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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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The demand functions for two products in the same market are

x 1 = 100 2 p 1 + 1.5 p 2 and x 2 = 145 + 0.5 p 1 0.75 p 2

Where p1 and p2 are the prices per unit (in dollars), and x1 and x2 are the numbers of units sold. Determine whether the products are complementary, substitutes, or neither.

To determine

To calculate: The product is complementary, substitute or neither if the demand functions for the two product is x1=1002p1+1.5p2 and x2=145+0.5p10.75p2.

Explanation

Given information:

The provided demand functions for the two product is x1=1002p1+1.5p2 and x2=145+0.5p10.75p2. 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=1002p1+1.5p2

And,

x2=145+0.5p10.75p2

Partially derivative of the demand function x1=1002p1+1.5p2 with respect to p2.

x1p2=p2(1002p1+1.5p2)=p2(100)2p1p2(1)+1

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