Price Elasticity of Demand

Price elasticity of demand measures the responsiveness of demand for a good to changes in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. A negative price elasticity of demand indicates an inverse relationship between price and quantity demanded, meaning that as price increases, quantity demanded decreases, and vice versa.

Calculation

Given that the price elasticity of demand is -0.75, we can use this information to calculate the percentage fall in price that will result in a 15% rise in demand.

Formula:
Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)

In this case, we know that the price elasticity of demand is -0.75, which means that for a 1% change in price, the quantity demanded will change by 0.75%. Let's assume that the initial price is P and the initial quantity demanded is Q.

Step 1:
Calculate the percentage change in quantity demanded:
Percentage Change in Quantity Demanded = 15%

Step 2:
Calculate the corresponding percentage change in price:
Percentage Change in Price = (Percentage Change in Quantity Demanded) / Price Elasticity of Demand
Percentage Change in Price = (15%) / (-0.75)
Percentage Change in Price = -20%

Step 3:
Calculate the percentage fall in price:
Percentage Fall in Price = Percentage Change in Price / Initial Price
Percentage Fall in Price = -20% / P

Therefore, a 20% fall in price would result in a 15% rise in demand for the given good.

Explanation

The price elasticity of demand of -0.75 indicates that the demand for the good is relatively inelastic. This means that a change in price will have a proportionately smaller effect on the quantity demanded.

In this case, a 15% rise in demand indicates that the quantity demanded will increase by 15% in response to a change in price. To achieve this increase in demand, the price needs to decrease by 20%. This is because the price elasticity of demand of -0.75 indicates that for every 1% change in price, the quantity demanded changes by 0.75%.

By understanding the price elasticity of demand, businesses can make informed decisions about pricing strategies. In this scenario, a 20% reduction in price would likely lead to a significant increase in demand, resulting in higher sales and potentially increased market share.

20%...