Find the elasticity of the demand function as a function of p.
-x = D(p) = 800 - p
C) E(p) = p(800 - p)

Question

Quizplus · Accepted Answer

The formula for elasticity of demand is:
E(p) = (p/x) * (dx/dp)
where x is the quantity demanded at price p. 
In this case, 
x = D(p) = 800 - p
Taking the derivative with respect to p, we get:
dx/dp = -1
Substituting x and dx/dp in the formula for elasticity, we get:
E(p) = (p/(800-p)) * (-1)
Simplifying, we get:
E(p) = -p/(800-p)^2
Therefore, the elasticity of demand as a function of p is B. The formula for elasticity of demand is:

E(p) = (p / D(p)) * (dD(p) / dp)

Substituting D(p) = 800 - p gives:

E(p) = (p / (800 - p)) * (-1)

Simplifying this expression gives:

E(p) = -p / (800 - p)^2

Therefore, the elasticity of demand as a function of p is given by choice B.

Find the Elasticity of the Demand Function as a Function