Final answer:
To find the elasticity at a given price, we need to calculate the percentage change in quantity when the price changes. In this case, the demand function is Q = √(630 - x), and we need to find the elasticity at x = 580.
Step-by-step explanation:
The elasticity of demand measures the responsiveness of the quantity demanded to a change in price. It is calculated as the percentage change in quantity divided by the percentage change in price. To find the elasticity at a given price, we need to calculate the percentage change in quantity when the price changes. In this case, the demand function is Q = √(630 - x), and we need to find the elasticity at x = 580.
To calculate the percentage change in quantity, we subtract the quantity at the new price (x = 580) from the quantity at the original price (x = 630), divide it by the average of the two quantities, and multiply by 100. So:
% change in quantity = (Q(x = 630) - Q(x = 580)) / ((Q(x = 630) + Q(x = 580)) / 2) x 100
Once we have the percentage change in quantity, we can calculate the elasticity as the percentage change in quantity divided by the percentage change in price. Whether the demand is elastic, inelastic, or unit elastic depends on the value of the elasticity. If the elasticity is greater than 1, the demand is elastic; if it is less than 1, the demand is inelastic; and if it is equal to 1, the demand has unit elasticity.