Page 58 - DECO405_MANAGERIAL_ECONOMICS

Unit 4: Consumer Behaviour (Utility Analysis)

At any point on AB, the consumer spends all his income but point C is unattainable. At point D Notes
or any other point in DOAB he does not spend all his income.

4.4 Consumer's Equilibrium with Cardinal Approach

!

Caution Law of Equi-marginal Utility or the principle of Equi-marginal utility says that
the consumer would maximise his utility if he allocates his expenditure on various goods
he consumes such that the utility of the last rupee spent on each good is equal.

Suppose the consumer's utility function is U = u (X). The consumer buys X. His total expenditure
is X. P .
x
Presumably, he wants to maximise the difference between his utility and expenditure

L = U(X) – X. P
x
By way of first order condition
dL du
P x 0
dx dx
du
The term stands for marginal utility X, MU , and P stands for price of X.
dx x x
Thus at equilibrium,
MU = P and … i
x x
MU = P and … ii
y y
MU P
x x
or MU y P y … iii
Then by cross-multiplying, we get
MU .P = MU .P … iv
x y y x
MU x MU y
or P P … v
x y
And note by definition
MU MU
x y
P P = MU , which is constant … vi
m
x y
Where,
MU = Marginal Utility of money
m
MU , MU = Marginal Utility of X and Y
x y
P , P = Unit price of X and Unit Price of Y respectively.
x y
The proportionality rule stated above (v) is the tenet of the Law of Consumer Equilibrium. The
assumption of diminishing marginal utility proportionality rule when considered along with
equi marginal concept imply that a single price prevails for a commodity in the market. This is
true of a perfectly competitive market.

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