   Chapter 11.5, Problem 10E ### 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 weekly demand function for a product is q = 5000 1 + e 2 p − 1 where p is the price in thousands of dollars and q is the number of units demanded. What is the elasticity of demand when the price is \$1000 and the quantity demanded is 595?

To determine

To calculate: The elasticity of demand function q=50001+e2p1 at p=1 and q=595.

Explanation

Given Information:

The provided function is q=50001+e2p1 when p=1 and q=595.

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 q=50001+e2p1,

Partially differentiate on both the sides with respect to p,

dqdp=5000e2p(2)(1+e2p)2=10000

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