Question

if the slice the price of a slice of pizza rises from $2.50 to $3, and the quantity demanded falls from 10,000 slices to 7,400 slices, using the formula for arc price elasticity (5 marks) i. What is the percentage change in price? ii. What is the percentage change in quantity? iii. What is the level of elasticity? iv. What is the interpretation the results of pizza rises from $2.

Answer 1

i.

$The\, percentage\, change\, in\, price \,=\frac{ P_{1}\, -\, P_{0}}{\frac{P_{1}\, +\, P_{0}}{2}}\\ But;\\ P_{1}\,=3\\ and\\ P_{0}\,= 2.5\\ Hence;\\ \mathbf{The\, percentage\, change\, in\, price \,=\frac{ 3\, -\, 2.5}{\frac{3\, +\, 2.5}{2}}\,=18.18\%}$

ii.

$The\, percentage\, change\, in\, quantity\,=\frac{ Q_{1}\, -\, Q_{0}}{\frac{Q_{1}\, +\, Q_{0}}{2}}\\ But;\\ Q_{1}\,=7,400\\ and\\ Q_{0}\,= 10,000\\ Hence;\\ \mathbf{The\, percentage\, change\, in\, quantity\,=\frac{ 7,400\, -\, 10,000}{\frac{7,400\, +\, 10,000}{2}}\,=-29.89\%}$

iii.

$\mathbf{Price\, elasticity\, of\, demand\,= \frac{Percentage\, change\, in\, quantity\, demanded}{Percentage\, change\, in\, price}}\\ \mathbf{Price\, elasticity\, of\, demand\,= \frac{-29.89}{18.18}= -1.64}$

iv.

Interpretation of the results

The arc price elasticity of pizza is greater than one, that is, 1.64. This implies that pizza has an elastic demand when the price of pizza ranges between $2.5 and $3.