   Chapter 14, Problem 29RE 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 The demand functions for two related products, product A and product B, are given by q A = 400   −   2 p A − 3 p B q B =   300   −   5 p A −   6 p B where p A and p B are the respective prices in dollars.(a) Find the marginal demand of q A with respect to p A .(b) Find the marginal demand of q B with respect to p B .(c) Are the products complementary or competitive?

(a)

To determine

To calculate: The marginal demand of qA with respect to pA if demand functions for product A and product B are given by qA=4002pA3pB and qB=3005pA6pB.

Explanation

Given Information:

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

qA=4002pA3pBqB=3005pA6pB

Where, pA and pB are the prices in dollars for product A and product B respectively.

Formula used:

For a demand function, of the form q=f(p1,p2), the marginal demand function is the partial derivative of the function q. Thus, the marginal demand of q with respect to the price p1 is given by qp1 and the marginal demand of q with respect to the price p2 is given by qp2.

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. The partial derivative of f with respect to x is denoted by fx.

Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1.

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0

(b)

To determine

To calculate: The marginal demand of qB with respect to pB if demand functions for product A and product B are given by qA=4002pA3pB and qB=3005pA6pB.

(c)

To determine

Whether the two goods, A and B, are competitive or complementary if demand functions for product A and product B are given by qA=4002pA3pB and qB=3005pA6pB.

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