Answer :
Final answer:
The elasticity of demand, E(p), is calculated using the percentage change in quantity demanded divided by the percentage change in price, not from a price-demand equation like x = f(p) = 20000 - 550p. The demand function of the form qd(p) = a * p−α is used for constant elasticity cases, but elasticity varies at different points on a demand curve such as P = 2/Q.
Explanation:
The price-demand equation does not directly give us the elasticity of demand, E(p). Rather, to find the elasticity of demand, we use the percentage change in quantity demanded divided by the percentage change in price. For example, if we are considering a change in price from $70 to $60 and the corresponding change in quantity demanded from 2,800 to 3,000 units, we would calculate the percentage changes and then divide the percentage change in quantity by the percentage change in price to get E(p).
When we speak about constant elasticity, we refer to a demand function that can be denoted as qd(p) = a * p−α, which allows us to draw conclusions about small changes in a general demand function. If a firm sets a price of $15 and then changes it to $14.80, leading to a change in quantity demanded from 25 to 26 units, we can calculate elasticity using the given formula.
Lastly, for a demand curve given by P = 2/Q, elasticity will differ at different price points such as 5 to 4 and 9 to 8 due to the nature of the demand curve, which shows that elasticity of demand is not constant and will change with different price levels.
