The price elasticity of demand is calculated using the midpoint formula:
Price Elasticity of Demand = (Percentage Change in Quantity Demanded / Percentage Change in Price) * 100
To find the percentage change in quantity demanded, we use the formula:
Percentage Change in Quantity Demanded = (New Quantity Demanded - Original Quantity Demanded) / ((New Quantity Demanded + Original Quantity Demanded) / 2) * 100
And for the percentage change in price, we use the formula:
Percentage Change in Price = (New Price - Original Price) / ((New Price + Original Price) / 2) * 100
Given the information provided:
Original price (P1) = $8
Original quantity demanded (Q1) = 320 bicycles
New price (P2) = $12
New quantity demanded (Q2) = 280 bicycles
Let's calculate the percentage changes:
Percentage Change in Quantity Demanded:
Percentage Change in Quantity Demanded = (280 - 320) / ((280 + 320) / 2) * 100
Percentage Change in Price:
Percentage Change in Price = (12 - 8) / ((12 + 8) / 2) * 100
Now we can calculate the price elasticity of demand using the midpoint formula:
Price Elasticity of Demand = (Percentage Change in Quantity Demanded / Percentage Change in Price) * 100
Substituting the calculated values, we have:
Price Elasticity of Demand = ((280 - 320) / ((280 + 320) / 2) * 100) / ((12 - 8) / ((12 + 8) / 2) * 100)
Simplifying further:
Price Elasticity of Demand = (-40) / (20 / 10)
Price Elasticity of Demand = -2
Therefore, the price elasticity of demand for Cynthia's Cycles is -2.
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