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Unit-7: Recent Developments in Demand Theory

IIC curve than IIC curve. Thus, the curve IIC does not give optimum solutions, however, the utility Notes
1
2
3
level is lower than IIC because it is above to consumer budget line 1| X –1| X . So only point M is
1
2
2
optimum normalized point.
Fig. 7.4
λ
2

1/X
1

M

IIC
3
IIC
2
IIC
1 λ
O 1
1/X
1

Difference between Direct and Indirect Utility Functions
Direct utility function is related to neutral curve system and also the indirect utility function is related
to indifferent curve which are known as indirect neutral curve. They are similar in following ways –
1. Both the curves look same.
2. Both are convex on the base.
3. Customer is neutral on any point of these curves because it obtains same functions on each.
But there is a main difference in these two types of curves. High direct neutral curves are related to high
function levels. Opposite to it, high indirect neutral curves are related to lower function levels.

7.4 The Expenditure Function

The expenditure function states that how the customer decreases its expenditure, derivation of
customer’s expenditure function depend on programming technique on given costs of products and
utility level.
Min ∑ P X
i i i
Subject to U (X) ≥ U …(1)
Where P X is total expenditure which is to be done minimum but with the condition that utility of
i
i
this restriction would not less than level U. Solution of equation (1) depends on the values of costs and
utility level which is written as:
X = f (P, U) i = 1, ..…n …(2)
i i

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