Question

Elasticity Assume that the demand for broccoli is given by D (p) tons and p is the price of a pound of broccoli. 5000 - 500p2, where D(p) is in 4. Find p such that the demand at p is unit elastic. Gives the exact value and an approximation with two significant digits. What does this price mean in terms of revenue?

Answer 1

The price at which demand is unit elastic for broccoli is p = 1/1000 or approximately p ≈ 0.001. A unit elastic price means that a 1% change in price will result in a 1% change in quantity demanded.

Step-by-step explanation:

The demand function for broccoli is given by D(p) = 5000 - 500p^2, where D(p) represents the demand in tons and p represents the price per pound of broccoli. To find the price at which demand is unit elastic, we need to find the price (p) such that the absolute value of the elasticity of demand is equal to 1.

Step 1: Calculate the derivative of the demand function with respect to price. This gives us the rate of change of demand with respect to price, or the demand elasticity:

dD/dp = -1000p

Step 2: Set the absolute value of the elasticity equal to 1 and solve for p:

|-1000p| = 1

1000p = 1

p = 1/1000

So the exact price at which demand is unit elastic is p = 1/1000, which is approximately p ≈ 0.001 (rounded to two significant digits).

In terms of revenue, a unit elastic price means that a 1% change in price will result in a 1% change in quantity demanded. This suggests that the revenue will remain the same regardless of the price, as the change in quantity demanded will offset the change in price.