If the demand function is given as 𝑋 = 100 − 3𝑝,find the elasticity of demand when price is 1

The elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in the price of that good. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

The formula for elasticity of demand (E) is:

E = (dQ/dP) * (P/Q)

Where:

• dQ/dP is the derivative of the demand function with respect to price (P)
• P is the price
• Q is the quantity demanded

Given the demand function X = 100 - 3P, we first need to find the derivative of this function with respect to price (P).

The derivative of X with respect to P is -3 (dX/dP = -3).

Next, we substitute P = 1 into the demand function to find the quantity demanded (Q) at this price:

Q = 100 - 3*1 = 97

Now we can substitute these values into the elasticity formula:

E = (-3) * (1/97) = -0.0309

So, the elasticity of demand when the price is 1 is -0.0309. This means that a 1% increase in price will result in a 0.0309% decrease in quantity demanded.