AS Level Economics 9708: PED and Total Revenue for Specialty Coffee

A boutique coffee roastery raises the price of its single-origin specialty coffee beans from $20 to $25 per 250g bag. As a result, the quantity of bags it sells each week falls from 400 to 340.

(a) Calculate the percentage change in price and the percentage change in quantity demanded. [2]

(b) Calculate the price elasticity of demand (PED) for these coffee beans, showing your working, and state whether demand is price elastic, price inelastic or unitary. [3]

(c) Calculate the roastery's total revenue from these coffee beans before and after the price rise, and use your answer to (b) to explain whether this change in total revenue is what you would expect. [3]

(d) State one determinant of price elasticity of demand that could help explain why demand for this specialty coffee is price inelastic. [2]

Part (a): Percentage changes in price and quantity demanded

Percentage change in price, using the original price of $20 as the base: $\%\Delta P = \frac{25-20}{20}\times100 = \frac{5}{20}\times100 = +25\%$

Percentage change in quantity demanded, using the original quantity of 400 bags as the base: $\%\Delta Q_d = \frac{340-400}{400}\times100 = \frac{-60}{400}\times100 = -15\%$

Part (b): Calculating and classifying PED

$PED = \frac{\%\Delta Q_d}{\%\Delta P} = \frac{-15}{25} = -0.6$

Ignoring the sign, the size of PED is $0.6$ . Since $0.6 < 1$ , demand for the specialty coffee beans is price inelastic: the percentage fall in quantity demanded (15%) is proportionately smaller than the percentage rise in price (25%).

Part (c): Total revenue before and after

Total revenue $= P \times Q$ .

Before the price rise: $TR_{\text{before}} = 20 \times 400 = 8{,}000$ So total revenue before was $8,000 per week.

After the price rise: $TR_{\text{after}} = 25 \times 340 = 8{,}500$ So total revenue after was $8,500 per week.

Total revenue rises by $500 per week. This is exactly what is expected when demand is price inelastic: because quantity demanded falls proportionately less (15%) than price rises (25%), the extra revenue earned on each bag still sold outweighs the revenue lost from selling fewer bags, so total revenue increases overall, consistent with the inelastic classification found in part (b).

Part (d): A determinant of PED

One determinant of price elasticity of demand is the proportion of income spent on the good. A 250g bag of specialty coffee beans makes up only a small share of a typical customer’s weekly spending, so even a noticeable percentage rise in its price (here, 25%) has little effect on the customer’s overall budget. Because the cost is relatively small in absolute terms, customers are less sensitive to the price change and are unlikely to cut back their buying habits much, which helps make demand for the coffee beans price inelastic, consistent with the inelastic value of $-0.6$ found in part (b).

Final answers

(a) $\%\Delta P = +25\%$ , $\%\Delta Q_d = -15\%$
(b) $PED = -0.6$ . Demand is price inelastic
(c) $TR_{\text{before}} =$ $8,000, $TR_{\text{after}} =$ $8,500. Total revenue rises, as expected for a price rise under inelastic demand
(d) A small proportion of income spent on the good makes demand price inelastic