility or ‘satisfaction’.

Of the three curves drawn in Figure 3.4, the one through A gives higher utility than the one through B. The curve through C gives the lowest utility of the three. To describe preferences, we don’t need to know the exact utility of each option; we only need to know which combinations provide more or less utility than others.

The curves we have drawn capture our typical assumptions about people’s preferences between two goods. In this model of Karim’s preferences, the goods are ‘consumption spending’ and ‘free time’. In other models, they will often be particular **consumer goods** such as food or clothing, and we refer to the person as a consumer. We typically assume the following:

*Indifference curves slope downward due to trade-offs*: If you are indifferent between two combinations, the combination that has more of one good must have less of the other good.*Higher indifference curves correspond to higher utility levels*: As we move up and to the right in the diagram, further away from the origin, we move to combinations with more of both goods.*Indifference curves are usually smooth*: Small changes in the amounts of goods don’t cause big jumps in utility.*Indifference curves do not cross*: Work through the steps in Exercise 3.1 to understand why.*As you move to the right along an indifference curve, it becomes flatter*.

- marginal rate of substitution (MRS)
- The trade-off that a person is willing to make between two goods. At any point, the MRS is the absolute value of the slope of the indifference curve.
*See also: marginal rate of transformation.*

To understand the last property in the list, we plot Karim’s indifference curves again in Figure 3.5. If he is at A, with 15 hours of free time and €540 of consumption, he would be willing to sacrifice €94 of consumption for an extra hour of free time, taking him to E (remember that he is indifferent between A and E). We say that his **marginal rate of substitution (MRS)** between consumption and free time at A is 94; it is the reduction in his level of consumption that would keep Karim’s utility constant following a one-hour increase of free time.

We have drawn the indifference curves as becoming gradually flatter because it seems reasonable to assume that the more free time and less consumption he has, the less willing he will be to sacrifice further consumption in return for free time, so his MRS will be lower. In Figure 3.5, we have calculated the MRS at each combination along the indifference curve. When Karim has more free time and less consumption, the MRS—the amount of spending he would give up to get an extra hour of free time—gradually falls.

The MRS corresponds to the slope of the indifference curve, and it falls as we move to the right along the curve. If you think about moving from one point to another in Figure 3.5, the indifference curves get flatter if you increase the amount of free time, and steeper if you increase consumption. When free time is scarce relative to consumption, Karim is less willing to sacrifice an hour for more consumption spending: his MRS is high and his indifference curve is steep.

As the analysis in Figure 3.5 shows, if you move up the vertical line through 15 hours, the indifference curves get steeper: the MRS increases. For a given amount of free time, Karim is willing to give up more consumption for an additional hour when he has high consumption, compared to when his consumption is low (for example, if he is struggling to afford enough food). By the time you reach A, where his consumption is €540, the MRS is high; consumption is so plentiful here that he is willing to give up €94 for an extra hour of free time.

The same reasoning applies if you fix consumption and vary the amount of free time. If you move to the right along the horizontal line for €282, the MRS becomes lower at each indifference curve. As free time becomes more plentiful, Karim becomes less and less willing to give up consumption for more time.

We have said that the MRS corresponds to the slope of the indifference curve, but note that the MRS is a positive number, while the slope of the indifference curve is negative. To be precise, the MRS is equal to the absolute value of the slope.

**Exercise 3.1** Why indifference curves never cross

In this diagram, IC_{1} is an indifference curve joining all the combinations that give the same level of utility as A. Combination B is not on IC_{1}.

- Does combination B give higher or lower utility than combination A? How do you know?
- Draw a sketch of the diagram, and add another indifference curve, IC
_{2}, that goes through B and crosses IC_{1}. Label the point at which they cross as C. - Combinations B and C are both on IC
_{2}. What does that imply about their levels of utility? - Combinations C and A are both on IC
_{1}. What does that imply about their levels of utility? - According to your answers to 3 and 4, how do the levels of utility at combinations A and B compare?
- Now compare your answers to 1 and 5, and explain how you know that indifference curves can never cross.

**Exercise 3.2** Your marginal rate of substitution

Imagine that you are offered a job at the end of your university course with a salary per hour (after taxes) of £12.50. Your future employer then says that you will work for 40 hours per week, leaving you with 128 hours of free time per week. You tell a friend: ‘at that wage, 40 hours is exactly what I would like.’

- Draw a diagram with free time on the horizontal axis and weekly pay on the vertical axis, and plot the combination of hours and the wage corresponding to your job offer, calling it A. Assume you need about 10 hours a day for sleeping and eating, so you may want to draw the horizontal axis with 70 hours at the origin.
- Now draw an indifference curve so that A represents the hours you would have chosen yourself.
- Now imagine you were offered another job requiring 45 hours of work per week. Use the indifference curve you have drawn to estimate the level of weekly pay that would make you indifferent between this and the original offer.
- Do the same for another job requiring 35 hours of work per week. What level of weekly pay would make you indifferent between this and the original offer?
- Use your diagram to estimate your marginal rate of substitution between pay and free time at A.

**Question 3.4** Choose the correct answer(s)

Figure 3.4, shows Karim’s indifference curves for free time and consumption. Based on this information, read the following statements and choose the correct option(s).

- The indifference curve through C is lower than that through B. Hence Karim prefers B to C.
- A, where Karim has €540 of consumption and 15 hours of free time, and D, where Karim has €250 of consumption with 20 hours of free time, are on the same indifference curve.
- At D, Karim has the same amount of free time but higher consumption.
- The opposite trade-off is true: going from G to D, Karim is willing to give up €73 of consumption for two extra hours of free time. Going from G to E, he is willing to give up two hours of free time for €123 of consumption.

**Question 3.5** Choose the correct answer(s)

What is the marginal rate of substitution (MRS)?

- The marginal rate of substitution represents the ratio of the trade-off at the margin, in other words, how much of one good the consumer is willing to sacrifice for one extra unit of the other.
- This is the definition of the marginal rate of substitution.
- The MRS is the amount of one good that can be substituted for one unit of the other while keeping utility constant.
- Utility doesn’t change as you move down the indifference curve. The MRS is the absolute value of the slope of the indifference curve: the trade-off between two goods that keeps utility constant.