3.5.notes - . 5. Similarly, the following also imply one...

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MAC 2233/001-006 Business Calculus, Fall 2011 CRN: 81700–81702, 81705, 81716, 81715 Assistants : Matthew Fleeman, Arbin Rai, Tadesse Zerihun, Vindya Kumari, Junyi Tu, Jing- han Meng On the price elasticity of demand 1. On p.249 in the text, an explanation for the price elasticity of demand should be: Price elasticity of demand = relative change in demand relative change in price = Δ x/x Δ p/p p x dx dp . 2. The following are di±erent (but equivalent and common) ways to write η : η = p x dx dp = p x 1 dp dx . The one given in the text, η = p/x dp/dx , is good also. 3. As it is typical for a demand function, the derivative dp dx < 0 (and also dx dp < 0). This shows that η is usually negative. 4. When studying for the price elasticity of demand, it is a good idea to remember that the following situations imply one another: | η | < 1 , - 1 < η < 0 , demand is inelastic, usually price is low and demand is high . When price is raised a little, demand drops by a relatively smaller proportion (so demand is inelastic), resulting in higher revenue
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Unformatted text preview: . 5. Similarly, the following also imply one another: | η | > 1 , η <-1 , demand is elastic, usually price is high and demand is low. When price is raised a little, demand drops by a relatively larger proportion (so demand is elastic), resulting in lower revenue . 6. Because of the reasoning given in notes 4 and 5, we see that the revenue R is (usually) maximized (or in some cases, minimized) when demand is unit elastic ( η =-1 or | η | = 1). In some situations, it is easier to use this property to determine when revenue is maximized. We shall see in class that dR dx = 0 i± | η | = 1. Example . The following diagrams give the graphs of revenue R and the price elasticity of demand η , respectively, against price p . Here, the demand equation is p =-. 05 x + 50, with (after some calculus) R = 20 p (50-p ) , η =-p 50-p ....
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This note was uploaded on 01/02/2012 for the course MAC 2233 taught by Professor Danielyan during the Fall '08 term at University of South Florida.

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3.5.notes - . 5. Similarly, the following also imply one...

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