d. Use the midpoint method to calculate the price elasticity of demand from $25 to $30. Explain whether demand is price elastic or price inelastic and interpret the value of this elasticity. (4 marks)
To calculate the price elasticity of demand using the midpoint method, we need the following formula:
Elasticity = ((Q2 - Q1) / ((Q1 + Q2) / 2)) / ((P2 - P1) / ((P1 + P2) / 2))
In this case:
Q1 = Initial quantity demanded ($25)
Q2 = Final quantity demanded ($30)
P1 = Initial price ($25)
P2 = Final price ($30)
Step 1: Calculate the change in quantity demanded:
Q2 - Q1 = $30 - $25 = 5
Step 2: Calculate the average quantity demanded:
(Q1 + Q2) / 2 = ($25 + $30) / 2 = 27.5
Step 3: Calculate the change in price:
P2 - P1 = $30 - $25 = 5
Step 4: Calculate the average price:
(P1 + P2) / 2 = ($25 + $30) / 2 = 27.5
Now, we can calculate the price elasticity of demand:
Elasticity = ((5 / 27.5) / (5 / 27.5)) = 1
Interpreting the value of elasticity:
Since the calculated elasticity is equal to 1, demand is considered to be unit elastic. Unit elasticity means that a 1% change in price will lead to an equal percentage change in quantity demanded. In this case, a 1% increase in price will result in a 1% decrease in quantity demanded, and vice versa.