If the price elasticity of demand for a product is 2 in absolute value, and the price elasticity of supply for the same product is 1, what is the predicted percentage change in price from a 5% fall in the supply?
a 1.67% fall in price
a 0.6% fall in price
a 1.67% rise in price
a 0.6% rise in price
To determine the predicted percentage change in price from a 5% fall in supply, we can use the concept of elasticity.
The formula for the change in price due to a change in supply is given by:
[ \frac{\Delta P}{P} = \frac{E_d}{E_d + E_s} \cdot \frac{\Delta Q}{Q} ]
Where:
Given:
Now, substituting the values into the formula:
[ \frac{\Delta P}{P} = \frac{2}{2 + 1} \cdot (-0.05) ]
Calculating the right side:
[ \frac{\Delta P}{P} = \frac{2}{3} \cdot (-0.05) = -\frac{2 \times 0.05}{3} = -\frac{0.1}{3} \approx -0.0333 ]
This means that the percentage change in price is approximately -3.33%.
To find the actual percentage change in price, we multiply by 100:
[ \Delta P \approx -3.33% ]
Since the question asks for the predicted percentage change in price from a 5% fall in supply, we can conclude that the price is expected to fall by approximately 3.33%.
However, none of the provided options match this result. It seems there may be a misunderstanding in the options provided or the calculations.
If we consider the options given, the closest interpretation might be that the price would rise or fall by a smaller percentage than calculated.
To summarize, based on the calculations, the predicted percentage change in price from a 5% fall in supply is approximately a 3.33% fall in price, which does not match any of the options provided.
If we were to choose the closest option based on the context of elasticity, we might consider the 1.67% fall in price as a potential answer, but it does not align with the calculated value.
Please verify the options or the context of the question for further clarification.