The Demand Function

As stated in the text, the basic determinants of market demand for a specific good such as Q₁ are (1) consumers’ tastes and preferences, which we can denote by Z; (2) the number of consumers in the market, N; (3) consumers’ money incomes, I; and (4) the prices of related goods, P₂, P₃, and so on.

Consider a typical consumer, which we will denote with the subscript "i." This individual selects some amount of good Q₁ (and amounts of all other goods) which gives her the greatest satisfaction. This amount will of course vary, depending on the price of good Q₁, the prices of all other goods, her income, and her preferences. We can write this relationship as: = f_i(P₁, P₂, P₃, -, I_i, Z_i). This individual’s demand curve for good Q₁ is found by holding constant the value of all variables other than the price of good Q₁ and graphing the resulting relationship between and P₁. This relationship is typically written = f_i(P₁| P₂, P₃, -, I_i, Z_i).

There are N consumers, each of whom have similar demands for good Q₁. The market demand for this good is simply the sum of all of the quantities demanded by the N consumers at each possible price:

= = f_i(P₁| P₂, P₃-, I_i, Z_i). For simplicity, this can be written more compactly as Q₁ = F₁(P₁| P₂, I, Z, N).

Written in this form, the function clearly shows that the market demand for a good is a relationship between the quantity demanded of a good and its price, holding constant the prices of all other goods, consumers’ incomes, consumers’ preferences, and the number of consumers. A change in any of the factors previously held constant will result in a different relationship between Q₁ and P₁. We would call this new relationship a change demand.