When the price of surfboards is equal to 2, the firm sells 10 surfboards and 20 scooters. When the price of surfboards increases to 4, the firm sells 6 surfboards and 10 scooters. What is the cross-price elasticity of scooters’ demand to the change in price of surfboards? Use mid-point formula to answer the question. Group of answer choices-1, surfboards and scooters are substitutes-0.75, surfboards and scooters are substitutes-1, surfboards and scooters are complements-0.75, surfboards and scooters are complementsNone of the other answers are correct
Question
When the price of surfboards is equal to 2, the firm sells 10 surfboards and 20 scooters. When the price of surfboards increases to 4, the firm sells 6 surfboards and 10 scooters. What is the cross-price elasticity of scooters’ demand to the change in price of surfboards? Use mid-point formula to answer the question. Group of answer choices-1, surfboards and scooters are substitutes-0.75, surfboards and scooters are substitutes-1, surfboards and scooters are complements-0.75, surfboards and scooters are complementsNone of the other answers are correct
Solution
The cross-price elasticity of demand measures the responsiveness of the quantity demanded of one good to a change in the price of another good. It is calculated as the percentage change in quantity demanded of Good B divided by the percentage change in the price of Good A.
In this case, we are looking at the change in demand for scooters as a result of a change in the price of surfboards.
The mid-point formula for cross-price elasticity of demand is:
E = [(Q2 - Q1) / ((Q2 + Q1) / 2)] / [(P2 - P1) / ((P2 + P1) / 2)]
Where:
- Q1 is the initial quantity demanded of scooters (20)
- Q2 is the final quantity demanded of scooters (10)
- P1 is the initial price of surfboards (2)
- P2 is the final price of surfboards (4)
Substituting these values into the formula, we get:
E = [(10 - 20) / ((10 + 20) / 2)] / [(4 - 2) / ((4 + 2) / 2)] E = [-10 / 15] / [2 / 3] E = -0.67 / 0.67 E = -1
Therefore, the cross-price elasticity of scooters’ demand to the change in price of surfboards is -1. This indicates that surfboards and scooters are complements, as an increase in the price of surfboards leads to a decrease in the demand for scooters. So, the correct answer is "-1, surfboards and scooters are complements".
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