Download Topic 4. Utility and consumer choice

ITE lecture no. 6, Friday October 14th
Topic 4. Utility and consumer choice
(1) Utility
October 14th 2005
Today’s lecture:




Total utility, marginal utility
Diminishing marginal utility
Consumer surplus
Optimal choices: 1 good + 2 goods
[Monday’s lecture: indifference curves]
Essential reading:
Sloman Chapter 4, Section 4.1
[read Section 4.3 for Monday’s lecture]
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ITE lecture no. 6, Friday October 14th
1. Consumer choice theory
 Explains the choices consumers
make given their limited incomes
 Provides insight into the decisions
underpinning demand curves
Key ideas:
a. Consumers are
rational
which is interpreted to mean:
b. Consumers have preferences:
i. they prefer more to less
P
ii. they can compare and rank
consumption options
?
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iii. their preferences are transitive:
P
and
P
=>
?
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c. Utility - what sort of comparisons can I
make?
i. cardinal:
The difference between a chocolate ice cream and vanilla
ice cream is bigger than the difference between vanilla ice
cream and plain yogurt
ii. ordinal
All I know is I prefer chocolate ice cream to vanilla and
vanilla to yogurt.
Is temperature an ordinal or cardinal
magnitude?
Much of 20th century economics based on
ordinal utility. This is now changing
d. Maximisation of utility: consumers seek
to obtain maximum satisfaction from
limited incomes.
Question: Do you believe that consumers
make their decisions ‘rationally’:
a) precisely ?
b) approximately ?
c) not at all
Correct answer is (b) – especially where risk is involved. Important
in financial markets.
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2. Total and marginal utility
Utility is a measure of the benefit or
satisfaction that consumers get from a
good or service. (19th century concept)
Total utility (TU): the benefit or
satisfaction that consumer gets from
consuming a particular quantity of a
good or service
Marginal utility (MU): the increase in
total utility obtained by consuming one
extra unit of a good or service.
MU = ΔTU/ΔQ
Using calculus: MU is the first derivative
of TU e.g:
TU = 60Q – 4Q2
MU = dTU/dQ = 60 – 8Q
The principle of diminishing MU:
As more units of a good are consumed,
additional units will provide less
satisfaction than previous units.
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Utility: "that property in any object, whereby it tends to produce
benefit, advantage, pleasure, good, or happiness...or...to prevent
the happening of mischief, pain, evil, or unhappiness"
Jeremy Bentham
Introduction to the Principles of Morals and Legislation (1789)
Jeremy Bentham’s ‘auto icon’ at UCL
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If we could measure utility…
[e.g. in units ‘utils’ or ‘hedons’]
Total utility
350
305
315
323
330
5
6
7
Total utility of bananas
300
265
250
200
200
150
110
100
50
0
1
2
3
4
Number of bananas per day
Marginal
utility
Marginal utility of bananas
350
300
250
200
150
110
90
100
65
40
50
10
8
7
5
6
7
0
1
2
3
4
Number of bananas per day
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3. Optimal choice: one good
 In practice we can’t measure utility
directly in utils – although we are
making progress
 But we can proceed on the basis that
MU is given by the amount of money a
person would be prepared to pay to
obtain one more unit of the good.
Price
MU = D
Qx
D = f(Px)
MU = f(Qx)
Optimal choice: choose that Qx where MU
= price
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4. Consumer surplus
Consumer
surplus
P*
Market
price
MU = D
Q*
1
Qx
consumer spending = P x Q
At Q*, MU = P*
But for every Qx up to Q*, MU > P
Consumer surplus: the excess of what
a person would have been prepared to
pay for a good over what the person
actually pays.
 In the diagram, this is the area under
the demand curve out to Q*, minus the
consumer’s spending
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5. Optimal choice: two goods
 We have a budget to spend on
coffee and
magazines.
 The marginal utility of a coffee is the
function MU(X)
MU(X)
X
; the price (in £) of coffee is P(X).
 The marginal utility of a magazine is
MU(X)
the function MU(Y);
The price
(in £) of a magazine is P(Y).
YX
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 Utility is maximised when
MU(X)
P(X)
=
MU(Y)
P(Y)
i.e. the marginal utility of coffee per £
spent is = the marginal utility of
magazines per £ spent.
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 Utility is maximised if
MU(X)
P(X)
=
MU(Y)
P(Y)
 because if…
MU(X)
P(X)
>
MU(Y)
P(Y)
…then the utility gained from spending
one more £ on X is greater than the utility
lost by spending one fewer £ on Y
and because if…
MU(X)
P(X)
<
MU(Y)
P(Y)
…then the utility lost from spending one
fewer £ on X is less than the utility gained
by spending one more £ on Y
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6. Conclusions of utility theory
1
The result that utility is maximised if…
MU(X)
P(X)
=
MU(Y)
P(Y)
…applies to any and all goods
2
Market price is related to marginal
utility, not total utility (the “paradox of
value”)
3. Other things being equal, a rise in the
price of X will lead to a fall in the
demand for X, because
MU(X)
P(X)
<
MU(Y)
P(Y)
Next lecture: indifference curves, budget
lines & optimal choice. Read Chapter 4
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Test your understanding…
The law of diminishing marginal utility
states that
(a) total satisfaction will decrease as
more units of a good are consumed
(b) the satisfaction from each additional
unit of the good consumed will
decrease
(c) total utility will become negative
(d) both (a) and (c)
Test your understanding…
By consumer surplus, economists mean
(a) the amount of a consumer’s income
left after spending
(b) market price multiplied by the
quantity of the good purchased
(c) the price paid for the last unit of the
good purchased
(d) the difference between the maximum
amount a person is willing to pay for
a good and its market price
Answers: first question (b), second question (d)
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