   Chapter 11, Problem 13T ### 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 for a product is p 2 +   3 p   + q =   1500 , where p is in dollars and q is the number of units. Find the elasticity of demand at p = 30. If the price is raised to \$31, does revenue increase or decrease?

To determine

To calculate: The elasticity of demand for p2+3p+q=1500 at p=30. If the price is raised to p=31, and also determine does the revenue increase or decrease.

Explanation

Given Information:

The provided expression is p2+3p+q=1500 when p=30 and 31.

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(fg)=fdgdx+gdfdx

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

Elasticity of demand= η=pqdqdp

Calculation:

The provided expression is p2+3p+q=1500,

Put p=30 in the equation, to get the value of q,

(30)2+3(30)+q=1500900+90+q=1500q=510

Hence, the value of q=510

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