A monopoly sells its good in the United​ States, where the elasticity of demand is negative 2.1​, and in​ Japan, where the elasticity of demand is negative 5.5.  Its marginal cost is ​$12.  At what price does the monopoly sell its good in each country if resales are​ impossible? 

To find the price at which the monopoly sells its good in each country, we can use the relationship between the price, marginal cost, and elasticity of demand. The formula for determining the price in each market under monopoly pricing is:

\[
P = \frac{MC}{1 + \frac{1}{E_d}}
\]

Where:
- $ P $ is the price.
- $ MC $ is the marginal cost.
- $ E_d $ is the price elasticity of demand (which is negative, but we use its absolute value for this formula).

### United States:
Given:
- $ E_d = -2.1 $ (so we use $ |E_d| = 2.1 $)
- $ MC = 12 $

\[
P_{\text{US}} = \frac{12}{1 + \frac{1}{2.1}} = \frac{12}{1 + 0.476} = \frac{12}{1.476} \approx 8.13
\]

The price in the United States is approximately **$8.13**.

### Japan:
Given:
- $ E_d = -5.5 $ (so we use $ |E_d| = 5.5 $)
- $ MC = 12 $

\[
P_{\text{Japan}} = \frac{12}{1 + \frac{1}{5.5}} = \frac{12}{1 + 0.182} = \frac{12}{1.182} \approx 10.15
\]

The price in Japan is approximately **$10.15**.

### Conclusion:
- The price in the United States is approximately **$8.13**.
- The price in Japan is approximately **$10.15**.

Would you like further details on any step or concept? Here are some related questions:

1. How does elasticity affect pricing strategies in monopolies?
2. Why can't resales between countries occur in this problem?
3. What would happen if the elasticity values were the same in both countries?
4. How does the marginal cost influence monopoly pricing?
5. How would the prices change if the marginal cost were different?

**Tip:** Higher elasticity (in absolute value) indicates more price sensitivity, leading to lower prices set by monopolies.

A monopoly sells its good in the United States, where the elasticity of demand is negative 2.1, and in Japan, where the elasticity of demand is negative 5.5. Its marginal cost is $12. At what price does the monopoly sell its good in each country if resales are impossible?

This problem explores how a monopoly sets different prices in two countries with distinct elasticities of demand. Learn how to calculate the prices using the elasticity of demand and marginal cost, with real-world data from the US and Japan. Suitable for advanced economics students.

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