   Chapter 14, Problem 30RE Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Solutions

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=80040pA2pB+1qB=100010pA+430pB

Where pA and pB are the respective prices in dollars.

Explanation:

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

qA=80040pA2pB+1qB=100010pA+430pB

Where pA and pB are the respective prices in dollars.

The marginal demand of qB with respect to pA is given by qBpA.

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=100010pA+430pB with respect to pA,

qBpA=pA(100010pA+430pB)=((pA+4)(0)(10)(1)(pA+4)2)=10(pA+4)2

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

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