Page 139 - DECO401_MICROECONOMIC_THEORY_ENGLISH

Microeconomic Theory

Notes still, they provide the starting point of the function of market figures. That is why the economists have
studied functions of demand through both the views, static as well as dynamic. Accepting the basic rules
of demand, they have predicated the multivariate demand functions, in which the demand of a product
is not only the function of its price but also the function of various other variables. These variables
include prices of other products, income of the consumer, consumer interests etc. These functions have
concentrated the supremacy on consumer market demand and not on personal consumer demands.
Then some demand functions study the different groups of products like eatable products, demand for
services etc. This is called The Pragmatic Approach to Demand Theory. We shall analyze certain some
demand functions below.

1. The Constant Elasticity of Demand Function
In many statistical studies, Constant Elasticity of Demand Function is used. It is based on general
believes of the relation between demand and its determinants like price of the product, price of related
goods, income of the consumer etc. It is assumed that income of the consumer and price of related
goods are constant. Based on this, in demand function, the relation between price-quantity can be
differentiated. As far as the shape of demand function (curve) is concerned, the curve is fitted based
upon statistical figures. But this curve is deceptive as it never shows accurate results and rather is based
on approximations.
The general form of Demand Function is,
Q = a . P P Y e st …(1)
b
c
d
x x 0
where, Q = Quantity of demanded product x
x
a = constant
p = price of x
x
b = price function of demand

p = price of other unrelated goods
0
c = cross elasticity
y = income of the consumer
d = income function of demand
e = basis of natural logarithms
f = trend factor for interest
t
The equation (1) is known as Constant Elasticity of Demand Function because the variables of demand
b, c and d are assumed to be constant.

Its Proof

To prove this we take the short multiple of price and product x, assuming other determinants of demand
as constant.
For constant price demand of demand function,
∆Q /Q
b = x x
∆P /P
x x
is a constant.
Using this feature mathematically, changing variables show the proportional change, we can write it
as, ∆log Q = b log P
x x
where ∆log Q = ∆Q , ∆Q , log P = ∆P /P and b is price function of demand.
x x x x x x

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