The general model of demand and supply can be highly

The general model of demand and supply can be highly useful in understanding
directional changes in prices and quantities that result from shifts in one curve or the
other. Often, though, we need to measure how sensitive quantity demanded or sup-
plied is to changes in the independent variables that affect them. This is the concept
of elasticity of demand and elasticity of supply . Fundamentally, all elasticities are
calculated in the same way: They are ratios of percentage changes. Let us begin with
the sensitivity of quantity demanded to changes in the own price.
1 Following usual practice, we show linear demand curves intersecting the quantity axis at a price of
zero. Real-world demand functions may be non-linear in some or all parts of their domain. Thus, linear
demand functions in practical cases are approximations of the true demand function that are useful for a
relevant range of values.
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Demand Analysis: The Consumer 9
2.2 Own-Price Elasticity of Demand
In Equation 1, we expressed the quantity demanded of some good as a function of
several variables, one of which was the price of the good itself (the good’s “own-price”).
In Equation 3, we introduced a hypothetical household demand function for gas-
oline, assuming that the household’s income and the price of another good (automo-
biles) were held constant. That function was given by the simple linear expression Q
x
d
= 57 – 6.39 P
x
. Using this expression, if we were asked how sensitive the quantity of
gasoline demanded is to changes in price, we might say that whenever price changes
by one unit, quantity changes by 6.39 units in the opposite direction; for example, if
price were to rise by €1, quantity demanded would fall by 6.39 liters per month. The
coefficient on the price variable (–6.39) could be the measure of sensitivity we are
seeking.
There is a drawback associated with that measure, however. It is dependent on
the units in which we measured Q and P . When we want to describe the sensitivity of
demand, we need to recall the specific units in which Q and P were measured—liters
per month and euros per liter—in our example. This relationship cannot readily be
extrapolated to other units of measure—for example, gallons and dollars. Economists,
therefore, prefer to use a gauge of sensitivity that does not depend on units of mea-
sure. That metric is called elasticity . Elasticity is a general measure of how sensitive
one variable is to any other variable, and it is expressed as the ratio of percentage
changes in each variable: %Δ y /%Δ x . In the case of own-price elasticity of demand ,
that measure is illustrated in Equation 5:
E
Q
P
p
d
x
d
x
x
=
%
%
Δ
Δ
This equation expresses the sensitivity of the quantity demanded to a change in
price. E
p
d
x
is the good’s own-price elasticity and is equal to the percentage change in
quantity demanded divided by the percentage change in price. This measure is inde-
pendent of the units in which quantity and price are measured. If quantity demanded
falls by 8% when price rises by 10%, then the elasticity of demand is simply –0.8. It
does not matter whether we are measuring quantity in gallons per week or liters per
day, and it does not matter whether we measure price in dollars per gallon or euros
per liter; 10% is 10%, and 8% is 8%. So the ratio of the first to the second is still –0.8.