   Chapter 11.5, Problem 11E ### 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 11 and 12, the demand functions for specialty steel products are given, where p is in dollars and q is the number of units. For both problems(a) find the elasticity of demand as a function of the quantity demanded, q.(b) find the point at which the demand is of unitary elasticity and find intervals in which the demand is inelastic and in which it is elastic.(c) use information about elasticity in part (b) to decide where the revenue is increasing, where it is decreasing, and where it is maximized.(d) use the graph of the revenue function R = p q to find where revenue is maximized. Is it at the same quantity as that determined in part (c)? p = 120 125 − q 3

(a)

To determine

To calculate: The elasticity of demand function p=120125q3.

Explanation

Given Information:

The provided function is p=120125q3.

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:

Consider the provided function,

p=120125q3,

Partially differentiate on both the sides with respect to p,

1=40(125q)23(1).dqdp

From this, compute the value of dqdp,

1=40(125q)23(1).dqdp1=40(125q)23

(b)

To determine

To calculate: The point for the expression p=120125q3 at which the demand is of unitary elasticity and the intervals in which the demand is inelastic and in which it is elastic.

(c)

To determine

Whether the revenue is increasing, where it is decreasing and where it is maximized. Use the information about elasticity in part (b) to decide this.

(d)

To determine

To graph: The function R=pq to find where the revenue is maximized, is it at the same quantity as that determined in part (c).

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