Question

For the demand function q = D(x) = 400/x find the following a ) The elasticity b ) The elasticity at x = 4 , stating whether the demand is elastic, inelastic, or has unit elasticity c ) The value( s) of x for which total revenue is a maximum (assume that x is in dollars)

Answer 1

a) To find the elasticity of the demand function q = D(x) = 400/x, we can use the formula:

Elasticity = (dQ/dx) * (x/Q)

where Q is the quantity demanded, and x is the price.

Taking the derivative of the demand function with respect to x, we get:

dQ/dx = -400/x^2

Plugging in the values, we get:

Elasticity = (-400/x^2) * (x/400/x) = -1

Therefore, the elasticity of the demand function is -1.

b) To find the elasticity at x = 4, we first calculate the quantity demanded at x = 4 as:

q = D(4) = 400/4 = 100

Then, we use the formula for elasticity:

Elasticity = (dQ/dx) * (x/Q) = (-400/16) * (4/100) = -1/10

Since the elasticity is less than 1, the demand is inelastic at x = 4.

c) To find the value of x for which total revenue is a maximum, we can use the formula:

TR(x) = x * D(x) = 400x/x = 400

Total revenue is a constant value of 400 for all values of x. Therefore, there is no specific value of x for which total revenue is a maximum.