Question: Consider two countries, A and B, engaged in international trade. Both countries produce cars and computers, and their production possibilities frontiers (PPFs) are given by the equations:
PPFA:3CA+2KA=120
PPFB:2CB+4KB=160
Opportunity Cost: To find the opportunity cost of one car in terms of computers, we calculate the slope of each country's PPF. The opportunity costs are 3223 for Country A and 1221 for Country B.
Comparative Advantage: Comparing opportunity costs, Country B has a comparative advantage in producing cars due to its lower opportunity cost (1221).
Trade and Specialization:
Specialization: Country A specializes in computers, and Country B specializes in cars.
Production After Specialization: Country A produces 40 computers, and Country B produces 10 cars.
Consumption and Trade: Country A exports 40 computers to Country B in exchange for 8 cars, benefiting both countries.
By understanding and applying the principles of comparative advantage, these countries optimize their production, trade, and consumption, leading to mutual gains.
Certainly! Let's work through the questions step by step:
Answers
1. Opportunity Cost
To find the opportunity cost of one car in terms of computers, we need to calculate the slope of each country's production possibilities frontier (PPF). The slope of the PPF represents the opportunity cost. The general formula for the slope is the negative ratio of the coefficients of the two goods. Therefore, the opportunity cost (\(OC\)) for both countries is:
\[ OC = -\frac{\text{Coefficient of }C}{\text{Coefficient of }K} \]
For Country A:
\[ PPF_A: 3C_A + 2K_A = 120 \]
\[ \text{Slope}_A = -\frac{3}{2} \]
For Country B:
\[ PPF_B: 2C_B + 4K_B = 160 \]
\[ \text{Slope}_B = -\frac{2}{4} = -\frac{1}{2} \]
So, the opportunity cost of one car in terms of computers is \( \frac{3}{2} \) for Country A and \( \frac{1}{2} \) for Country B.
2. Comparative Advantage
To determine comparative advantage, compare the opportunity costs. The country with a lower opportunity cost has a comparative advantage.
Country A: \(OC_A = \frac{3}{2}\)
Country B: \(OC_B = \frac{1}{2}\)
Therefore, Country B has a comparative advantage in producing cars (lower opportunity cost).
3. Trade and Specialization
Given the world price of cars is 5 computers, both countries can benefit from trade.
Let's assume the terms of trade are \(1 \text{ car} = 5 \text{ computers}\).
Specialization
- Country A specializes in producing computers (lower opportunity cost), and Country B specializes in producing cars.
Production After Specialization
- Country A produces only computers, and Country B produces only cars.
- Let's say Country A produces 40 computers, and Country B produces 10 cars.
- **Consumption and Trade:**
- Country A exports computers to Country B in exchange for cars.
- If Country A trades 40 computers (its excess) with Country B and receives 8 cars in exchange (40 computers / 5 computers per car), both countries are better off.
In summary, by specializing in the production of goods in which they have a comparative advantage and engaging in trade, both countries can consume more of both goods than if they tried to produce both goods on their own.
Remember, these numerical examples are for illustration purposes, and you can adjust the quantities based on the specific calculations.
Happy studying!
Economics Homework Helper
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