The law is based on the assumption that the other determinants of demand, viz. income of the consumer, tastes and preferences of the consumer, prices of the related goods, future expectations, size and composition of population, distribution of income, etc. do not change during the operation of the law.
If they do change, the law may fail to operate. For example, if with the fall in the price of the good, consumer develops disliking for it or his income declines, he may not buy more of it.
The law of demand indicates only the direction of the change of demand corresponding to a change in price. It does not say anything about the magnitude of change in the quantity demanded.
For example, if price of apples comes down from Rs. 12 per kg. to Rs. 10 per kg., the law tells us that quantity demanded for apples will increase. But, it does not tell the amount by which the quantity demanded for apples will increase as a result of a fall in price.
The law of demand can be illustrated through a demand curve. In Fig. 1.6, price is measured along the Y-axis and quantity demanded is measured along the X-axis. DD is the demand curve of the good under consideration. At the price OP1, the quantity demanded is OQ1. If the price of the good falls to OP2, the quantity demanded increases to OQ2.
The demand curve is downward sloping, which is in accordance with the law of demand. It should be remembered that while drawing the demand curve, all the determinants of demand (except price of the good in question) are assumed to remain constant.
Only the relationship between price and quantity demanded of the commodity is described. The effect of a change in other determinants of demand is discussed later in this chapter.
The functional relationship between demand and price can be expressed as: Qx= f(Px)
Where Qx is demand and Px is the own price of good ‘X’.
The above expression shows that price is the cause variable and demand is effect variable. Alternatively, price is the independent variable, while demand is dependent variable. In technical terms, independent variable (here, price) is also called exogenous variable, while dependent variable (here, demand) is called endogenous variable.
When the demand curve for a good is a straight line, the corresponding demand function will have a linear equation of the form Qx= a – bPx
Here, ‘a’ is the quantity intercept and ‘b’ is the slope. dQx/dPx expresses the rate at which quantity demanded changes, with change in the price. Negative sign in the equation shows inverse price- demand relationship. For plotting the demand curve, we normally use the inverse demand curve Px = a – bQx Here, = a/b is the price intercept and = 1/b is the slope of inverse demand curve and equals dPx/dQx. This inverse form of the demand curve indicates each given quantity demanded, the maximum price a consumer (or consumers) would be willing to pay rather than doing without that quantity. The normal form of the demand curve can also be similarly defined.