# 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.

1. Calculate the value of the price elasticity.
2. Explain what type of demand.
3. 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**