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Learn Basic EconomicsLesson 4: Preference and Utility
It is the preferences of consumers that lead to the shape of the demand
curve.
Consumers want to maximise their utility, utility maximisation is influenced
by preferences and budget constraints.
Constrained maximisation is finding the combination of goods that makes
the consumer best off.
There are a few assumptions made about preference:
Completeness, when comparing 2 goods one is always preferred (valued
more) than the other, the consumer cannot be unsure which good they
prefer.
Transitivity, if a consumer prefers a to b, and they prefer b to c, then they
cannot prefer c to a.
Non-satiation, the consumer will always prefer to have more regardless of
how much they already have.
Properties of indifference curves (or preference maps)
Indifference curves show all the combinations
of consumption along which an individual is
indifferent (where utility is constant).
3 coffees and 3 donuts (a) is better than 4
coffees and 1 donut (b) or 1 coffee and 4
donuts (c).
Key properties of indifference curves:
• Consumers prefer higher indifference curves
• Indifference curves always slope downwards
• Indifference curves cannot cross
a
b
c
Utility The Utility function is a mathematical representation of preferences.
For example: Utility = 𝐶 ∗ 𝐷 (Coffee * Donuts)
Utility is an ordinal concept not a cardinal concept (we are able to rank goods but it is not
possible to measure the happiness they produce.)
Marginal Utility is how your utility changes with each additional unit of a good (derivative
of utility function).
As you can see, this is not a linear function.
Where the number of Coffees is constant at 2, we can calculate the utility for the given
number of Donuts:
1 donut and 2 coffees = 1 ∗ 2 = 2 = 1.41
2 donuts and 2 coffees = 2 ∗ 2 = 4 = 2
3 donuts and 2 coffees = 3 ∗ 2 = 6 = 2.45
4 donuts and 2 coffees = 4 ∗ 2 = 8 = 2.83
5 donuts and 2 coffees = 5 ∗ 2 = 10 = 3.16
As we saw from the previous graph the more Donuts you have the greater utility you also
have. However, there is diminishing marginal utility with each additional donut. (where U
= 𝐶 ∗ 𝐷 )
1 donut and 2 coffees the utility increases from 0 to 1.41, marginal utility = 1.41
2 donuts and 2 coffees the utility increases from 1.41 to 2, marginal utility = 0.59
3 donuts and 2 coffees the utility increases from 2 to 2.45, marginal utility = 0.45
4 donuts and 2 coffees the utility increases from 2.45 to 2.38, marginal utility = 0.38
The marginal utility clearly decreases with each additional donut, when the number of
coffees is constant.
Here is a graph of the margin
utility of donuts, where the
number of coffees is 2.
Marginal Utility always
decreases, but it also always
remains positive (due to non-
satiation).
(1,1.41)
(2,0.59)(3,0.45) (4,0.38) (5,0.33)
The Marginal Rate of Substitution is a mathematical concept that links preference utility
with preference maps.
The marginal rate of substitution is equal to the slope of the indifference curve: =∆C
∆D
(coffee and movies).
It is the rate at which you are willing to trade of the Y axis for the X axis.
The Marginal rate of substitution is always diminishing as indifference curves always slope
downwards.
The MRS from (1,4) to (2,2) = −2
1= -2, this means you
would be willing to give up 2 coffees for 1 donut.
The MRS from (2,2) to (4,1) = −1
2= -0.5, this means
you would be willing to give up 0.5 coffees for 1 donut.
When you have 4 coffees the marginal utility for the last
2 coffees is low, but there is a high marginal utility for
donuts in comparison.
The marginal rate of substitution can also be defined as:
M.R.S = −Marginal Utility (for the x axis)
Marginal Utility (for the y axis)
Marginal Utility is thus a negative function of quantity.
In this example:
M.R.S = − (
−1
1)
(3
−0.5)
= - 1
6
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