6) In an open economy, the domestic demand and supply for product X are given by D(P)=120-P and S(P)=2P respectively. The country is small and the world price of X is $70. The country currently has a $ 10 tariff on import and a $15 tariff on export. Find the country's deadweight loss.
6) In an open economy, the domestic demand and supply for product X are given by D(P)=120-P and S(P)=2P respectively. The country is small and the world price of X is $70. The country currently has a $ 10 tariff on import and a $15 tariff on export. Find the country's deadweight loss.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Problem Statement
**Question 6:**
In an open economy, the domestic demand and supply for product X are given by D(P) = 120 - P and S(P) = 2P respectively. The country is small, and the world price of X is $70. The country currently has a $10 tariff on import and a $15 tariff on export. Find the country's deadweight loss.
**Explanation:**
- D(P) = 120 - P: Domestic demand equation for product X, where `P` is the price.
- S(P) = 2P: Domestic supply equation for product X, where `P` is the price.
- World price of X = $70.
- $10 tariff on import.
- $15 tariff on export.
The task is to calculate the deadweight loss the country experiences due to the tariffs imposed on imports and exports.
To solve this problem, follow these steps:
### Calculation Steps:
1. **Determine the Domestic Equilibrium:**
- Set D(P) equal to S(P) to find the domestic equilibrium price and quantity.
\[
120 - P = 2P
\]
Solving for `P`:
\[
120 = 3P
\]
\[
P = 40
\]
2. **Calculate Domestic Equilibrium Quantity:**
\[
Q = 120 - P = 120 - 40 = 80
\]
3. **Determine Quantities with World Price:**
- At the world price of $70, the domestic supply and demand are as follows:
- Domestic demand:
\[
Q_d = 120 - 70 = 50
\]
- Domestic supply:
\[
Q_s = 2 \times 70 = 140
\]
4. **Calculate Imports and Exports Without Tariffs:**
- Without tariffs, the country would import the difference between domestic demand and supply at the world price.
\[
Imports = Q_d - Q_s = 50 - 140 = -90
\]
Since the value is negative, this implies exports of 90 units.
5. **Incorporate Tariffs:**
- With a $10 import tariff, the adjusted import price would be $80 ($70 world price + $10 tariff).
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d98c794-b13e-4730-afe8-143f60931f40%2F2d3fe0fe-bb37-43d3-9dc0-343beb8080f6%2Fpkkhp9c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**Question 6:**
In an open economy, the domestic demand and supply for product X are given by D(P) = 120 - P and S(P) = 2P respectively. The country is small, and the world price of X is $70. The country currently has a $10 tariff on import and a $15 tariff on export. Find the country's deadweight loss.
**Explanation:**
- D(P) = 120 - P: Domestic demand equation for product X, where `P` is the price.
- S(P) = 2P: Domestic supply equation for product X, where `P` is the price.
- World price of X = $70.
- $10 tariff on import.
- $15 tariff on export.
The task is to calculate the deadweight loss the country experiences due to the tariffs imposed on imports and exports.
To solve this problem, follow these steps:
### Calculation Steps:
1. **Determine the Domestic Equilibrium:**
- Set D(P) equal to S(P) to find the domestic equilibrium price and quantity.
\[
120 - P = 2P
\]
Solving for `P`:
\[
120 = 3P
\]
\[
P = 40
\]
2. **Calculate Domestic Equilibrium Quantity:**
\[
Q = 120 - P = 120 - 40 = 80
\]
3. **Determine Quantities with World Price:**
- At the world price of $70, the domestic supply and demand are as follows:
- Domestic demand:
\[
Q_d = 120 - 70 = 50
\]
- Domestic supply:
\[
Q_s = 2 \times 70 = 140
\]
4. **Calculate Imports and Exports Without Tariffs:**
- Without tariffs, the country would import the difference between domestic demand and supply at the world price.
\[
Imports = Q_d - Q_s = 50 - 140 = -90
\]
Since the value is negative, this implies exports of 90 units.
5. **Incorporate Tariffs:**
- With a $10 import tariff, the adjusted import price would be $80 ($70 world price + $10 tariff).
-
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