Question

Sales were 4,000 at a price of $200 but fell to 3,800 when the price was increased to $220. Calculate the percentage change in sales, the percentage change in price, and the price elasticity of demand. (THREE PART)

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Answer 1

It is given that sales were 4,000 when price was $200. So, the quantity demanded equals Sales/Price = 4,000/200 = 200 units.

Sales fell to 3,800 when the price increased to $220. So, the new quantity demanded equals 3,800/220 = 17.27 units.

Percentage change in price can be calculated by the following formula:

$\fn_phv \frac{New\: Price-Old\: Price}{Old\: Price}\times 100$

$\fn_phv \frac{220-200}{200}\times 100$

$\fn_phv \frac{20}{200}\times 100=10$

So, there is a 10% increase in price.

Percentage change in sales can be calculated by the following formula:

$\fn_phv \frac{New\: Sales-Old\: Sales}{Old\: Sales}\times 100$

$\fn_phv \frac{3,800-4,000}{4,000}\times 100$

$\fn_phv \frac{-200}{4,000}\times 100=-5$

So, there is a 5% fall in sales.

The price elasticity of demand can be calculated by the following formula:

$\fn_phv \frac{New\: Quantity\: Demanded-Old\: Quantity\: Demanded}{New\: Price-Old\: Price} \: \frac{Old\: Price}{Old\: Quantity\: Demanded}$

$\fn_phv \frac{17.27-20}{220-200} \times \frac{200}{20}$

$\fn_phv \frac{-2.27}{20} \times \frac{200}{20}$

$\fn_phv =-1.135$

Therefore, the price elasticity of demand is -1.135.