Question

Used he consumer demand equation for tissues is given by q=8,100−180p+p²

, where p is the price per case of tissues and q is the demand in weekly sales. Determine the price elasticity of demand E when the price is set at $25. (Round your answer to three decimal places.) E=............. Interpret your answer. When the price is set at $25, the demand is going At that price level, the demand is If they raise prices, revenue will by.............. % per 1% increase in price.

Answer 1

To determine the price elasticity of demand, use the formula to calculate the percentage change in quantity demanded and price, then calculate the price elasticity using the ratio of the percentage changes. The price elasticity measures the responsiveness of demand to price changes.

Step-by-step explanation:

To determine the price elasticity of demand, we need to calculate the percentage change in quantity demanded and the percentage change in price. The formula to calculate the percentage change is:

Percentage Change = ((New Value - Old Value) / Old Value) * 100

Using this formula, we can calculate the percentage change in quantity demanded as:

Percentage Change in Quantity = ((q(25) - q(20)) / q(20)) * 100 = ((8100 - 180(25) + (25)^2 - (8100 - 180(20) + (20)^2)) / (8100 - 180(20) + (20)^2)) * 100

Substituting the given values, we can calculate the percentage change in quantity demanded. By using the same formula, we can calculate the percentage change in price as:

Percentage Change in Price = ((p(25) - p(20)) / p(20)) * 100 = ((25 - 20) / 20) * 100

Substituting the given values, we can calculate the percentage change in price. The price elasticity of demand (E) is then calculated as the absolute value of the ratio of the percentage change in quantity demanded to the percentage change in price:

E = (Absolute Value of Percentage Change in Quantity) / (Absolute Value of Percentage Change in Price)

Therefore, we can substitute the calculated values to find the price elasticity of demand E. Interpretation: The price elasticity of demand measures the responsiveness of demand to changes in price. A price elasticity greater than 1 indicates that demand is elastic, meaning that a change in price will result in a greater percentage change in quantity demanded. In this case, if the price is set at $25, the demand is going to decrease.