Unit 3

UTILITY ANALYSIS

Prof. Prabha Panth,Osmania University

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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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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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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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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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Total and Marginal UtilityNumber of X

consumedTotal Utility = ΣMU Marginal Utility : ∆TU

∆Q

1 10 102 18 83 24 64 28 45 30 26 30 07 28 -28 24 -4

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Graphical representation

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

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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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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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Equilibrium with price

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.

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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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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

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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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MU and Demand curves

MU curve

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Utils

0X

P=6

Q=3

a

P=8 b

Q=2

Demand Curve

Price

X0

P=6 a

Q=3

P=8b

Q=2

d

Assuming that MU of Re.1 = 1

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ORDINAL UTILITY – INDIFFERENCE CURVES ANALYSIS

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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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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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Diagram of ICA

B

0

TU1

C1

B1

A1

C2

B2

A2

TU2

Any two points on an indifference curve provide the same level of utility.

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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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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

A

B0 Pb/Pa

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Consumer’s equilibrium• Is at the point where the budget line is a slope to the highest

indifference curve.

A

B0 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.