   Chapter 11.5, Problem 6E ### 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.Suppose that the demand for a product is given by   2 p 2 q   = 10 , 000   +   9000 p 2 . (a) Find the elasticity when p = $50 and q = 4502.(b) Tell what type of elasticity this is: unitary, elastic, or inelastic.(c) How would revenue be affected by a price increase? (a) To determine To calculate: The elasticity of demand function 2p2q=10000+9000p2 at p=$50 and q=4502.

Explanation

Given Information:

The provided function is 2p2q=10000+9000p2 when p=\$50 and q=4502.

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 is given by:

η=pq.dqdp

Calculation:

The provided function is 2p2q=10000+9000p2,

Partially differentiate on both the sides with respect to p,

2p2dqdp+4pq=18,000p

From this, compute the value of dqdp,

2p2dqdp+4pq=18,000p2p2dqdp=18,

(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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