Transcript Midpoint Formula

Calculating Elasticity of Demand (or
Supply) Using the Midpoint Formula
• Elasticity!
– Think of Elasticity as a reaction (in quantity) to a
change in price
– Elasticity can be:
• Elastic (Elasticity of Demand [Ed] is greater than 1) or
– Ed > 1
• Unitary Elastic (equal to 1)
– Ed = 1
• Inelastic (less than 1)
– Ed <1
• Infinite
– When we are dividing by zeo
P
D
Q
In this case, eye-ball the Demand Curve. It is steep. Because it is so steep,
we know that it will be inelastic
Calculating Midpoint
• We’ll use an example (inelastic demand)
• GAS RISES FROM $4.00 to $5.00
– (let’s hope not)
• Quantity Demanded falls from 100 to 90 gallons
• See the next slide
P
PRICE OF GAS!
$5.00
$4.00
D
90
Let’s put some numbers to this
100
Q
ELASTICITY OF DEMAND DEFINED
MATHEMATICALLY
• Mathematically the formula is…
• PEoD = (% Change in Quantity Demanded)/(%
Change in Price)
– First Calculate the % Change in Quantity Demanded
» [QDemand(NEW) - QDemand(OLD)] / QDemand(OLD)
– Second, Calculate the % Change in Price[Price(NEW) Price(OLD)] / Price(OLD)
– Finally, take the values from each and go back to the formula
above (% Change in Quantity Demanded/% Change in Price
The Midpoint Formula
• The problem with the previous formula, is that
you can only use it going in one direction
(PRICE INCREASES FROM $4.00 to $5.00
– IT DOESN’T WORK VICE VERSA!
• Won’t give the same result from $5.00 to $4.00
• The midpoint Formula solves the problem
Our Example
• Price Went up from $4.00 to $5.00
– It went up by one ($1.00)
– The midpoint between $4.00 and $5.00 is $4.50
• Quantity Demanded decreased from 100 to 90
– It went down by 10 gallons
– The midpoint between 100 and 90 is 95
Our Example Continued
• So, now that we have the numbers, let’s
calculate the percentage change
• First we’ll solve for quantity
• Q2 –Q1/MIDPOINT
– % Change in quantity using midpoint is as
follows…
• (90-100)/95 = -.10
• We will use ABSOLUTE VALUES!
– So it’s 10%
MIDPOINT FORMULA (cont)
• Now we will solve for price
– P2 – P1/MIDPOINT
– ($5.00-$4.00)/$4.50
– .22 or 22%
•
•
•
•
FINALLY (drumroll…..)
% Change in Quantity /%Change in price
10%(.10)/22%(.22) = .45
SINCE .45 IS LESS THAN ONE (1) IT IS INELASTIC!