A manager faces price elasticity of demand for a product X equal to -0.5. Now the manager wishes to increase sales of product X by 15%. By what percentage should the price change?
Understand the Problem
The question is asking for the percentage change in price that would be needed to achieve a 15% increase in the sales of product X, given its price elasticity of demand is -0.5. This requires applying the formula for price elasticity of demand.
Answer
The price should decrease by $30\%$.
Answer for screen readers
The percentage change in price required is $-30%$.
Steps to Solve
- Understand the formula for price elasticity of demand
The price elasticity of demand (PED) is given by the formula: $$ PED = \frac{%\text{ change in quantity demanded}}{%\text{ change in price}} $$
- Substitute known values into the formula
Here, we have:
- PED = -0.5
- % change in quantity demanded = 15%
Now substituting the values we know: $$ -0.5 = \frac{15%}{%\text{ change in price}} $$
- Solve for the percentage change in price
Rearranging the equation to find the % change in price: $$ %\text{ change in price} = \frac{15%}{-0.5} $$
- Calculate the percentage change in price
Now perform the calculation: $$ %\text{ change in price} = \frac{15}{-0.5} = -30% $$
This means the price must decrease by 30%.
The percentage change in price required is $-30%$.
More Information
A 30% decrease in price is needed to achieve a 15% increase in sales, given a price elasticity of demand of -0.5. This illustrates how an inelastic demand means larger price changes are necessary to achieve desired changes in quantity sold.
Tips
- Not accounting for the negative sign in price elasticity, which indicates an inverse relationship between price and quantity demanded.
- Confusing the effects of elasticity, leading to incorrect interpretations of the results.
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