   Chapter 11.5, Problem 9E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Suppose the demand function for a product is given by p = 1 2 ln ( 5000 − q q + 1 ) where p is in hundreds of dollars and q is the number of tons.(a) What is the elasticity of demand when the quantity demanded is 2 tons and the price is \$371?(b) Is the demand elastic or inelastic?

(a)

To determine

To calculate: The elasticity of demand function p=12ln(500qq+1) at p=3.71 and q=2.

Explanation

Given Information:

The provided function is p=12ln(500qq+1) when p=3.71 and q=2.

Formula Used:

As per the product rule, if two functions are given in the form f(x).g(x), then the derivative is given as:

ddx(f.g)=f.dgdx+g.dfdx

If p=f(q) is the demand for the q units and price p, then at the points (qA,pA), then,

Elasticity of demand function is given by:

η=pq.dqdp

Calculation:

The provided function is p=12ln(500qq+1),

Partially differentiate on both the sides with respect to p,

1=12(15000q(1).dqdp1q+1.dqdp)2=[q+1+5000q(5000q)(q+1)]

(b)

To determine

The type of elasticity this is: unitary, elastic or inelastic.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 