The correct answer is: C. $${e_a} = \frac{{{Q_1} – {Q_2}}}{{{P_1} – {P_2}}} \div \frac{{{Q_1} – {Q_2}}}{{{P_1} + {P_2}}}$$
The arc elasticity of demand is a measure of the responsiveness of the quantity demanded of a good or service to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.
The formula for arc elasticity is:
$$e_a = \frac{\frac{Q_2 – Q_1}{Q_1 + Q_2}}{\frac{P_2 – P_1}{P_1 + P_2}}$$
where:
- $Q_1$ is the initial quantity demanded
- $Q_2$ is the final quantity demanded
- $P_1$ is the initial price
- $P_2$ is the final price
The arc elasticity of demand can be positive, negative, or zero. A positive arc elasticity indicates that the quantity demanded increases when the price decreases. A negative arc elasticity indicates that the quantity demanded decreases when the price decreases. A zero arc elasticity indicates that the quantity demanded is not affected by a change in price.
The arc elasticity of demand is a useful tool for businesses to understand how consumers will respond to changes in price. It can also be used to compare the responsiveness of different goods and services to changes in price.
Here is a brief explanation of each option:
- Option A: This option is incorrect because it divides the percentage change in quantity demanded by the percentage change in price, but then adds the two quantities together. This does not make sense mathematically.
- Option B: This option is incorrect because it divides the percentage change in quantity demanded by the percentage change in price, but then subtracts the two quantities together. This also does not make sense mathematically.
- Option C: This option is correct because it divides the percentage change in quantity demanded by the percentage change in price, and then divides the result by the average of the initial and final prices. This is the correct formula for calculating arc elasticity.
- Option D: This option is incorrect because it does not include any of the correct formulas for calculating arc elasticity.