# Demand Function

The quantity demanded of a commodity is influenced by a number of its determinants i.e. the price of the same commodity, prices of related commodities, income of the consumer, his taste and preference, change in fashion, change in consumer's expectation, advertisement etc. It implies that there is a relationship between the quantity demanded and these determinants. This is called functional relationship. This type of functional relationship between quantity demanded of a commodity and its affecting factors or determinants is known as a demand function. Thus, a demand function is nothing more than the functional relationship between demand for a commodity and its determinants.
The demand function can be expressed symbolically as;

Qdx = f(Px, Py, Y, T, Ce, Ad...........)

Here, Qdx = Quantity demanded,
Px = Price of the same commodity that is demanded,
Py = Price of the related commodity,
Y = Income of the consumer,
T = Taste and preference,
Ce = Consumer's expectation,

2- Types of Demand functions
Generally, there are two types of demand function as a linear demand function and non-linear demand function.

2.1- Linear Demand Function
As the price of a commodity and its demand both change in the equal ratio, then it is called linear demand function. In other words, if the slope of a demand curve is constant throughout its length, it is the linear demand function.
The linear demand function is expressed in a symbolic form as;

Qdx = a  + bPx ..... (i)

Where;
Qdx = Demand for good-X,
a = Autonomous demand or demand at zero price,
b = Slope of demand curve,
Px = Price of good-X

For example,
Given the linear demand function Qdx = 6 - 2Px  find quantity demanded of good-X at prices  0, 1, 2 and 3, and also plot in a diagram.

Solution;
Given the demand function, the quantities demanded of good-X at various prices are as;
Qdx at price  0 = Qdx = 6 - 2.0
= 6,
Qdx at price  1 = Qdx = 6 - 2.1
= 4,
Qdx at price  2 = Qdx = 6 - 2.2
= 2,
Qdx at price  3 = Qdx = 6 - 2.3
= 0,

Demand schedule
 Price of good-X (Px) 0 1 2 3 Quantity of good-X (Qdx) 6 4 2 0

Plotting the schedule in a diagram
2.2- Non-linear demand function
As the price of a commodity and its demand both change in an unequal ratio, then it is called non-linear demand function. In other words, if the slope of a demand curve changes all along the demand curve, it is the non-linear demand function.

The non-linear demand function is expressed in a power function as;
\Qdx\ =\aPx^b

Where,
Qdx = Quantity demanded of good-X,
a = Demand intercept or autonomous demand or demand at zero price,
Px = Price of good-X
b = Slope of Demand curve,

for example;
Demand schedule
Px                                                       Qdx
1                                                            8
2                                                           4
3                                                            1

I- When the price changes from 1 t0 2 and quantity from 8 to 4 units, the slope is as,
ΔP = P₂ - P₁
= 2 - 1
= 1
ΔQ = Q₂ - Q₁
= 4 - 8
= -4
Sl0pe, b = run/rise            (because we measure dependent variable Q on X-axis)
= -4/1
= -4
II- When the prices change from 2 t0 3 and quantity from 4 to 1 units, the slope is as,
ΔP = P₂ - P₁
= 3 - 2
= 1
ΔQ = Q₂ - Q₁
= 1 - 4
= -3
Sl0pe, b = run/rise
= -3/1
= -3

It shows that the slope of demand curve at different points of combination between the price and quantity demanded is not equal to each other. so it is non-linear demand curve as shown in the following figure.

3- Determinants of Demand
There are various factors which influence quantity demanded of a commodity. These factors are also called the determinants of demand. Some determinants of demand which have been explained below.

3.1- Price of the commodity
One of the most important determinant of demand is the price of the same commodity that the consumer demands for. When the price of the commodity rises, the consumer demands for a small quantity of that commodity and on the contrary, with a fall in its price, he/she demands for a large quantity of the commodity. So the price of the commodity is the one which determines how much quantity of the commodity the consumer demands for.

3.2- Income of the consumer
A change in the income of the consumer also affects the demand for a commodity. When the income of a consumer increases, generally the demand for a normal good increases but the demand for an inferior good falls. On the other hand, the demand for the normal good falls with a decrease in income but at the same time, the demand for the inferior good increases. Hence income of the consumer is an important determinant of of demand.

3.3- Price of related goods
Another determinant of demand is the price of related goods. The related goods are of two types i.e. substitutable and complementary. In case of substitutable goods, quantity demanded of a good, say Fanta, increases due to rise in the price of another good, say Pepsi,  and vice-versa (positively sloping demand curve). Likewise, in case of complementary good, the demand for one good, say Torch, falls due to rise in the price of another good, say Batteries,  and vice-versa (negatively sloping demand curve). Thus, the price of related goods also determines the quantity demanded of a good.

3.4- Taste, habit and fashion
Taste, habit and fashion are also important determinants of consumer's demand. The demand for a particular good change due to change in taste, habit and fashion of the consumer. When the consumer is habitual to a good that is flavoring him, he/she demands for a large quantity of the good and vice-versa. Similarly, when a particular good exists in fashion, its demand increases but the demand for that good falls when it goes out of fashion. Thus, these factors determine the quantity demanded of a good.

A advertisement is a medium of motivating and attracting the consumer towards a good. When advertisement of a good is repeatedly done, the consumers are naturally attracted towards the good and they demand for a large quantity. Consequently, the demand for the good rises but it may reverse with the absence of advertisement. So advertisement is also one of the determinants of demand.

3.6- Seasons
Seasons also determine the quantity demanded of a good and service. In a particular season, demand for a certain good increases whereas in some other seasons its demand may fall to the lowest level. For example, demand for cotton clothes increases in summer season but in winter their falls to the lowest level. Similarly, there is an increase in demand for umbrella in rainy season where as its demand falls in other season. Thus, the demand for a good is determined by the season as well.

3.7- Size of population
The size of population is also an influencing factor of quantity demanded of a good and service. When the size of population grows, naturally the demand for normal goods and services goes high and vice-versa. Similarly increase or decrease the number of certain age groups determine the demand for a particular good. For example, increase in the number of children in a particular area causes an increase in demand for playing items like dolls, toys etc.

3.8- Expectation to change in price in future
An expectation to change in the price of a good in future affects the demand for that good. When there is an expectation to rise in the price of a particular good in future, the consumer starts to store a large quantity in present and its demand increases. On the contrary, if it is expected to fall the price of a particular good in future, the consumer postpone the current purchasing plan which results a fall in its demand. Thus the expectation to change in the price of a good in future influences the demand.

3.9- Distribution of national income
A distribution of national income also affects the quantity demanded of a good and service. When the distribution of national income is unequal, some people are rich but a majority of people are poor. In such a situation  average demand for goods is low because the poor has high propensity to consume but less purchasing power whereas the rich has more purchasing power but they have a very low propensity to consume. If income is equally distributed among the people the poor can maintain high purchasing power and the average demand for goods increases. Thus distribution of income is also a determinant of demand.

3.10- Tax
Tax system is also one of the determinants of demand. Imposition of high rate of direct and indirect taxes to the consumer reduces their purchasing power. Consequently, demand for goods and services falls whereas tax release increases the real income of the consumer and demand for goods and services goes up.