Chapter 14.3, Problem 3CP

### 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

# 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.

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