On most​ days, the price of a rose is​ $1, and​ 8,000 roses are purchased. On​ Valentine's Day, the price of a rose jumps to​ $2, and​ 30,000 roses are purchased.
Part 2
Use the line drawing tool to illustrate the price and quantity increase.  Label the line you draw ​'D Subscript 1​'.
Part 3
Carefully follow the instructions​ above, and only draw the required objects.  
Part 4
Based on this​ information, we do not know much about the price elasticity of demand for roses because the demand curve was not constant.
Part 5
​However, we do have constant supply.  What is price elasticity of​ supply?  
  
enter your response here ​(enter your response to 2 decimal places​).

To calculate the price elasticity of supply (PES), we use the following formula:

\[
\text{PES} = \frac{\%\ \text{change in quantity supplied}}{\%\ \text{change in price}}
\]

### Step 1: Calculate the percentage change in quantity supplied

Initially, 8,000 roses were sold at $1, and 30,000 roses were sold at $2.

\[
\%\ \text{change in quantity} = \frac{30,000 - 8,000}{8,000} \times 100 = \frac{22,000}{8,000} \times 100 = 275\%
\]

### Step 2: Calculate the percentage change in price

The price increased from $1 to $2.

\[
\%\ \text{change in price} = \frac{2 - 1}{1} \times 100 = 100\%
\]

### Step 3: Calculate the price elasticity of supply

\[
\text{PES} = \frac{275\%}{100\%} = 2.75
\]

So, the price elasticity of supply is **2.75**.

Would you like further details on this or have any additional questions?

Here are 5 questions that extend the discussion:
1. How does a price elasticity of supply greater than 1 affect the market?
2. What would happen if the supply of roses were inelastic instead?
3. Can the price elasticity of demand be calculated from the given data?
4. What factors could cause the supply curve for roses to shift?
5. How would a constant demand curve alter the elasticity calculation?

**Tip**: A supply elasticity greater than 1 indicates that producers are very responsive to price changes, increasing supply significantly when prices rise.

On most days, the price of a rose is $1, and 8,000 roses are purchased. On Valentine's Day, the price of a rose jumps to $2, and 30,000 roses are purchased. Use the line drawing tool to illustrate the price and quantity increase. Label the line you draw 'D Subscript 1'. Carefully follow the instructions above, and only draw the required objects. Based on this information, we do not know much about the price elasticity of demand for roses because the demand curve was not constant. However, we do have constant supply. What is price elasticity of supply? (enter your response to 2 decimal places).

Learn how to calculate the price elasticity of supply in the context of the rose market during Valentine's Day. With an increase in price from $1 to $2 and a rise in quantity from 8,000 to 30,000 roses, this problem provides a detailed step-by-step solution to calculate the PES, highlighting core concepts like supply and demand, percentage change, and elasticity. Suitable for students in Grades 11-12 and college economics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation