Math Problem Statement

The price of a cheeseburger increases from 26 to 30. As a result, the owner of a burger shop increases the quantity supplied from 250 to 450. The price elasticity of supply is [Answer]. (In decimal numbers, with three decimal places.)

Solution

The problem asks for the price elasticity of supply using the midpoint formula. Let's break it down.

Price Elasticity of Supply Formula:

Es=%ΔQs%ΔPE_s = \frac{\%\Delta Q_s}{\%\Delta P}

Where:

  • %ΔQs\%\Delta Q_s is the percentage change in quantity supplied.
  • %ΔP\%\Delta P is the percentage change in price.

Midpoint Formula:

%ΔQs=Q2Q1Q2+Q12\%\Delta Q_s = \frac{Q_2 - Q_1}{\frac{Q_2 + Q_1}{2}} %ΔP=P2P1P2+P12\%\Delta P = \frac{P_2 - P_1}{\frac{P_2 + P_1}{2}}

Given:

  • Initial price, P1=26P_1 = 26
  • New price, P2=30P_2 = 30
  • Initial quantity supplied, Q1=250Q_1 = 250
  • New quantity supplied, Q2=450Q_2 = 450

Step 1: Calculate the percentage change in quantity supplied:

%ΔQs=450250450+2502=200350=0.5714\%\Delta Q_s = \frac{450 - 250}{\frac{450 + 250}{2}} = \frac{200}{350} = 0.5714

Step 2: Calculate the percentage change in price:

%ΔP=302630+262=428=0.1429\%\Delta P = \frac{30 - 26}{\frac{30 + 26}{2}} = \frac{4}{28} = 0.1429

Step 3: Calculate the price elasticity of supply:

Es=0.57140.1429=4.000E_s = \frac{0.5714}{0.1429} = 4.000

So, the price elasticity of supply is 4.000.

Would you like more details or have any questions?

Related Questions:

  1. How does price elasticity of supply differ from price elasticity of demand?
  2. What factors affect the elasticity of supply?
  3. How does elasticity of supply impact pricing decisions for firms?
  4. Can elasticity of supply be negative? Why or why not?
  5. How do different types of goods (luxury vs necessity) affect elasticity of supply?

Tip: Always double-check units and make sure you use the midpoint formula correctly for more accurate results in elasticity calculations!

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Math Problem Analysis

Mathematical Concepts

Economics
Price Elasticity
Supply and Demand

Formulas

Price Elasticity of Supply: Es = (%ΔQs) / (%ΔP)
Midpoint Formula for %ΔQs = (Q2 - Q1) / ((Q2 + Q1) / 2)
Midpoint Formula for %ΔP = (P2 - P1) / ((P2 + P1) / 2)

Theorems

Elasticity and its effect on supply in microeconomics

Suitable Grade Level

Grades 11-12