Question

The number of units demanded x for a product is given by the demand function x(p)=100-4p , where p is the price per unit of the good and 0

a. find the expression of priselasticity that is Elpx(p)

b. calculate the price elasticity if the price is given at p=5 and an interpretation of the result

Answer 1

To find the expression for price elasticity, differentiate the demand function x(p) with respect to p. The price elasticity of demand can be expressed as: Elpx(p) = (dx/dp) * (p/x(p)). Substitute the demand function and evaluate the expression at a given price.

Step-by-step explanation:

To find the expression for price elasticity, we need to differentiate the demand function x(p) with respect to p. The price elasticity of demand can be expressed as:

Elpx(p) = (dx/dp) * (p/x(p))

Substituting the demand function x(p) = 100 - 4p, we get:

Elpx(p) = (d(100-4p)/dp) * (p/(100-4p))

Taking the derivative and simplifying, we get:

Elpx(p) = -4 * (p/(100-4p))

To calculate the price elasticity at p=5, we substitute p=5 into the expression:

Elpx(5) = -4 * (5/(100-4*5)) = -0.2632

The price elasticity is approximately -0.2632 at p=5. This means that a 1% increase in price will result in a 0.2632% decrease in quantity demanded.