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Extreme cases

15 February, 2016 - 09:58

The elasticity decreases in going from high prices to low prices. This is true for most non-linear demand curves also. Two exceptions are when the demand curve is horizontal and when it is vertical.

When the demand curve is vertical, no quantity change results from a change in price from P_{1} to P_{2}, as illustrated in Figure 4.2. Therefore, the numerator in Equation 4.1 is zero, and the elasticity has a zero value.

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Figure 4.2 Limiting cases of price elasticity 
 

When the demand curve is vertical (D_{v}), the elasticity is zero: a change in price from P_{1} to P_{2} has no impact on the quantity demanded because the numerator in the elasticity formula has a zero value. When D becomes more horizontal the elasticity becomes larger and larger at Qo, eventually becoming infinite.

In the horizontal case, we say that the elasticity is infinite, which means that any percentage price change brings forth an infinite quantity change! This case is also illustrated in Figure 4.2 using the demand curve D_{h}. As with the vertical demand curve, this is not immediately obvious. So consider a demand curve that is almost horizontal, such as D' instead of D_{h}. In this instance, we can achieve large changes in quantity demanded by implementing very small price changes. In terms of Equation 4.1, the numerator is large and the denominator small, giving rise to a large elasticity. Now imagine that this demand curve becomes ever more elastic (horizontal). The same quantity response can be obtained with a smaller price change, and hence the elasticity is larger. Pursuing this idea, we can say that, as the demand curve becomes ever more elastic, the elasticity value tends towards infinity.