CALCULATION – OWN-PRICE ELASTICITY The %age change in quantity demanded of a good divided by the %age change in price of the good. Two ways in making the calculation – point Formula and midpoint formula. The latter is more precise. • Point formula – (Q2 – Qu)/Q1 / (P2 – P1)/P1 • Midpoint formula – (Q2-Qa)/[(Q2 + Q1)/2] / (P2-P1)/[(P2 + P1)/2]. Example – Table 1 – Prices and quantity demanded of organic apples Price Quantity Demanded range (a) P1 P2 $10 9 4 86 مه | | o | (b) 10 P1 P2 (c) P13 PL مساج 14 16 18 Using table 1 and midpoint formula at (a), price drops from $10 to $9 and demand rises from 2 to 4; the own-price elasticity = (4-2)/([4+2)/2] / [(9-10)/((9+10)/2]= 2/3/(-1/9.5) = 2×9.5/3 = -19/3 = -6.33. Absolute value > 1, thus elastic. At (c) price drops from $3 to $2 and demand rises from 16 to 18, the own-price elasticity = (18-16)/((18+16)/2]/(2-3)/[(2+3)/2] = 2/17/ -1/2.5 = 5/-17 = -0.294. Absolute value is less than one but greater than zero, thus inelastic. Please see interpretations below. INTERPRETATIONS OWN-PRICE ELASTICITY Ep = 0 Perfectly elastic Ep > 1 elastic 0
The Correct Answer and Explanation is :
Own-Price Elasticity of Demand Calculation
The own-price elasticity of demand (Ep) measures how the quantity demanded of a good changes in response to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. There are two formulas commonly used to calculate price elasticity: the point formula and the midpoint formula. The midpoint formula is generally preferred for its precision because it gives the same result regardless of the direction of change (i.e., whether the price increases or decreases).
Point Formula:
The point formula for elasticity is:
[
E_p = \frac{(Q_2 – Q_1)}{Q_1} \Big/ \frac{(P_2 – P_1)}{P_1}
]
Where:
- ( Q_1 ) and ( Q_2 ) are the initial and final quantities demanded, respectively.
- ( P_1 ) and ( P_2 ) are the initial and final prices, respectively.
Midpoint Formula:
The midpoint formula for elasticity is:
[
E_p = \frac{(Q_2 – Q_1)}{\left(\frac{Q_2 + Q_1}{2}\right)} \Big/ \frac{(P_2 – P_1)}{\left(\frac{P_2 + P_1}{2}\right)}
]
Where:
- The numerator calculates the percentage change in quantity demanded relative to the average quantity, and the denominator calculates the percentage change in price relative to the average price.
Example: Using the Midpoint Formula
In the example you provided, we have the following:
At point (a): Price drops from $10 to $9, and quantity demanded rises from 2 to 4.
Using the midpoint formula:
[
E_p = \frac{(4 – 2)}{\left(\frac{4 + 2}{2}\right)} \Big/ \frac{(9 – 10)}{\left(\frac{9 + 10}{2}\right)}
]
Calculating the numerator:
[
\frac{(4 – 2)}{\left(\frac{4 + 2}{2}\right)} = \frac{2}{3}
]
And the denominator:
[
\frac{(9 – 10)}{\left(\frac{9 + 10}{2}\right)} = \frac{-1}{9.5}
]
Now, calculate the own-price elasticity:
[
E_p = \frac{2/3}{-1/9.5} = \frac{2 \times 9.5}{3} = \frac{19}{3} = -6.33
]
The absolute value of the elasticity is 6.33, which is greater than 1, meaning the demand is elastic. This means that the percentage change in quantity demanded is greater than the percentage change in price.
At point (c): Price drops from $3 to $2, and quantity demanded rises from 16 to 18.
Using the midpoint formula:
[
E_p = \frac{(18 – 16)}{\left(\frac{18 + 16}{2}\right)} \Big/ \frac{(2 – 3)}{\left(\frac{2 + 3}{2}\right)}
]
Calculating the numerator:
[
\frac{(18 – 16)}{\left(\frac{18 + 16}{2}\right)} = \frac{2}{17}
]
And the denominator:
[
\frac{(2 – 3)}{\left(\frac{2 + 3}{2}\right)} = \frac{-1}{2.5}
]
Now, calculate the own-price elasticity:
[
E_p = \frac{2/17}{-1/2.5} = \frac{2 \times 2.5}{17} = \frac{5}{17} = -0.294
]
The absolute value of the elasticity is 0.294, which is less than 1, meaning the demand is inelastic. This means that the percentage change in quantity demanded is less than the percentage change in price.
Interpretation of Elasticity:
- Elastic demand (Ep > 1): When the absolute value of elasticity is greater than 1, the demand is considered elastic, meaning consumers are highly responsive to price changes. A small change in price results in a larger percentage change in quantity demanded.
- Inelastic demand (0 < Ep < 1): When the absolute value of elasticity is less than 1, the demand is inelastic. In this case, consumers are less responsive to price changes, and a price change causes a smaller percentage change in quantity demanded.
- Unitary elasticity (Ep = 1): This occurs when the percentage change in quantity demanded equals the percentage change in price, resulting in an elasticity of 1.
- Perfectly elastic demand (Ep = ∞): When demand is perfectly elastic, consumers will only buy the product at one price and will not purchase it at any other price.
- Perfectly inelastic demand (Ep = 0): When demand is perfectly inelastic, the quantity demanded does not change at all in response to a price change.
In this example, at point (a), the demand is elastic, and at point (c), the demand is inelastic.