Math Problem Statement

Suppose the demand for a certain brand of sandals is given by the equation , where Q is the quantity demanded and P is the price. Calculate the own-price elasticity of demand at P=$30 if the price declines from $30 to $25. Please round your answer to 2 decimal places.

Solution

To calculate the own-price elasticity of demand (PED), we can use the formula:

Ed=% change in quantity demanded% change in priceE_d = \frac{\% \text{ change in quantity demanded}}{\% \text{ change in price}}

This can be rewritten as:

Ed=ΔQ/QΔP/PE_d = \frac{\Delta Q / Q}{\Delta P / P}

where:

  • ΔQ\Delta Q is the change in quantity demanded,
  • ΔP\Delta P is the change in price,
  • QQ is the initial quantity demanded, and
  • PP is the initial price.

Since you haven't provided the actual demand equation, I need to know the specific demand function to calculate the quantity demanded at the initial price of $30 and the new price of $25.

Could you please provide the demand equation? It should be something like Q=abPQ = a - bP, or similar. Once I have that, I can compute the elasticity for you.

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Math Problem Analysis

Mathematical Concepts

Elasticity of Demand
Percentage Change
Demand Function

Formulas

Elasticity of Demand: Ed = (ΔQ / Q) / (ΔP / P)

Theorems

Price Elasticity of Demand

Suitable Grade Level

College-Level Economics or Advanced High School Economics