Chapter 14, Problem 7T

### 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

# Suppose the demand functions for two products are q 1 =   300   −   2 p ,   −   5 p 2  and   q 2 =   150   −   4 p 1   −   7 p 2 where q 1 and q 2 represent quantities demanded and p 1 and p 2 represent prices. What calculations enable us to decide whether the products are competitive or complementary? Are these products competitive or complementary?

To determine

The method to decide whether the two products are competitive or complementary and then calculate whether the two products are competitive or complementary. Suppose the demand functions for two products are q1=3002p15p2 and q2=1504p17p2 where q1 and q2 represent quantities demanded and p1 and p2 represent prices.

Explanation

Given Information:

The demand functions for two products are q1=300âˆ’2p1âˆ’5p2 and q2=150âˆ’4p1âˆ’7p2.

Calculation:

Consider the functions q1=300âˆ’2p1âˆ’5p2 and q2=150âˆ’4p1âˆ’7p2.

To find whether two products with demand functions q1(p1,p2) and q2(p1,p2) are competitive or complementary,

1) calculate âˆ‚q1âˆ‚p2 and âˆ‚q2âˆ‚p1.

2) if the signs of âˆ‚q1âˆ‚p2 and âˆ‚q2âˆ‚p1 are positive, then the two products are competitive and if âˆ‚q1âˆ‚p2 and âˆ‚q2âˆ‚p1 are negative, then the two products are complementary.

Consider the problem, the demand functions for two products are q1=300âˆ’2p1âˆ’5p2 and q2=150âˆ’4p1âˆ’7p2 where q1 and q2 represent quantities demanded and p1 and p2 represent prices.

The marginal demand of q1 with respect to p2 is given by âˆ‚q1âˆ‚p2

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