Chapter 11.5, Problem 8E

### 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

# In Problems 1 -8, p is in dollars and q is the number of units.Suppose that the demand for a product is given by ( p + 1 ) q + 1 = 1000 (a) Find the elasticity when p = $39.(b) Tell what type of elasticity this is.(c) How would a price increase affect revenue? (a) To determine To calculate: The elasticity of demand function (p+1)q+1=1000 at p=$39.

Explanation

Given Information:

The provided function is (p+1)q+1=1000 when p=\$39.

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+1)q+1=1000,

Partially differentiate on both the sides with respect to p,

(p+1).12.(q+1)12dqdp+q+1=0

From this, compute the value of dqdp,

(p+1).12.(q+1)12dqdp+q+1=0(p+1).12.(q+1)12dqdp=q+1dqdp=2q+1(p+1)

(b)

To determine

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

(c)

To determine

How will a price increase affect the total revenue.

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