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14209an7.4-6 - X takes on certain values we use a...

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c Kendra Kilmer April 14, 2009 Section 7.2 - Applications in Business and Economics 1. Consumers’ and Producers’ Surplus (a) Consumers’ Surplus Definition: The consumers’ surplus represents the total savings to consumers who are willing to pay more than ¯ p for the product but are still able to buy the product for ¯ p . (b) Producers’ Surplus Definition: The producers’ surplus represents the total gain to producers who are willing to supply units at a lower price than ¯ p but are still able to supply units at ¯ p . 4
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c Kendra Kilmer April 14, 2009 Example 1: If p = D ( x ) = 80 e - 0 . 001 x and p = S ( x ) = 30 e 0 . 001 x find the following: a) Equilibrium Point b) Consumers’ Surplus at the equilibrium price level. c) Producers’ Surplus at the equilibrium price level. 5
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c Kendra Kilmer April 14, 2009 2. Probability Density Functions Let X be a continuous random varialbe. To find the probability that
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Unformatted text preview: X takes on certain values, we use a probability density function , f ( x ) , satisfying the following conditions: 1. f ( x ) ≥ 0 for all real x . 2. The area under the graph of f ( x ) over (-∞ , ∞ ) is exactly 1. 3. If [ c , d ] is a subset of (-∞ , ∞ ) , then P ( c ≤ X ≤ d ) = Example 2: A manufacturer guarantees a product for one year. The time to failure of a product after it is sold is given by the probability density function f ( t ) = ( . 01 e-. 01 t if t ≥ otherwise where t is in months. What is the probability that a buyer chosen at random will have a product failure: a) During the warranty period? b) During the second year after purchase? Section 7.2 Homework Problems: 13,17,19,43,47,51,57, and supplemental problems 4-7. 6...
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