Demand Function

Demand function shows the relationship between the quantity demanded of a good and the various factors that affect interact or influence the determination of quantity demanded.
All the factors influencing the demand for a good can be briefly expressed in the following functional relationship:

Q_x^d = f(P_x, P_y, P_z ,….. P_n, Y , T)
Where,    
Q_x^d   shows the quantity of a good X demanded,
P_x     stands for the price of good X,
P_y , P_z , .. P_n    stands for prices of all other goods (other than good X) which may be substitutes  
Of or complementary to good X,

Y stands for income of the households,
T stands for tastes and preferences of the households,
And f shows the functional relationship between the demand for good X and the other Variable, uiz., Py , . . Pn , Y and T , etc. in simple words, this functional relationship Shows that the demand for a good X depends upon the price of X, the prices of Other goods Py , P , .. The income of the consumers and their tastes and preferences.

The demand function is just a shorthand expression of the relationship between the quantity demanded of a commodity (left hand side) and the variables that determine it (right hand side). The tern ‘function’ is indicator of this precise quantitative relationship between variables on the right side of the equation and the variable on the left side.

Since, quantity demanded of a good is dependent upon so many variables (factors), we usually pick up one such variable and study its impact on quantity demanded, assuming that all other variables remain unchanged or are constant. Thus, we can examine the impact of an increase in the price of good X on quantity demanded of X on the assumption that prices of all other goods, consumers’ income, their tastes and preferences, etc., remain constant or unchanged. Thus we can examine the impact of change of each individual variable on demand on this assumption that other factors or influences remain unchanged.