The demand function is a mathematical expression of the relationship between the quantity of goods or services that is demanded and changes in a number of economic factors, such as its own price, the prices of substitutes and complementary goods, income, credit terms the level of advertising, etc. The quantity demanded is the dependent variable the other factors and independent variables.
The quantity of a commodity that is demanded by an individual household is affected by five main variables, viz.,:
(i) The price of the commodity;
(ii) The prices of other commodities;
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(iii) The income of the household;
(iv) Various ‘sociological’ factors; and,
(v) The tastes and preferences of the household.
The above list can be conveniently summarised in, what is called a demand function.
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This is expressed as follows:
qdn = f(P1, P2, …., Pn-1, Y, S)
when qdn is the quantity that the household demands of some commodity, say, n; pn is its price; p1 … pn-1 are the prices of all other commodities; Y is the income of the household; and S is a shorthand expression of various sociological factors, such as the number of children in the family, its place of residence (e.g., big city, small town, village).
The form of the demand function, f, is determined by the tastes of the members of the household. Demand for consumer durables is influenced by consumers’ existing stocks of them: the more people have such goods already, the fewer will with to buy them. The demand function is a shorthand way of saying that quantity demanded depends on several variables listed on the right hand side. The form of the function determines the sign and the magnitude of that dependence.
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If we make the ceteris paribus assumption, i.e., if we assume that all except one of the variable on the right hand side of the demand function is held constant the function may be expressed as:
Qdn = f(Pn)
We now allow the only variable, pn, to change and we may consider how the quantity demanded qdn changes.