Price and Demand Function

There is a huge country wide protest against central government’s decision to raise fuel prices on 25th of June, 2010. Indian Government has released state owned control on fuel prices on Friday and raised prices of fuel to overcome budget deficit.
Price is the trickiest affair that affects the whole society’s life style and living hood.
The price hike for essential commodities has negative impact on society’s overall life style. But for normal goods, consumers are in a better position to react with respect to price hike.

How price affects the market?

The short answer of the above question can be written as “price affects the demand of any product.” So, price is a factor for demand function of a product.

This discussion is restricted on normal goods only. Also, here the basic economic concept of price is discussed with respect to demand of a normal goods.

What is demand function?

Demand function is the symbolic statement of relationship in between demand for a product (dependant variable) and its determinants (independent variables).
If a demand function has a single independent variable, then it is called simple demand function. When demand function has many independent variables, then it is called dynamic demand function.

Simple demand function:

In simple demand function, it is assumed that, quantity demanded for a product X depends only on its price (Px), other factors remaining constant.
Subsequently it is written as,

Dx = f(Px), where quantity demanded (Dx) is dependant variable and Price (Px)is independent variable.

The form of equation depend on the demand-price relationship. Depend on the relation of demand and price, the demand function can be linear or non linear.

Linear demand function:

The simplest form of linear demand function can be expressed as,

Dx = -m Px + c;

where, c = quantity demanded for price zero
-m = slope of the demand curve, physically it means change in Dx for change in Px;
Here slope is constant (dDx/dPx) = constant

This is an equation of straight line (y=-mx+c), where “c” and “-m” are constants.
If values of “-m” and “c” are known, then for a given price, quantity demanded for a product can be calculated.
Say for any market condition, m=10 and c=100,
Then the equation becomes, Dx=-10Px+100.
By this equation different set of demand for a product can be calculated for different set of price.
For example,
if Px = 5, then Dx = -10x5 + 100 = 50

if Px = 6, then Dx = -10x6 + 100 = 40

if Px = 7, then Dx = -10x7 + 100 = 30

if Px = 8, then Dx = -10x8 + 100 = 20

if Px = 9, then Dx = -10x9+100 = 10

Non-linear demand function:
The simplest form of non-linear demand function can be expressed as,

Dx = a Px-b;

where a & b = constant
Here slope of the demand curve, physically it means change in Dx for change in Px is not constant;
i.e. (dDx/dPx) is not constant

Dynamic demand function:

It is also known as multi variable demand function.
In long run the market demand for a product depends on the combined impact of all independent variables. So in this case demand is function of various independent variables, and the equation can be expressed as,

Dx = f(Px, Ps, Pc, Y, T, A);

where quantity demanded (Dx) is dependant variable and all other variables are independent.
Px = Price of the product
Ps = Price of substitute goods
(Substitute goods are almost equal goods which serve the same purpose. Tea and café are substitute goods for each other)
Pc = Price of complementary goods
(Complementary goods that usually are consumed together; Demand for one falls when the other's price rises and vice versa. Café and sugar are complementary goods for each other)
Y = Consumer’s income
T = Consumer’s taste
A = Firm’s advertisement expenditure

If relations between Dx and Px, Ps, Pc, Y, T and A are linear, then the probable equation may be expressed as,

Dx = a + b Px + c Ps + d Pc + j Y + m T + n A;

where a, b, c, d, j, m & n are constant.

In normal market condition demand function react in the dynamic model, where price of the product plays the most crucial role.