## Market Demand Function

The market demand function for a product is a statement of the relation between the aggregate quantity demanded and all factors that affect this quantity. In functional form, a demand function may be expressed as

/(Price of X, Prices of Related Quantity of Goods, Expectations of Price

(4.1) Product X = Qx = Changes, Consumer Incomes, Demanded Tastes and Preferences, Advertising

Expenditures, and so on)

The generalized demand function expressed in Equation 4.1 lists variables that commonly influence demand. For use in managerial decision making, the relation between quantity and each demand-determining variable must be specified. To illustrate what is involved, assume that the demand function for the automobile industry is

This equation states that the number of new domestic automobiles demanded during a given year (in millions), Q, is a linear function of the average price of new domestic cars (in \$), P; the average price for new import cars (in \$), PI; disposable income per household (in \$), I; population (in millions), Pop; average interest rate on car loans (in percent), i; and industry advertising expenditures (in \$ millions), A. The terms a1, a2, . . ., a6 are called the parameters of the demand function. Assume that the parameters of this demand function are known with certainty, as shown in the following equation:

(4.3) Q = -500P + 210PX + 200I + 20,000Pop - 1,000,000i + 600A

Equation 4.3 states that automobile demand falls by 500 for each \$1 increase in the average price charged by domestic manufacturers; it rises by 210 with every \$1 increase in the average price of new luxury cars (PX), a prime substitute; it increases by 200 for each \$1 increase in disposable income per household (I); it increases by 20,000 with each additional million persons in the population (Pop); it decreases by 1 million for every 1 percent rise in interest rates (i); and it increases by 600 with each unit (\$1 million) spent on advertising (A).

To derive an estimate of industry demand in any given year, each parameter in Equation 4.3 is multiplied by the value of the related variable and then summed. Table 4.1 illustrates this process, showing that the estimated annual demand for new domestic automobiles is 8 million cars, assuming the stated values of each independent variable.