Question

In an hour, Sue can produce 40 caps or 4 jackets and Tessa can produce 80 caps or 4 jackets. a. Calculate Sue's opportunity cost of producing a cap. b. Calculate Tessa's opportunity cost of producing a cap. c. Who has a comparative advantage in producing caps? d. If Sue and Tessa specialize in producing the good in which they have a comparative advantage, and they trade 1 jacket for 15 caps, who gains from the specialization and trade?

Short answer

a. \(\frac{1}{10}\) jackets per capb. \(\frac{1}{20}\) jackets per capc. Tessa d. Both Sue and Tessa gain.

Step-by-step solution

Calculate Sue's Opportunity Cost of Producing a Cap

First, determine how many jackets Sue can produce instead of one cap. Sue can produce 40 caps or 4 jackets in an hour. The opportunity cost of producing one cap is the number of jackets she could have produced instead. Thus, Sue's opportunity cost is \[ \text{Opportunity Cost of 1 Cap for Sue} = \frac{4 \text{ jackets}}{40 \text{ caps}} = \frac{1}{10} \text{ jackets per cap} \]

Calculate Tessa's Opportunity Cost of Producing a Cap

Next, determine how many jackets Tessa can produce instead of one cap. Tessa can produce 80 caps or 4 jackets in an hour. The opportunity cost of producing one cap is the number of jackets she could have produced instead. Thus, Tessa's opportunity cost is \[ \text{Opportunity Cost of 1 Cap for Tessa} = \frac{4 \text{ jackets}}{80 \text{ caps}} = \frac{1}{20} \text{ jackets per cap} \]

Determine Comparative Advantage in Producing Caps

Comparative advantage is determined by comparing opportunity costs. Whichever person has the lowest opportunity cost for producing caps has the comparative advantage. Sue's opportunity cost of producing a cap is \( \frac{1}{10} \text{ jackets per cap} \) and Tessa's opportunity cost is \( \frac{1}{20} \text{ jackets per cap} \). Since \( \frac{1}{20} < \frac{1}{10} \), Tessa has the comparative advantage in producing caps.

Determine Gains from Specialization and Trade

Sue and Tessa should specialize in the goods for which they have the comparative advantage. Tessa should produce caps, and Sue should produce jackets. When they trade, we need to check if both gain from the trade. We trade 1 jacket for 15 caps.For Sue: Instead of producing 1 jacket (which costs 10 caps), she gets 15 caps, benefiting her by 5 caps.For Tessa: Instead of producing 15 caps (which costs 0.75 jackets), she gets 1 jacket, benefiting her by 0.25 jackets.

Key concepts

Comparative Advantage

Comparative advantage is a key concept in understanding international trade and economics. It explains why it can be beneficial for countries or individuals to specialize in producing certain goods and then trade with others. For example, in our exercise, we compared the opportunity costs of Sue and Tessa for producing caps.

Sue's opportunity cost for producing one cap is 0.1 jackets, while Tessa's is 0.05 jackets. Since Tessa has the lower opportunity cost, she has a comparative advantage in producing caps. This means Tessa can produce caps more efficiently than Sue. Understanding comparative advantage helps us identify the most efficient producer for a given task or product.

By specializing in their comparative advantage, individuals or nations can produce more goods and trade these for other goods at a mutually beneficial rate, leading to more overall production and consumption.

In our example, Tessa should focus on producing caps because she gives up fewer jackets per cap produced compared to Sue.

Specialization and Trade

Specialization and trade are processes where different parties focus on producing specific goods or services and then trade to obtain other desired goods or services. This idea builds on the concept of comparative advantage. In the given exercise, Sue and Tessa should each specialize in the product they are comparatively more efficient at producing.

Sue should specialize in making jackets since her opportunity cost for producing caps is higher. Tessa should specialize in making caps as she has the lower opportunity cost for caps.

By specializing, they can maximize their production efficiency. Sue can produce more jackets while Tessa can produce more caps. They can then trade these products with each other to meet their respective needs.

• Specialization leads to a higher total output of goods.
• It utilizes the efficiency of each producer effectively.
• Parties can focus on improving their skills and production techniques in their area of specialization.

This approach makes the best use of resources and leads to efficient use of time and skills.

Gains from Trade

Gains from trade occur when different parties obtain more goods or services through trading than they would if they tried to produce everything on their own. This concept becomes clear when individuals or nations specialize in goods where they have a comparative advantage and then trade for other goods.

In our exercise, if Sue and Tessa trade 1 jacket for 15 caps, both parties gain from the trade. Sue benefits because she receives 15 caps in exchange for 1 jacket. Producing 1 jacket herself would cost her the equivalent of 10 caps, so she effectively gains 5 caps through the trade.

On the other hand, Tessa gains because she gets 1 jacket in exchange for 15 caps. Producing a jacket herself would cost her 0.75 jackets' worth of effort in terms of caps, so she effectively gains 0.25 jackets through the trade.

These gains highlight how trade allows both parties to achieve better outcomes than they would by producing alone. They obtain more goods at a lower opportunity cost through exchange. Gains from trade:

• Increase overall consumption possibilities.
• Utilize resources more efficiently.
• Encourage production specializations and improvements.

As a result, specialization and trade lead to increased wealth and efficiency for all involved parties.