Chapter 11, Problem 40RE

### Mathematical Applications for the ...

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

Chapter
Section

### Mathematical Applications for the ...

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

# Elasticity Suppose the weekly demand function for a product is given by p =   100 e − 0.1 q where p is the price in dollars and q is the number of tons demanded.(a) What is the elasticity of demand when the price is $36.79 and the quantity demanded is 10?(b) How will a price increase affect total revenue? (a) To determine To calculate: The elasticity of demand for p=100e0.1q at p=$36.79 and q=10.

Explanation

Given Information:

The provided expression is p=100e0.1q at p=\$36.79 and q=10.

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 p=100e0.1q,

Partially differentiate on both the sides of function p=100e0.1q with respect to p,

dpdp=ddp(100e0.1q)1=100e0.1q(0.1)dqdp

From this, compute the value of dqdp,

1=100e0

(b)

To determine

The affect on total revenue function if price gets increased.

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