09a.elasticity - MAC 2233/001-006 Business Calculus Fall...

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MAC 2233/001-006 Business Calculus, Fall 2011 CRN: 81700–81702, 81705, 81716, 81715 Name: Two points . Professor : Stephen Suen Section: Peer Leaders : Hana Aboul-Hosn, Toni Jung, Renan Mendonca 9. The price elasticity of demand . The price elasticity of demand measures the effect of price on demand. It is defined as η = p x · 1 dp/dx = p x · dx dp Δ x/x Δ p/p = % change in demand % change in price . Note that for products that satisfy the Law of Demand , (that is, higher price results in lower demand, and lower price results in higher demand,) η is always negative (because dp dx is always negative). Example . (The price elasticity of demand.) Consider the demand function p = - 0 . 05 x + 50 , 0 x 1000 , where p is price in dollars, and x is quantity demanded of a certain product. (a) Find a formula for η as function of x . Solution. We find that dp dx = - 0 . 05. Thus, η = p x · 1 dp/dx = p x · 1 - 0 . 05 = - 20 p x = - 20( - 0 . 05 x + 50) x = - 1000 - x x . (b) Suppose that current demand is x = 400, find p and evaluate η . Solution. We take the demand function, and substitute x = 400 to find that p = 30 dollars. Using the formula for η found in (a), we have η = - 1000 - x x = - 1000 - 400 400 = - 1 . 5 .
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