You are the manager of a monopoly that sells a product to two groups of consumers in different parts of the country. Analysts at your firm have determined that group 1’s elasticity of demand is −4, while group 2’s is −2. Your marginal cost of producing the product is $30.

a. Determine your optimal markups and prices under third-degree price discrimination.

Instructions: Enter your responses rounded to two decimal places.

Markup for group 1: 

 

Price for group 1: $ 

 

Markup for group 2: 

 

Price for group 2: $ 



To determine the optimal markups and prices under third-degree price discrimination, we need to use the formula for the optimal markup for a monopoly:

\[
\text{Price} = \frac{\text{Marginal Cost}}{1 + \frac{1}{\text{Elasticity of Demand}}}
\]

Where:
- $ \text{Elasticity of Demand} $ is the price elasticity of demand for each group,
- $ \text{Marginal Cost} $ is given as \$30.

### Step 1: Markup and Price for Group 1

- Elasticity of demand for group 1: $ E_1 = -4 $.
- Marginal cost: MC = \$30.

Using the formula:

\[
\text{Price for Group 1} = \frac{30}{1 + \frac{1}{-4}} = \frac{30}{1 - \frac{1}{4}} = \frac{30}{0.75}
\]

Now, calculate the price and markup:

\[
\text{Price for Group 1} = 40.00
\]

To find the markup:

\[
\text{Markup for Group 1} = \text{Price} - \text{Marginal Cost} = 40.00 - 30 = 10.00
\]

### Step 2: Markup and Price for Group 2

- Elasticity of demand for group 2: $ E_2 = -2 $.

Using the same formula:

\[
\text{Price for Group 2} = \frac{30}{1 + \frac{1}{-2}} = \frac{30}{1 - \frac{1}{2}} = \frac{30}{0.5}
\]

Now, calculate the price and markup:

\[
\text{Price for Group 2} = 60.00
\]

To find the markup:

\[
\text{Markup for Group 2} = \text{Price} - \text{Marginal Cost} = 60.00 - 30 = 30.00
\]

### Final Results:
- **Markup for group 1**: 10.00
- **Price for group 1**: $40.00
- **Markup for group 2**: 30.00
- **Price for group 2**: $60.00

Let me know if you'd like more details or explanations!  

Here are 5 related questions for you to consider:
1. How would changes in marginal cost affect the prices for each group?
2. What happens to prices if the elasticity for one of the groups becomes more elastic (higher in absolute value)?
3. Can you explain why group 2 has a higher price compared to group 1?
4. How would you calculate consumer surplus for each group?
5. How would the introduction of a competitor affect the prices?

**Tip**: Elasticity of demand is crucial in price discrimination because more elastic groups are charged lower prices to maximize profit.

You are the manager of a monopoly that sells a product to two groups of consumers in different parts of the country. Analysts at your firm have determined that group 1’s elasticity of demand is −4, while group 2’s is −2. Your marginal cost of producing the product is $30. Determine your optimal markups and prices under third-degree price discrimination.

Learn how to calculate the optimal markups and prices for a monopoly using third-degree price discrimination. This example analyzes two groups with different demand elasticities (-4 and -2) and a marginal cost of $30. Detailed steps and formulas are provided for determining the optimal pricing strategy for each group.

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