Individual Demand Function

The behavior of a buyer is influenced by many factors; the price of the good, the prices of related goods (compliments and substitutes), incomes of the buyer, the tastes and preferences of the buyer, the period of time and a variety of other possible variables. The quantity that a buyer is willing and able to purchase is a function of these variables. In individual's demand function for a good (Good X) might be written:

QX = fX(PX, Prelated goods, income (M), preferences,...)

QX = the quantity of good X;

PX = the price of good X;

P related goods = the prices of compliments or substitutes;

Income (M) = the income of the buyers;

Preferences = the preferences or tastes of the buyers.

The demand function is a model that "explains" the change in the dependent variable (quantity of the good X purchased by the buyer) "caused" by a change in each of the independent variables. Since all the independent variable may change at the same time it is useful to isolate the effects of a change in each of the independent variables.

To represent the demand relationship graphically, the effects of a change in PX on the QX are shown. The other variables, (Prelated goods, M, preferences,...) are held constant. Figure shows the graphical representation of demand.

P_x

Р₁ d

d

0 q₁ q_x

Since (Prelated goods, M, preferences,...) are held constant, the demand function in the graph shows a relationship between PX and QX in a given unit of time (ut).

The demand function can be viewed from two perspectives.

The demand is usually defined as a schedule of quantities that buyers are willing and able to purchase at a schedule of prices in a given time interval (ut), ceteris paribus.

QX = f(PX), given incomes, price of related goods, preferences, etc.

Demand can also be perceived as the maximum prices buyers are willing and able to pay for each unit of output, ceteris paribus.

PX = f(QX), given incomes, price of related goods, preferences, etc.

Market Demand Function

When property rights are nonattenuated (exclusive, enforceable and transferable) the individual's demand functions can be summed horizontally to obtain the market demand function.

For the market the demand function can be represented by adding the number of buyers (B, or population),

QX = fX(PX, P related goods, income (M), preferences,... B), where B represents the number of buyers.

Using ceteris paribus the market demand may be stated QX = f(PX), given incomes, price of related goods, preferences, B, etc.

P_x D

D

0 Q_x