For the following demand equation compute the elasticity of demand and determine whether the demand is elastic, unitary, or inelastic at the indicated price. p = 141 − x2; p = 94 E(94)=?
For the following demand equation compute the elasticity of demand and determine whether the demand is elastic, unitary, or inelastic at the indicated price. p = 141 − x2; p = 94 E(94)=?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
For the following demand equation compute the elasticity of demand and determine whether the demand is elastic, unitary, or inelastic at the indicated price.
p = 141 − x2; p = 94
E(94)=?
Expert Solution
Step 1
Sol:-
To compute the elasticity of demand at a price of p = 94, we first need to find the corresponding quantity demanded. We can do this by substituting p = 94 into the demand equation and solving for x:
p = 141 − x² 94 = 141 - x² x² = 141 - 94 x² = 47 x = √47 x ≈ 6.86
So when the price is 94, the quantity demanded is approximately 6.86.
Next, we can compute the elasticity of demand using the formula:
E = (ΔQ / Q) / (ΔP / P)
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