Question

A garden shop determines the demand function q=D(x)=5 x+500/10 x+9 during early summer for tomato plants where q is the number of plants sold per day when the price is x dollars per plant.

(a) Find the elasticity.

Answer 1

To calculate the elasticity of demand for a given price change, we find the percentage changes in quantity and price, and then use the formula for price elasticity of demand. The elasticity values for the price change from 5 to 4 and from 9 to 8 will differ due to varying relative changes along the demand curve.

Step-by-step explanation:

The elasticity of demand measures how sensitive the quantity demanded is to a change in price. To calculate elasticity, we must determine the percentage change in quantity demanded and the percentage change in price using the formula for price elasticity of demand, which is:

Elasticity (E) = (Percentage change in quantity) / (Percentage change in price)

Given the demand curve P = 2/Q, we need to find the change in quantity as the price changes from 5 to 4 and from 9 to 8. For the price drop from 5 to 4, the corresponding quantities (Q) are 2/5 and 2/4, respectively. For the price drop from 9 to 8, the corresponding quantities are 2/9 and 2/8.

Now, we can calculate the percentage changes in price and quantity for each scenario and then find the elasticity. The values obtained for each scenario will be different because the calculation considers relative changes in price and quantity, which are not constant across the demand curve.