DEMAND FUNCTION

The relationship between a variable and its determinants is known as a function.  A demand function describes the dependence relationship between the demand for a commodity or service and the factors or variables affecting it such as its own price, the prices of substitutes and complementary goods, income of the consumer, credit terms, advertisement expenditure etc. 

The quantity demanded is the dependent variable and the determining factors are independent variables. The effect of each independent variable on the dependent variable can be estimated statistically.

Here is a simple case of demand function.

Assume that all determinants of demand, except price remain constant. This is a case of short run demand function, where quantity demanded of a commodity varies with its price. This demand function, symbolically, may be expressed as:

                                                D_x = f (P _x)                                                              

Where,

D_x = Quantity demanded of commodity X

P _x = Price of commodity X

In this demand function D _x is dependent variable and P_x is independent variable.

The independent variable causes a change in the dependent variable. If we are able to know the quantitative relationship between the dependent and independent variables, the demand function may take the form as:

                                         D_x= a - bP_x                                                                                         

Where,

a= a constant denoting maximum quantity demanded at zero price.

b = change in quantity demanded due to change in price (DD/ DP). This ratio also remains constant.

If we are able to find out the values of ‘a’ and ‘b’, we can prepare a demand schedule showing quantities demanded at different levels of price. When the quantity demanded and price relationship results in the form of a linear demand curve, a demand function is said to be a linear demand function. From the demand function, price function can be easily obtained. As the slope of the demand curve changes all along the curve, a demand function is said to be nonlinear. A nonlinear demand function takes the form of a power function.

In the short run, factors other than price of the commodity were assumed to be constant. However, in the long run, other factors may also change. Long run demand for a product depends on the composite impact of all its determinants operating simultaneously. Therefore, for the purpose of estimating long- term demand for a product, all its relevant determinants are taken into account. A function of this kind is called a multivariate or dynamic demand function. A demand function of this sort states that quantity demanded of a commodity (D _x) depends on its price, price of related goods, consumer’s income, advertisement expenditure, consumer’s taste etc. This multivariate demand function, symbolically, can be expressed as

                                   D _x = f (P _x, Y, P_s, P_c, A, T)                                           

Where, Y = consumer’s income, Ps = price of substitutes, Pc = price of complements, A= Advertisement expenditure, T = Consumer’s taste

If all the independent variable can be easily quantified, and the relationship is linear, then the demand function may be rewritten in the form

                      D _x = a + bP_x + cY + dPs + gPc + hA + jT                                

 where, ’a’ is a constant, b,c,d,g,h, and j are the coefficients of relationship between quantity demanded of X and the respective independent variables. Other independent variables such as population of the country, expectations of the consumers may also be included.