Page 323 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes a cos(log ) b sin(log )
x
x
xy” + y’ =
x
x y” + xy’ = y
2
12.3 Economic Applications

12.3.1 Demand Function

We know that demand of a commodity, in a given time period, depends upon its own price,
prices of other commodities, income of the consumer etc. In order to understand the behaviour
of demand in response to changes in one of the above variables, say price, we assume the
remaining variables, income and prices of other commodities etc., as constant. Consequently,
we can define three types of relations, given below:
1. The relationship of demand of a commodity with its own price is termed as the price
demand or the law of demand.
2. The relationship of demand of a commodity with income of the consumer is termed as
income demand.
3. The relationship of the demand of a commodity with the price of other commodity is
termed as cross demand.
Price Demand

Other things, like income of the consumer, price of other commodities, taste and habits of the
consumer etc., remaining constant, the quantity demanded of commodity (x ) varies inversely
d
with its price (p). Mathematically we say that x is a function of p. Symbolically, we write x = f(p).
d d
dx d
Since x decreases as p increases, we have 0, under normal conditions of demand.
d
dp
Price Elasticity of Demand

The price elasticity of demand or simply the elasticity of demand, is defined as the negative of
the ratio of proportionate change in quantity demanded to proportionate change in price. It is
d log x
denoted by where . (The subscript of x is dropped for convenience.)
d
d log p
d log x dp 1 dx dx p
We can also write p
d
dp d log p x dp dp x

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