   Chapter 14.3, Problem 3CP 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

If the demand functions for two products are q 1 =   200   −   3 p 1 −   4 p 2  and  q 2 =   50   −   6 p 1 − 5 p 2  find the marginal demand of ( a ) q 1 with respect to  p 1 .         ( b ) q 2 respect to  p 2 .

(a)

To determine

To calculate: The marginal demand of q1 with respect to p1. The demand functions for two products are q1=2003p14p2 and q2=506p15p2.

Explanation

Given Information:

The demand functions for two products are q1=2003p14p2 and q2=506p15p2.

Formula used:

For a demand function, of the form q=f(p1,p2), the marginal demand function is the partial derivative of the function q. Thus, the marginal demand of q with respect to the price p1 is given by qp1 and the marginal demand of q with respect to the price p2 is given by qp2.

For a function f(x,y), the partial derivative of f with respect to x is calculated by taking the derivative of f(x,y) with respect to x and keeping the other variable y constant. The partial derivative of f with respect to x is denoted by fx.

Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1.

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x)

(b)

To determine

To calculate: The marginal demand of q2 with respect to p2. The demand functions for two products are q1=2003p14p2 and q2=506p15p2.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 