Chapter 14, Problem 30RE

### 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

# Marginal demand Suppose that the demand functions for two related products, A and B, are given by q A = 800 − 40 p A − 2 p B + 1 q B = 1000 − 10 p A + 4 − 30 p B where p A and p B are the respective prices in dollars. Determine whether the products are competitive or complementary.

To determine

Whether the two products, A and B, are competitive or complementary if the demand functions for products A and B are given by qA=80040pA2pB+1 and qB=100010pA+430pB.

Explanation

Given Information:

The demand functions for products, A and B, are given as,

qA=800âˆ’40pAâˆ’2pB+1qB=1000âˆ’10pA+4âˆ’30pB

Where pA and pB are the respective prices in dollars.

Explanation:

Consider the demand functions for products, A and B, are given as,

qA=800âˆ’40pAâˆ’2pB+1qB=1000âˆ’10pA+4âˆ’30pB

Where pA and pB are the respective prices in dollars.

The marginal demand of qB with respect to pA is given by âˆ‚qBâˆ‚pA.

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.

Partial differentiate the function qB=1000âˆ’10pA+4âˆ’30pB with respect to pA,

âˆ‚qBâˆ‚pA=âˆ‚âˆ‚pA(1000âˆ’10pA+4âˆ’30pB)=âˆ’((pA+4)(0)âˆ’(10)(1)(pA+4)2)=10(pA+4)2

Therefore, the marginal demand of qB with respect to pA is âˆ‚qBâˆ‚pA=10(pA+4)2

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