In this article we will discuss about the perfectly elastic and imperfectly inelastic demand for a good, explained with the help of diagrams.
If, in spite of a change in the price (p) of a good, its quantity demanded (q) does not change at all, then it is said that the demand for the good is perfectly inelastic w.r.t. price. In this case, the demand curve for the good would be a vertical straight line like DD in Fig. 2.3. In this figure, at each price, demand for the good is OM = constant, i.e., even if there is a change in p, q would not change at all.
Therefore, the law of demand is not effective here. Since, at any point on the vertical straight line demand curve, we have p > 0 and q = constant (> 0), and since, in this case, demand does not change even if price changes, i.e., dp ≠ 0 and dq = 0, from (2.4): e = 0. Therefore, when demand is perfectly inelastic, e = 0.
On the other hand, if the quantity demanded (q) of a good changes even when there has been no change in its price (p), the demand for the good is called perfectly elastic w.r.t. price. The demand curve for the good in this case would be a horizontal straight like DD in Fig. 2.4. Here also an exception to the law of demand can be obtained.
Since, at any point on a horizontal straight line demand curve, p = constant (> 0) and q is any value ≥ 0, and since here, in spite of there being no change in p, (dp = 0), q may undergo a change, (dq ≠ 0), from (2.4): e = ∞. Therefore, when demand is perfectly elastic, e = ∞.