Math Problem Statement
If the demand curve for slices of pizza is given as Q = 300 minus 16p, then the point elasticity of demand when price is $ 1.50 is A)-24 B)-16 C) -0.1154 D)-0.087
Solution
To calculate the point elasticity of demand, we use the formula:
Step 1: Differentiate
The derivative of with respect to is:
Step 2: Calculate at
Substitute into the demand function:
Step 3: Use the elasticity formula
Simplify:
Final Answer:
The point elasticity of demand is:
Would you like further clarification or additional examples?
Here are 5 related questions to consider:
- How is elasticity interpreted in terms of consumer behavior?
- What happens to total revenue if demand is elastic and price decreases?
- How do you calculate point elasticity at other price points?
- What is the difference between point elasticity and arc elasticity?
- How would a perfectly inelastic demand curve affect elasticity?
Tip: Always check whether the elasticity formula is applicable for the given data (e.g., point elasticity
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Math Problem Analysis
Mathematical Concepts
Economics
Elasticity of Demand
Derivatives in Calculus
Formulas
Elasticity of demand formula: Ed = (dQ/dP) * (P/Q)
Demand function: Q = 300 - 16P
Theorems
Point Elasticity of Demand
Suitable Grade Level
Undergraduate Economics or High School Advanced Mathematics
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