Cardinal and Ordinal Utility - basics

1. Unit 3
UTILITY ANALYSIS

2. Utility
• Utility is the want-satisfying power of a good or
service.
• Usually referred to as “satisfaction” derived from
consumption.
• Utility is subjective, based on whims and fancies
of consumers.
• But early Neo-classical economists assumed that
it can be measured – called Cardinal Utility
Analysis.
• Walras, called the want satisfying power of goods
as utils.
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3. Cardinal Utility Theory
• Assumes that utility can be measured in
cardinal units.
• The consumer is rational, wants to maximise U
• Ceteris paribus – wants, tastes, income, etc
are all constant.
• Static analysis, no change in time,
• Consumer is independent, not influenced by
other factors (snob effect, bandwagon effect).
• Law of satiety applies.
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4. Total Utility
• Total utility: the aggregate utility that the
consumer gets from the total number of units he
consumes.
• At a given moment of time, as the consumer
increases his consumption, his TU also increases.
• But this increase is at a diminishing rate,
• After reaching the level of maximum satisfaction,
point of satiety, TU starts decreasing.
• Over consumption.
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5. Marginal Utility
• MU is the extra or additional satisfaction from
consuming an additional unit of a commodity.
• MU = change in TU divided by the change in quantity
of the commodity consumed.
MUx = ∆TU
∆Qx
• As consumption increases, MU decreases.
• Law of Diminishing MU: As the consumption of any
commodity increases, the MU will start decreasing,
ceteris paribus.
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6. Total and Marginal Utility
Number of X
consumed
Total Utility = ΣMU Marginal Utility :
∆TU
∆Q
1 10 10
2 18 8
3 24 6
4 28 4
5 30 2
6 30 0
7 28 -2
8 24 -4
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7. Graphical representation
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0
Utils
Commodity X
TUx
TU max
6
30
MUx
* When TU is
rising, MU > 0.
* When TU is
max, MU = 0
* When TU is
falling, MU < 0

8. Consumer’s Equilibrium
• How much will a rational consumer consume?
• Rationality implies, maximising satisfaction or
utility, i.e. 6 X, when TU is maximum.
• Free goods, no prices.
• When TU is maximum, MU is zero.
• Beyond 6 X, there is disutility.
• So consumer will stop his consumption when
TU is max, or MU = 0, assuming P = 0.
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9. Consumer’s Equilibrium with P
• But the P may not be zero.
• Assume that the P of an apple is Rs.6.
• Assume that the utility of a rupee is 1 util.
• Now a rational consumer will try to equate the
utility of the apple consumed with the value
of the money he is giving in exchange.
• In other words, he will equate the P of the
apple with the MU of the apple that he is
consuming.
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10. Equilibrium with price
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TUx
MUx X
Utils
P=6
24
Utils
a
b
Q=3
At a, the MU of X
= price (6).
Consumer stops
at this point,
beyond this his
MU < P.
If he consumes
4x, then his MU =
4, and P = 6.

11. Consumer’s surplus
• According to Marshall, consumer’s surplus is the
excess of TU over the expenditure on buying the
product.
• Assumption: MU of money is constant, and equal
to 1.
• Consumer’s surplus = ΣMUx – (Px.Qx)
• When P falls, consumer’s surplus increases,
i.e. the consumer gets more U than the total
expenditure on the commodity.
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12. Consumer’s Surplus
• At price Rs.6, he buys 3x,
and his total expenditure =
Rs.18.
• But his total utility from
consuming 3x was 24.
• Consumer’s surplus is = 24
– 18 = 6, i.e. TU > total
expenditure on 3x.
• TU = aQ, expenditure is bQ,
so CS = ab.
• If P falls, CS increases,
• If P increases, CS falls.
• This concept is used in the
case of monopolies and
taxation.
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Utils
X
TUx
P=6
Q=3
U = 24
Utils
Consumer’s
surplus
a
b
0

13. MU and Demand curve
• MU is the basis of the shape of demand
curve.
• As Q, MU. Inverse relationship.
• Consumer equates MU with P.
• If P increases, Q decreases, for MU = P.
• If P falls, then Q increases.
• At each equilibrium point, P = MU.
• The schedule of Ps, and Qs actually depicts
the MU at each Price.
• Instead of depicting MU and Q, we can depict
P and Q relationship  the Demand curve.
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14. MU and Demand curves
MU curve
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14
Utils
0
X
P=6
Q=3
a
P=8 b
Q=2
Demand Curve
Price
X
0
P=6 a
Q=3
P=8
b
Q=2
d
Assuming that
MU of Re.1 = 1

15. ORDINAL UTILITY –
INDIFFERENCE CURVES ANALYSIS
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16. Ordinal Analysis
• Hicks and Allen pointed out that:
a) Utility is not measureable,
b) Consumers do not consume just one
commodity, but a group or set of commodities.
c) Utility can be ranked or ordered – one
combination of goods may give greater/lesser
satisfaction than others.
d) When price changes, it leads to both a
substitution effect and an income effect.
Marshall had ignored the income effect.
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17. Indifference curve analysis
• An indifference curve shows the various
combinations of 2 goods (A and B) that yield the
same level of total utility to a consumer.
• Based on the following assumptions:
– Two goods which are close but not perfect substitutes.
– Both goods are consumed together in different
combinations.
– Prices are given, also utility is known.
– The consumer orders his consumption based on the
utility he gets – ordinal utility.
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18. Diagram of IC
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A
B
0
TU1
C1
B1
A1
C2
B2
A2
TU2
Any two points on an
indifference curve
provide the same level
of utility.

19. Properties of ICs
1. ICs slope down to the right, showing that A
and B are substitutes.
2. ICs are convex to the origin, showing that the
rate of substitution is not constant, but
decreasing.
3. Higher indifference curves give higher levels
of utility.
4. Indifference curves cannot cut each other.
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20. Budget constraint
• The amount of A and B consumed depends on
their two prices and Income of consumer.
QA. PA + QB.PB = consumer’s income Y
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A
B
0 Pb/Pa

21. Consumer’s equilibrium
• Is at the point where the budget line is a slope to the highest
indifference curve.
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A
B
0
TU1
TU2
1
2
3
1,2 and 3 are all
combinations
where the Budget
line = IC.
But at 1, the
consumer is on the
highest IC.
Here the slope of
the Budget line =
slope of the IC.