. 
© 1999  2004 Douglas A. Ruby
Revised: 02/13/2003
Market Analysis
DemandSide Shocks
Price Elasticity of Demand
Microeconomics

Tutorial: The Price Elasticity of Demand
Working with a linear demand function, we discover that the Price elasticity of demand
'η'_{p}
changes with change in market price. Specifically this measure ranges from negative infinity (at the
reservation price) to zero (where market price is zero). On the upper half of the function,
quantity demanded is described as being fairly price sensitive or Price elastic such that:
%ΔQ_{d} > %ΔP
On the lower half of the function, quantity demanded is described as being price insensitive or
Price Inelastic such that:
%ΔQ_{d} < %ΔP
We can use the diagram below to experiment with this elasticity measure.
 Use the mouse to drag the P scrollbutton to see changes in market price.
 Press Reset to start over.
Answers are below.
A. Move the scrollbutton close to a market price of $150 and click the mouse. Now drag the button down until you
have changed the price by $25.00. By how much, in percentage terms has the price changed? What is the approximate
percentage change in quantity? Which percentage change is larger? What has been the effect on revenue?
B. Move the scrollbutton close to a market price of $75 and click the mouse. Now drag the button down until you
have changed the price by $25.00. By how much, in percentage terms has the price changed? What is the approximate
percentage change in quantity? Which percentage change is larger? What has been the effect on revenue?
C. Move the scrollbutton close to a market price of $50 and click the mouse. Now drag the button up until you
have changed the price by $25.00. Does revenue increase or decrease with this change in price?
D. When demand is Price Elastic what can you conclude about the relationship
between changes in market price and revenue? How about when demand is Price Inelastic?
E. The formula for the Price Elasticity of Demand can be written as follows:
η_{p} = %ΔQ / %ΔP
= (ΔQ/Q)/(ΔP/P)
= (ΔQ/Q)(P/ΔP)
= (ΔQ/ΔP)(P/Q)
= (ΔQ)(P)/(ΔP)(Q)
Using this last expression we find that numerator: '(ΔQ)(P)' is defined by the
TealGreen shaded area and the denominator: (ΔP)(Q)
is defined by the Blue shaded area. Thus the ratio of these two area provide
a graphical look at the elasticity computation. Drag the Price button in both the elastic and inelastic
ranges of the demand curve and compare the areas of these two shaded regions.
Answers...
A. Working with this particular demand equation, a $25.00 change in price will
result in a 25 unit change in quantity demanded. Given a starting price of $150,
and quantity of 50 units, quantity demanded changes by 50% (ΔQ = 25, baseQ = 50).
The price has changed by only 16.6% (ΔP = $25.00, baseP = $150). In this situation
the quantity demanded is starting from a low base value and the base price is relatively high.
Thus the %change in quantity is likely to be greater than the %change in price  demand is Price
Elastic (η_{p} = 50%/16.6% > 1.0).
B. In this case, we are starting with a higher base value for quantity demanded. The percentage
change in quantity is 20% (ΔQ = 25 units, baseQ = 125) and the percentage in Price is 33.3%
(ΔP = $25.00, baseP = 75.00 a much smaller base value). The %change in quantity demanded is less than
the %change in price  demand is Price Inelastic
C. In the Price Inelastic range of demand, an increase in
market price will result in an increase in revenue.
D. When demand is Price Elastic market price and revenue move in opposite
directions (i.e., P , Revenue
and viceversa). When demand is Price Inelastic
market price and revenue move in the same direction (i.e., P , Revenue
and viceversa).
