Question

Would the estimated price elasticity of demand for movie tickets have been different if we had not used the average-values formula? How?

Short answer

Yes, there are different price elasticities for different methods.

Step-by-step solution

Given Information

The estimated price elasticity of demand for movie tickets are different

Explanation Part (1)

For calculating price elasticity average formula is,

$\frac{\text{change in}Q}{\text{sum of quantities}/2}÷\frac{\text{change in}P}{\text{sum of prices}/2}$

By using the percentage method,

$\frac{\text{change in}Q}{\text{original Quantity}}\times \frac{\text{original price}}{\text{change in price}}$

Explanation Part (2)

let the Increase in the ticket price be from $\mathrm{\$}7.84\text{to}\mathrm{\$}8.08$,

hence the demand for movie tickets decreases from $1.34to1.26$billion

By using the average formula,

$=\frac{0.08}{1.34+1.26/2}÷\frac{0.24}{7.84+8.08/2}=2.04$

By using the percentage method,

$=\frac{1.34-1.26}{1.34}\times \frac{7.84}{8.08-7.84}=1.95$

Hence they have different price elasticities.