. © 1999 - 2004
Douglas A. Ruby
Revised: 02/13/2003

Market Analysis

Demand-Side 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:
%ΔQd > %ΔP
On the lower half of the function, quantity demanded is described as being price insensitive or Price Inelastic such that:
%ΔQd < %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:
ηp = %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 Teal-Green 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,
base-Q = 50). The price has changed by only 16.6% (ΔP = $25.00, base-P = $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 (ηp = |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, base-Q = 125) and the percentage in Price is 33.3% (ΔP = $25.00, base-P = 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 vice-versa). When demand is Price Inelastic market price and revenue move in the same direction (i.e., P , Revenue and vice-versa).