Question

The demand for a certain item is Q(p)=−0.8p+20 p represents the price of an item and Q represents the number of items sold at that price. Evaluate the demand elasticity E when p=8 : E(8)=

Answer 1

The elasticity of demand when the price falls from 5 to 4 and from 9 to 8 is 1. This means that the quantity demanded is perfectly responsive to changes in price.

Step-by-step explanation:

Elasticity of demand measures the responsiveness of the quantity demanded of a product to a change in its price. It is calculated by taking the percentage change in quantity demanded and dividing it by the percentage change in price. To find the elasticity of demand when the price falls from 5 to 4, first calculate the percentage change in quantity demanded and the percentage change in price. Then divide the percentage change in quantity demanded by the percentage change in price to find the elasticity of demand.

When the price falls from 5 to 4:

1. Percentage change in quantity demanded = (Q(4) - Q(5)) / Q(5) = (2/(5) - 2/(4)) / (2/(5)) = -1/5 = -0.2
2. Percentage change in price = (4 - 5) / 5 = -1/5 = -0.2
3. Elasticity of demand = -0.2 / -0.2 = 1

To find the elasticity of demand when the price falls from 9 to 8, repeat the same steps:

1. Percentage change in quantity demanded = (Q(8) - Q(9)) / Q(9) = (2/(9) - 2/(8)) / (2/(9)) = -1/9 = -0.111
2. Percentage change in price = (8 - 9) / 9 = -1/9 = -0.111
3. Elasticity of demand = -0.111 / -0.111 = 1

Since both calculations result in an elasticity of demand equal to 1, we would expect the answers to be the same.