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Unformatted text preview: 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 = relative (percentage) change in demand relative (percentage) 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 = 100e- . 01 x , x ≥ , 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 = e- . 01 x . Thus, η = p x · 1 dp/dx = p x · 1 e- . 01 x = − 100e- . 01 x x · 1 e- . 01 x = − 100 x . (b) Suppose that current demand is x = 120, find p and evaluate η . Solution. We take the demand function, and substitute x = 120 to find that p = 100e- (0 . 01)(120) ≈ 30 . 12 dollars. Using the formula for η found in (a), we have η = − 100 x = − 100 120 = − 5 6 ≈ − . 8333 ....
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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.
- Fall '08