David K.H. Begg, Gianluigi Vernasca-Economics-McGraw Hill Higher Education (2011)

4.1 The price responsiveness of demand
Using ( 4) you can find the elasticity at any point of a demand curve, linear or non-linear. There are special cases
in which the elasticity is constant along a demand curve. Consider the following direct demand function:
Q D = 100
p
The demand function in (5) is non-linear (try to plot it!). In this case, the derivative of the direct demand is:
dQV 100
-- =--
dP P2
Suppose we want to know the elasticity of demand at P = 5. At that price the quantity demanded according to
(5) is Q0 = 20. In this case, we have dQ0!dp = -[100/(5)2] = -4. Applying equation (4) we have:
5
PED =-4-=-l
20
(5)
at P = 5 the demand is unit elastic. What about at P = 10? In this case, the
quantity demanded is Q0 = 100/10 = 10 and then dQ0!dp = -[100/(10)2] =
-1. The PED is:
If the demand elasticity is -1 ,
demand is unit elastic.
10
PED =-1-=-l
10
the PED is still -1. Indeed, any demand function of the form Q 0 =Al P, where A is any positive constant, has
the property that the elasticity of demand is constant along the demand curve.
Determinants of price elasticity
Why is the price elasticity of demand for a good high (-5) or low (-0.5)? The answer lies in consumer
tastes. If it is a social necessity to own a television, higher TV prices have little effect on quantity demanded.
IfTV s are considered a frivolous luxury, the demand elasticity is much higher. Psychologists and sociologists
can explain why tastes are as they are. As economists, we can identify some considerations likely to affect
consumer responses to changes in the price of a good. The most important consideration is the ease with
which consumers can substitute another good that fulfils approximately the same function.
Consider two extreme cases. Suppose the price of all cigarettes rises by 1 per cent. The quantity of cigarettes
demanded will hardly respond. People who can easily quit smoking have already done so. In contrast,
suppose the price of a particular brand of cigarettes rises by 1 per cent, all other brand prices remaining
unchanged. We expect a much larger quantity response. Consumers switch from the dearer brand to other
brands that also satisfy the nicotine habit. For a particular cigarette brand the demand elasticity is quite high.
Our example suggests a general rule. The more narrowly we define a commodity (a particular brand of
cigarette rather than cigarettes in general), the higher will be the price elasticity of demand.
Measuring price elasticities
Table 4.2 confirms that the demand for broad categories of basic commodities, such as fuel, food or even
services to household, is inelastic. As a category, only alcohol seems to have an elastic demand. Households
simply do not have much scope to alter the broad pattern of their purchases.
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