   Chapter 9.3, Problem 48E ### 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

# Consumer expenditure Suppose that the demand for x units of a product is x = 10 , 000 − 100 p where p dollars is the price per unit. Then the consumer expenditure for the product is E ( p ) = p x ( 10 , 000 − 100 p ) = 10 , 000 p − 100 p 2 What is the instantaneous rate of change of consumer expenditure with respect to price at(a) any price p? (b) p = 5 ? (c) p = 20 ?

(a)

To determine

To calculate: The instantaneous rate of change of consumer expenditure with respect to price when the expenditure is given by

E(p)=px=p(10,000100p)

Where p is the price and x is the demand.

Explanation

Given Information:

The expenditure is given by

E(p)=px=p(10,000100p)

Where p is the price and x is the demand.

Formula used:

If a function f(x) is defined in the interval [x,x+h], then its instantaneous rate of change is given by the derivative as

f(x)=limh0f(x+h)f(x)h

Calculation:

Consider the provided statement,

The expenditure is given by

E(p)=px=p(10,000100p)

Where p is the price and x is the demand.

Substitute p=p+h in E(p) to get,

E(p+h)=(p+h)(10,000100(p+h))=10,000p+10,000h100(p

(b)

To determine

To calculate: The instantaneous rate of change of consumer expenditure with respect to price at p=5 when the expenditure is given by

E(p)=px=p(10,000100p)

Where p is the price and x is the demand.

(c)

To determine

To calculate: The instantaneous rate of change of consumer expenditure with respect to price at p=20 when the expenditure is given by

E(p)=px=p(10,000100p)

Where p is the price and x is the demand.

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