Price Elasticity of Demand and Supply: Question 8

Worked solution

Step 1: Calculate the percentage change in price and quantity demanded

$\%\Delta P = \frac{25-20}{20}\times100 = +25\%$

$\%\Delta Q_d = \frac{400-800}{800}\times100 = -50\%$

Step 2: Calculate PED and classify demand

$PED = \frac{-50}{25} = -2.0$

Since the size of PED, ignoring the sign, is $2.0$, and $2.0 > 1$, demand for this board game is price elastic.

Step 3: Calculate total revenue before and after the price rise

Before the price rise: $20 \times 800 = 16\,000$ which is $16,000 per month.

After the price rise: $25 \times 400 = 10\,000$ which is $10,000 per month.

Step 4: Interpret the result

Because demand for the board game is price elastic, the percentage fall in quantity demanded (50%) is proportionately larger than the percentage rise in price (25%). The revenue lost from selling far fewer games outweighs the extra revenue earned on each game still sold, so total revenue falls, from $16,000 to $10,000.

Step 5: Rule out the other options

• Option B ($16,000 to $20,000) comes from pairing the new price with the original quantity ($25 \times 800 = 20\,000$) instead of the new quantity.
• Option C (unchanged at $16,000) ignores the fact that quantity demanded has fallen sharply.
• Option D ($16,000 to $8,000) comes from pairing the original price with the new quantity ($20 \times 400 = 8\,000$) instead of the new price.

Final answer

Total revenue falls from $16,000 to $10,000, option A. This is because demand for the board game is price elastic ($PED=-2.0$), so a price rise reduces total revenue.