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. 

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