Demand Elasticity Question

Question

Suppose that the demand for a certain item is Q=10+1p^2.

p represents the price of an item and Q represents the number of items sold at that price.

Evaluate the demand elasticity E at p=0.3:

E(0.3) = 

Answer 1

To calculate the demand elasticity E at a specific price, you can use the formula for price elasticity of demand:

E = (dQ/dp) * (p/Q)

Here, Q represents the quantity demanded, and p represents the price of the item. You're given the demand function as Q = 10 + p^2.

First, we need to find dQ/dp, which is the derivative of the demand function with respect to price p. Let's calculate it:

dQ/dp = d/dp (10 + p^2) = 0 + 2p = 2p

Now, you can plug this into the demand elasticity formula:

E(0.3) = (2 * 0.3) * (0.3 / (10 + 0.3^2))

E(0.3) = 0.6 * (0.3 / (10 + 0.09))

E(0.3) = 0.6 * (0.3 / 10.09)

E(0.3) ≈ 0.0187

So, the demand elasticity at a price of 0.3 is approximately 0.0187.