Explanation Given information: Table 1.30 gives data for the linear demand curve for a product, where p is the price of the product and q is the quantity sold every month at that price. Table 1.30 p (dollars) 16 18 20 22 24 q (tons) 500 460 420 380 340 Concept Used: The quantity, q of an item that is manufactured and sold depend on its price, p. As the price increases, manufacturers are usually willing to supply more of the product, whereas the quantity demanded by consumers falls. The supply curve, for a given item, relates the quantity, q, of the item that manufacturers are willing to make per unit time to the price, p, for which the item can be sold. The demand curve relates the quantity, q, of an item demanded by consumers per unit time to the price, p, of the item. Calculation: Steps Description p r i c e o f p r o d u c t ( $ ) p 16 18 | q u a n t i t y ( t o n s ) q 500 460 Pick any two pointsfrom the table provided about the price of the product (p) and the quantity sold every month at that price (q) Calculation (Continued): Here q = m ⋅ p + b where m is slope and b is y-intercept. m = q 2 - q 1 p 2 - p 1 m = 460 − 500 18 − 16 = − 40 2 = − 20 m = - 2 0 Interpretation of slope: For increase of price every dollar, the quantity sold every month at that price will decrease by 20 tons To determine (b) To find: A formula for the demand curve ( p as a function of q )

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 1.4, Problem 31P

To determine

(a)

To find:

A formula for the demand curve( q as a function of p )

To determine

(b)

To find:

A formula for the demand curve ( p as a function of q )

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Chapter 1.4, Problem 30P

Chapter 1.4, Problem 32P

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APPLIED CALCULUS (WILEY PLUS)

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(a) To find: A formula for the demand curve( q as a function of p )

Solution Summary: The author explains the formula for the demand curve, where q is the quantity sold every month at that price. As the price increases, manufacturers are willing to supply more of the item.