Respuesta :
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:
[tex]percentage change in price = ({\frac{P_{2} - P_{1}}{Average price})*100[/tex]
[tex]Average Price = \frac{P_{2} + P_{1}}{2}[/tex]
In this question, P₁ is $18 and P₂ is $14
Substituting the values in the formula above we get,
[tex]Average Price = \frac{14 + 18}{2}[/tex]
[tex]Average Price = \frac{32}{2}[/tex]
[tex]Average Price = 16[/tex]
[tex]percentage change in price = (\frac{14 - 18}{16})* 100[/tex]
[tex]percentage change in price = (\frac{-4}{16}) * 100[/tex]
[tex]percentage change in price = -25[/tex]%
b. Percentage change in quantity demanded of skateboards
The percentage change in quantity of skateboards using the midpoint formula is:
[tex]percentage change in quantity = (\frac{Q_{2} - Q_{1}}{Average Quantity})*100[/tex]
In this question, Q₁ is 330 and Q₂ is 350
Substituting the values in the formula above we get,
[tex]Average quantity = \frac{Q_{2} + Q_{1}}{2}[/tex]
[tex]Average quantity = \frac{350 + 330}{2}[/tex]
[tex]Average quantity = 340[/tex]
[tex]percentage change in quantity = (\frac{350 - 330}{340})*100[/tex]
[tex]percentage change in quantity = (\frac{20}{340})*100[/tex]
[tex]percentage change in quantity = 5.8823529[/tex]%
c. Cross Elasticity of demand of skateboards and pizza
We calculate the cross elasticity of demand as follows:
[tex]Cross Elasticity Demand = \frac{percentage change in quantity of skateboards}{percentage change in price of pizza}[/tex]
[tex]Cross Elasticity Demand = \frac{0.058823529}{-0.25}[/tex]
[tex]Cross Elasticity Demand = -0.235294118[/tex]
[tex]Cross Elasticity Demand = -23.53[/tex]%
