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:

Ed=dQdPPQE_d = \frac{dQ}{dP} \cdot \frac{P}{Q}

Step 1: Differentiate Q=30016PQ = 300 - 16P

The derivative of QQ with respect to PP is: dQdP=16\frac{dQ}{dP} = -16

Step 2: Calculate QQ at P=1.50P = 1.50

Substitute P=1.50P = 1.50 into the demand function: Q=30016(1.50)=30024=276Q = 300 - 16(1.50) = 300 - 24 = 276

Step 3: Use the elasticity formula

Ed=161.50276E_d = \frac{-16 \cdot 1.50}{276}

Simplify: Ed=24276=0.087E_d = \frac{-24}{276} = -0.087

Final Answer:

The point elasticity of demand is: 0.087(D)\boxed{-0.087} \quad \text{(D)}


Would you like further clarification or additional examples?
Here are 5 related questions to consider:

  1. How is elasticity interpreted in terms of consumer behavior?
  2. What happens to total revenue if demand is elastic and price decreases?
  3. How do you calculate point elasticity at other price points?
  4. What is the difference between point elasticity and arc elasticity?
  5. 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

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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