Math Problem Statement
Use the price-demand equation to find E (p), the elasticity of demand x=f(p)=155-30 in (p)
Solution
To find the elasticity of demand , we need to apply the formula for elasticity in terms of price-demand function:
Given:
Let's proceed step-by-step:
Step 1: Find
Differentiate with respect to :
Step 2: Substitute into the elasticity formula
Now we substitute and into the elasticity formula:
Step 3: Simplify the expression
The terms cancel out, giving:
Thus, the elasticity of demand is:
Would you like further details on this process or have any other questions?
Here are some related questions you might consider:
- What is the interpretation of a negative elasticity value?
- How does the elasticity of demand change as increases?
- What does it mean if at a particular price ?
- How can this elasticity value be used to predict revenue changes with price adjustments?
- What are the conditions under which this demand function would be considered elastic or inelastic?
Tip: Remember, elasticity greater than 1 (in magnitude) indicates elastic demand, less than 1 indicates inelastic demand, and exactly 1 means unitary elasticity.
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Math Problem Analysis
Mathematical Concepts
Elasticity of Demand
Differentiation
Price-Demand Functions
Formulas
E(p) = (p / x) * (dx/dp)
x = f(p) = 155 - 30ln(p)
dx/dp = -30/p
Theorems
Elasticity formula
Chain Rule in Differentiation
Suitable Grade Level
Grades 11-12
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