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

D P 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

D P Q Let’s put some numbers to this PRICE OF GAS! $4.00 $

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!