   Chapter 11.5, Problem 2E ### 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

# In Problems 1 -8, p is in dollars and q is the number of units.(a) Find the elasticity of the demand function 2 p +   3 q =   150 at the price p = 15.(b) How will a price increase affect total revenue?

(a)

To determine

To calculate: The elasticity of demand function 2p+3q=150 at p=15.

Explanation

Given Information:

The provided function is 2p+3q=150 and p=15.

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+4q=80,

Partially differentiate on both the sides of above with respect to p,

2dpdp+3dqdp=0

From this, compute the value of dqdp,

2+3dqdp=03dqdp=2

(b)

To determine

How will a price increase affect the total revenue.

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