The management of a fruit juice pro- duction company was directed by the shareholders to increase the revenue from the sale of its product. The management decided to increase the price of the fruit juice from $7 to $$ 10 per unit and this led to a fall in quantity demanded from 150 units to 30 units.
Use the information above to answer the questions that follow.
(a) Calculate the;
(i) Percentage increase in the price; (ii) percentage decrease in the quantity demanded
(iii)coefficient of price elasticity of demand for the fruit juice.
(b) Is the demand for the fruit, price elastic or inelastic? Give a reason for your
answer.
(c) Did the management of the company achieve its objective of increasing revenue? Explain your answer.
(d) From your answers in 2a(iii), was the increase in the price of the fruit juice a rational strategy to employ in order to increase revenue? Explain your answer.
2a (i) Percentage increase in price
= \(\frac{\text{(change in price 100)}}{\text{Old price}}\) x 100
= \(\frac{$(10 - 7)}{7}\) x 100
OR
\(\frac{$3}{7}\) x 100 = 42.86% or 42.9%
(ii) Percentage decrease in quantity demanded
= \(\frac{\text{(change in quantity demanded)}}{\text{Old quantity}}\) x 100
= \(\frac{30}{150}\) x 100
OR Δ
= \(\frac{120}{150}\) x 100 = (-)80%
(iii) Coefficient of price elasticity of demand
= \(\frac{\text{(% change in quantity demanded)}}{\text{% change in price}}\)
(-) \(\frac{80%}{31.86%}\) = (-) 1.87 OR 1.9
Alternatively,
\(\frac{Δ Q}{Δ P}\) x \(\frac{P}{Q}\)
= \(\frac{120}{3}\) x \(\frac{7}{150}\) = \(\frac{840}{450}\) = 1.87 OR 1.9
(b) The demand for the fruit juice is price elastic. This is because the coefficient is greater than on. OR The percentage change in quantity demanded is great- er than percentage change in price OR the percentage change in price is lower than the percentage change in quantity demanded.
(c) The management of the company did not achieve its set objective of increasing revenue because total revenue de- creased. When price was $7, total revenue
(TR)=PXQ=$ 7×150 = $1,050
while when price increased to $ 10.
Total revenue,
(TR) = P×Q = $ 10×30 = $ 300. Reve- nue reduced by $ 750
(d) Increasing the price of the fruit juice in order to increase revenue is not a rational strategy to employ. Since the demand for the fruit juice is price elastic, an increase in its price will lead to a greater reduction in quantity demanded thus decreasing total revenue. OR Because demand is elastic the product has substitutes, increasing its price will drive its consumers to its substitutes thus reducing demand
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