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Math 142 Lecture Notes for Section 4.5 Section 4.5 - 1 Elasticity of Demand Example 4.5.1: Suppose that you have the options to invest in two possible stocks: Gallente and Caldari. Your friendly neighborhood financial analyst suggests that Gallente will have increased earnings of an additional $3.00 per year over several years, whereas Caldari’s earnings will only increase by $2.00 per year. Which stock is a better purchase? Definition 4.5.2: Relative and Percentage Rates of Change • The relative rate of change of a function is the value: • The percentage rate of change of a function is the value: Example 4.5.3: Returning to our initial example, if Gallente costs $75.00 per share and Caldari costs $25.00 per share, what are their relative and percentage rates of change? Math 142 Lecture Notes for Section 4.5 2 Definition 4.5.4: Elasticity of Demand: If price and demand are related by the function x = f (p) where x is the quantity demanded and p is the price. Then the elasticity of demand, E(p) is given by What does E(p) mean? Math 142 Lecture Notes for Section 4.5 3 Summary: Example 4.5.5: If E(p) = 1.75 and price is decreased by 5%, what happends to the demand? Does the revenue increase or decrease? Math 142 Lecture Notes for Section 4.5 4 Example 4.5.6: Given that x = f (p) = 7500 − p2 , determine whether demand is elastic, inelastic, or has unit elasticity at the indicated values of p. (a) p = 25 (b) p = 50 (c) p = 75 Math 142 Lecture Notes for Section 4.5 5 Example 4.5.7: The price-demand equation for a new coffee beverage at AstroDollars, the Frapresso, is p = 7 − 0.02x where x is the number of beverages purchased in a 24-hour period. The current price of a Frapresso is $3.25. In order to generate additional revenue from the sale of Frapressos at AstroDollars, would you recommend a price increase or a price decrease? Section 4.5 Suggested Homework: 1, 7-23(odd)