Math 142 Lecture Notes for Section 4.5
Section 4.5 -
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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
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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
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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
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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
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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)