Math Problem Statement
In this problem, p is in dollars and q is the number of units.
The demand function for a product is given by q = 400 − p2 .
(a) Find the formula for the elasticity of demand at any price as a function of the variable p . E(p)
Solution
To find the elasticity of demand at any price , we can use the formula for price elasticity of demand, which is defined as:
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Find : From the demand function, we have:
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Find : Differentiate with respect to :
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Substitute and into the elasticity formula: Simplifying this gives:
Thus, the formula for the elasticity of demand at any price is:
Would you like further details or explanations? Here are some related questions to consider:
- How does the elasticity of demand change as increases?
- What are the implications of elasticity being negative?
- How can we determine the point of unit elasticity?
- How does this demand function compare to linear demand functions?
- What factors could affect the demand function in real-world scenarios?
Tip: Remember that elasticity values greater than 1 indicate elastic demand, while values less than 1 indicate inelastic demand.
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Math Problem Analysis
Mathematical Concepts
Calculus
Elasticity of Demand
Functions
Formulas
E(p) = (dq/dp * p) / q
q = 400 - p^2
dq/dp = -2p
Theorems
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Suitable Grade Level
Grades 11-12
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