A dealer in deep freezers increased the price of his product from $450 to $500 and sales dropped from 800 units to 600 units a week.
Use the information above to answer the questions that follow.
(a)(i) Calculate the price elasticity of demand
(ii) What type of elasticity is it? Explain your answer
(b)Calculate the (i) total revenue of the company before and after price increase; (ii) change in total revenue.
(c) What is the effect of the increase in price on the total revenue?
(d) State two factors influencing price elasticity of demand.
Explanation
(a)(i) \(P_1\) = $450, \(P_2\) = $500 \(\Delta\)P = $500
\(Q_1\) = 800 units, \(Q_2\) = 600 units \(\Delta\)Q = -200 units
Price Elasticity = \(\frac{\Delta Q}{Q} \times \frac{P}{\Delta P} \) OR \( \frac{\Delta Q}{\Delta P} \times \frac{P}{Q} \)
= \(\frac{-200}{800} \times \frac{450}{50} \)
= \(\frac{-1}{4} \times \frac{9}{1} \)
= [-2.25]
OR
\(\frac{\text{% change in quantity demanded}}{\text{% change in price}} \)
% Change in Quantity Demanded = \(\frac{600 - 800}{800} \times 100 \) = -25%
% Change in Price = \(\frac{500 - 450}{450} \times 100 \) = 11.1%
Therefore, \(\frac{\text{% change in quantity demanded}}{\text{% change in price}} \) = \(\frac{25\%}{11.1\%} \) = [-2.25]
(ii) Demand is price elastic because the coefficient is greater than 1.
(b)(i) Total revenue before = $450 x 800 = $360,000
Total revenue after = $500 x 600 = $300,000
(ii) Change in total revenue = $360,000 - $300,000 = $60,000
(c) The firm's revenue has fallen by $60,000 after the price increase.
(d) Factors influencing price elasticity of demand;
(i) Availability of substitutes: Commodities with close substitutes tend to have elastic demand while those without close substitute have inelastic demand.
(ii) Degree of necessity: Necessities tend to have inelastic demand while luxuries tend to have elastic demand.
(iii) Percentage of income spent on the commodity: Commodities that takes a very small percentage of consumers' incomes tend to be price inelastic while those that take a very large proportion of one's income tend to have elastic demand.
(iv) Habit or strength of consumer's taste: Goods which are habit-forming tend to have inelastic demand and vice versa.
(v) Income of consumer: Very high income earners tend to have inelastic demand for many goods while low income earners have elastic demand for many commodities. (vi) Time factor: In the short-run, most goods do not have sub-stitutes and so demand is inelastic, but in the long-run when goods have substitutes, demand is elastic.
(vii) Scope of definition of the good: The broader the definition e.g (food) demand is inelastic, but if the definition is narrow e.g (yam) demand is elastic.
(viii) Number of uses of the commodity: If a comodity has several uses, demand is elastic, but if there is only one use demand is inelastic.
(ix) Degree of durability: If a commodity is durable, it has inelastic demand and vice versa.