Lesson 10
Elasticity of Demand
Announcements
Popper 09 today
Homework
Quiz
1
Suppose you are the marketing manager of a retail business and it’s your job to
make decisions about the pricing of your products. You’d make better decisions if
you had information about what effect a small change in price would have on the
demand for your product. If there would be no real change in demand, you might
consider raising the price BUT if a price increase would cause a big drop in
demand, you might urge the CEO to keep prices right where they are.
The measure of the responsiveness of demand to a change in its price has a name:
ELASTICITY OF DEMAND. It is a ratio.
E ( p) 
percent change in demand
percent change in price
Let’s look at how a formula for this came about. Take your demand function and
solve it for x. This will give you x  f ( p ) where x is the quantity and this is a
demand function with an independent variable of p, price.
If we increase the price by h dollars and then look at finding that quantity we are
looking at f ( p  h) . (this should be looking familiar…)
The percent change in demand is
100 
f ( p  h)  f ( p )
f ( p)
The percent change in price is
100 
h
p
Now take the ratio and simplify:
100 
f ( p  h)  f ( p )
f ( p)
h
100 
p
2
We now have
p  f ( p  h)  f ( p ) 

f ( p) 
h
The second factor is the AROC which we’ll approximate with the derivative. This
works as long as h is VERY small. This quantity is almost always negative so the
actual formula makes it positive by multiplying by negative one.
So now
E ( p)  
p  f '( p)
f ( p)
With p is the price and f(p) is the demand function solved for p. It is also a
requirement that the demand function be differentiable at p.
Popper 09
Question 1
3
Example:
Given a demand function:
x + 3p – 12 = 0
Find the elasticity of demand:
Solve the demand function for x:
Take it’s derivative:
Plug it all into the formula (and don’t forget the minus sign!):
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Popper 09
Question 2
5
Now there are descriptors for the way revenue responds to elasticity: it is elastic,
unitary, or inelastic.
ELASTIC demand at p:
An increase in unit price will cause demand to decrease or
A decrease in unit price will cause demand to increase
E ( p)  1
at p is elastic demand
UNITARY demand at p:
An increase in unit price will cause the demand to stay about the same
E ( p)  1
at p is unitary demand
INELASTIC demand at p:
An increase in unit price will cause revenue to increase or
A decrease in unit price will cause revenue to decrease
E ( p)  1
is inelastic demand
(think: elastic works like I expect; inelastic is ii/dd)
What type of demand do we have in our example above when p = 5?
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Popper 02
Question 3
7
Example
Suppose the demand for a product is p  .02 x  492
Find the elasticity of demand
Find E(100) and interpret the results in terms of vocabulary and outcomes
(will raising the price increase revenues or not?)
Find E(500) and interpret the results in terms of vocabulary and outcomes
(will raising the price increase revenues or not?)
8
Popper 03
Question 4
9
Here is another application of elasticity.
Example
If E(p) = 0.5 when p = 250, what effect will a 1% increase in price have on
revenue?
RECALL:
E ( p) 
percent change in demand
and E ( p )  1 is inelastic demand
percent change in price
Example
If E(p) = 3/2 when p = 250, what effect will a 1% increase in price have on
revenue?
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Popper 09
Question 5
11
All the rest of the popper questions:
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7
8
9
10
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