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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Complementary and Substitute Products In Exercises 65 and 66, determine whether the demand functions describe products in the same market that are complementary, substitutes, or neither. Using the notation of Example 4, let x1 and x2 be the demands for two products whose prices per unit (in dollars) are p1 and p2, respectively. See Example 4.

x 1 = 150 2 p 1 + 1.8 p 2 , x 2 = 350 + 3 4 p 1 1.9 p 2

To determine

To calculate: The product is complementary, substitute or neither if the demand functions for the two product is x1=1502p1+1.8p2 and x2=350+34p11.9p2.

Explanation

Given information:

The provided demand functions for the two product is x1=1502p1+1.8p2 and x2=350+34p11.9p2. Where, p1 and p2 are the price and x1 and x2 are the number of units sold.

Formula used:

Consider the function z=f(x,y) then for the value of zx consider y to be constant and differentiate with respect to x and the value of zy consider x to be constant and differentiate with respect to y.

Calculation:

Consider the provided demand function is,

x1=1502p1+1.8p2

And,

x2=350+34p11.9p2

Partially derivative of the demand function x1=1502p1+1.8p2 with respect to p2.

x1p2=p2(1502p1+1.8p2)=p2(150)2p1p2(1)+1

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