Question

The price of a large pizza decreased from $18.00 to $14.00. As a result, the quantity demanded of skateboards increased from 330.00 to 350.00.
Using the midpoint formula, what is the percentage change observed for the price of a large pizza? Give your answer to two decimal places.

Using the midpoint formula, what is the percentage change observed for the quantity demanded of skateboards? Give your answer to two decimal places.

What is the cross-price elasticity of demand between pizzas and skateboards? Give your answer to two decimal places.

Answer 1

Answer:

a. The percentage change in pizza prices is -25.00%.

b. The percentage change in pizza prices is 5.88%.

c. The cross elasticity of demand for pizza and skateboards is -23.53%.

We follow these steps to arrive at the answer.

a. Percentage change in price of pizza

The percentage change in price of pizza using the midpoint formula is:

$percentage change in price = ({\frac{P_{2} - P_{1}}{Average price})*100$

$Average Price = \frac{P_{2} + P_{1}}{2}$

In this question, P₁ is $18 and P₂ is $14

Substituting the values in the formula above we get,

$Average Price = \frac{14 + 18}{2}$

$Average Price = \frac{32}{2}$

$Average Price = 16$

$percentage change in price = (\frac{14 - 18}{16})* 100$

$percentage change in price = (\frac{-4}{16}) * 100$

$percentage change in price = -25$%

b. Percentage change in quantity demanded of skateboards

The percentage change in quantity of skateboards using the midpoint formula is:

$percentage change in quantity = (\frac{Q_{2} - Q_{1}}{Average Quantity})*100$

In this question, Q₁ is 330 and Q₂ is 350

Substituting the values in the formula above we get,

$Average quantity = \frac{Q_{2} + Q_{1}}{2}$

$Average quantity = \frac{350 + 330}{2}$

$Average quantity = 340$

$percentage change in quantity = (\frac{350 - 330}{340})*100$

$percentage change in quantity = (\frac{20}{340})*100$

$percentage change in quantity = 5.8823529$%

c. Cross Elasticity of demand of skateboards and pizza

We calculate the cross elasticity of demand as follows:

$Cross Elasticity Demand = \frac{percentage change in quantity of skateboards}{percentage change in price of pizza}$

$Cross Elasticity Demand = \frac{0.058823529}{-0.25}$

$Cross Elasticity Demand = -0.235294118$

$Cross Elasticity Demand = -23.53$%