2.2 KiB
Price Elasticity
We can calculate how our projected profits change when increasing or decreasing the price of our product.
|E_d| = \frac{\Delta Q(\%)}{\Delta p(\%)}
If E_d > 1 the price is elastic, when E_d < 1 the price is inelastic and when E_d = 1 the price is unitary.
If we break the formula down, it is basically % Change in Quantity / % Change in price.
Example:
You sell 10.000 reams of paper at 100€/ream, you raise the price to 150€/ream and sell 7.000 reams.
The Price Elasticity is now \displaystyle \frac{\frac{QN-QI}{(QN+QI)/2}}{\frac{PN-PI}{(PN+PI)/2}}
$QN$= old Quantity $QI$= new Quantity $PN$= old Price $PI$= new Price
So when we replace the variables with our numbers we get:
\displaystyle E_d = \frac{\frac{10000-7000}{(10000+7000)/2}}{\frac{100-150}{(100+150)/2}}
\displaystyle E_d \approx −0.88
This means the price is inelastic. Meaning changes in price result in small changes to demand.
Moar Examples:
At a price of € 4 the quantity demanded of a particular good is 100 units.
- Calculate the value of the price elasticity.
- Explain what type of demand.
- Plot the elasticity of demand
In each case:
a) If the price increases to 5 € and quantity demanded decreases to 90 units. b) If the price increases to 5 € and quantity demanded decreases to 50 units. c) If the price increases to 5 € and quantity demanded decreases to 75 units. d) If the price increases to 5 € and quantity demanded remains unchanged. e) If the price stays the same and the quantity demanded increases by 10 units.
\displaystyle a = \frac{\frac{100-90}{(100+90)/2}}{\frac{4-5}{(4+5)/2}} \approx -0.47
→ Inelastic
\displaystyle b = \frac{\frac{100-50}{(100+50)/2}}{\frac{4-5}{(4+5)/2}} = -3
→ Elastic
\displaystyle c = \frac{\frac{100-75}{(100+75)/2}}{\frac{4-5}{(4+5)/2}} \approx -1.28
→ Elastic
\displaystyle d = 0
→ Perfectly Inelastic
\displaystyle e = \frac{(100-110)/((100+110)/2)}{(4-4)/((4+4)/2)} = -\frac{2}{0} = Infinity
→ Perfectly Elastic
Example 3:
ppu = 30 quantity = 300
new ppu = 45 new quantity = 225
\displaystyle E_d = \frac{(300-225)/((300+225)/2)}{(30-45)/((30+45)/2)} \approx |-0.71|
→ Inelastic