Illustrating Preferences and Constraints using a Traditional Framework
By Corné van Walbeek
Every consumer has to make choices about how best to spend their money. This hand-out is about
how, as an economist, you can model that choice-making process. The CORE curriculum considers
how people choose between the amount they want to consume and how much free time they have.
Here, we illustrate the choice making process in a more general and intuitive way.
In this hand-out, we will use the same ideas as those used in the CORE curriculum but will apply it to
two consumer products, like rice and meat, or electricity and food. Often, we simply use generics:
product X and product Y. In the CORE curriculum, the two products were more abstract: consumption
and leisure time.
To model the way people make choices, we are going to use two tools: indifference curves and a
budget constraint. Indifference curves show how much people like things and what they are willing to
exchange of one product to get more of another product (i.e. their preferences). However, people
can’t have all the things they want: they are limited, or constrained, by how much they can afford to
buy. A person’s budget sets a limit on what they can get. We use a budget line to show the
combinations of products a person can buy with the money that they have available to spend (their
budget constraint). We’ll see how these two tools can be combined to show how a person reacts to
things like a change in their income, or a change the price of a product.
Representing consumer’s preferences
To keep things simple we’ll only work with two products, X and Y. This will allow us to build our model
on a simple graph. Working with three or more products might be more realistic, but is far more
difficult (don’t hold your breath, you’ll only get to it when you study general equilibrium theory in fifth
year).
In the discussion below, we will make product X rice (measured in kg consumed per month) and
product Y meat (also measured in kg per month). In the CORE text, the two products were amount of
free time per day (as product X) and total consumption per day (as product Y). It is important to realise
that there is a time dimension attached to the consumption of each of the products. It is immaterial
what the time dimension is (e.g. per day, week or month), but it is important to realise that it is there.
However, because the time dimension associated with consumption is always implied, we typically do
not focus on it in subsequent analysis.
Let’s accept that people can buy fractions of a unit. In our example of rice and meat, it is perfectly
plausible that a person consumes 0.6 kg, or 1.4 kg of any of the products, rather than integer values.
Had the two products been computers or cars, it would be rather unrealistic to consume 0.6 or 1.4
units. But please look beyond the unrealism and awkwardness of this. In Economics we don’t want to
get bogged down with such minor mathematical detail. We typically assume that, in representing
consumer preferences, people are quite happy with non-integer quantities of the goods that are
considered.
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,Imagine that, as a well-meaning philanthropist, I approach you and offer you different combinations
of X (rice) and Y (meat). The different combinations are shown in the table below:
Combination A B C D E
Product X (rice) 1 2 3 4 5
Product Y (meat) 8 5 3 2 1.5
You look at these various combinations and you tell me that you are indifferent between them. In
other words, you are equally happy with each of them. Each one of these combinations gives you the
same amount of utility. Utility can be thought about as “happiness” or “use”. Combination A would
give you little rice and lots of meat, whereas combination E would give you lots of rice and little meat.
You insist that you are equally happy with these two combinations, as well as with the other
combinations of rice and meat, as shown in the table above. Of course, there are other combinations
(with non-integer quantities) of rice and meat that will give you the same utility (like possibly 1.25 kg
of rice and 7.13 kg of meat), but it is not possible or feasible to show all of these different combinations
as there are infinitely many different combinations.
We can show these combinations of rice and meat that give the consumer the same level of utility as
a curve on a graph. This is called an indifference curve. It shows all the possible combinations of two
goods that give a consumer the same amount of utility (enjoyment).
Figure 1
The slope of an indifference curve is called the marginal rate of substitution (or MRS). It is the amount
of one good you’d be willing to give up to obtain one more unit of the other i.e. what you would
require to substitute towards or away from a particular good. Normally, if you have a lot of product
Y, and only a little of product X, you would not mind losing one unit of Y even if you only got a little of
X in exchange. But if you only had a little of product Y, and were about to have another unit taken
away, you would need a lot of product X to compensate you for the loss. The convex shape of the
indifference curve shows a decreasing marginal rate of substitution (MRS). A curve that is convex has
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, a steep slope/gradient when X is small, but the gradient when X increases. Thus, as we move down
the indifference curve, the slope of the curve decreases, which is exactly what the MRS represents.
Imagine that you find yourself at point A, with 8 kg of meat and only 1 kg of rice. How much meat
would you be willing to give up for an additional 1 kg of rice? The indifference curve shows that if you
handed over 3 kg of meat to gain one extra kg of rice, you would still get the same total utility.
Now that you’re at point B, let’s ask again: “How much meat would you be willing to give up for an
additional 1 kg of rice?” Rice is now less scarce (i.e. more abundant), and you don’t have as much meat
as at point A. The graph shows that you would only be willing to give up 2 kg of meat for an additional
kg of rice.
Traditionally, the marginal rate of substitution (MRS) is defined as the amount of product Y that a
consumer is willing to give up in order to obtain one extra unit of product X. This is also the approach
that is taken in the CORE curriculum. (We can also define the MRS as the amount of product X that
the consumer is willing to give up in order to get an additional unit of product Y. It is not wrong, but
less intuitive graphically). Moving from point A to point B, the MRS was 3, because you were willing to
give up 3 kg of meat to gain 1 kg of rice, while keeping total utility the same. Between point B and
point C the MRS was 2, because you were willing to give up 2 kg of meat to gain 1 kg of rice. You can
confirm for yourself that between point C and point D the MRS is equal to 1 and between point D and
point E the MRS is equal to 0.5
Graphically, we can think of the MRS as the slope of the indifference curve. At point A, the slope is
steep (i.e. it has a high gradient) which means that we are willing to give up a lot of product Y in order
to gain an additional unit of product X while keeping total utility constant. As we move along the
indifference curve, the gradient becomes smaller, which means that the MRS is decreasing. As this
happens, we are willing to give up increasingly smaller quantities of product Y in order to gain an
increasing quantity of product X.
All the points on the indifference curve that we have drawn above imply the same level of utility.
There are other combinations of the two products that give higher levels of utility, and others where
total utility is lower. On the assumption that more is better (this is a standard assumption that we
make in Economics), a higher indifference curve (i.e. one that is further away from the origin) will yield
a higher level of utility than a lower indifference curve because it will allow us to consume more than
on a lower indifference curve. Logically, there will be many possible indifference curves on a graph.
This is called an indifference map, which is illustrated below.
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