Question

In the ancient country of Roma, only two goods, spaghetti and meatballs, are produced. There are two tribes in Roma, the Tivoli and the Frivoli. By themselves, the Tivoli each month can produce either 30 pounds of spaghetti and no meatballs, or 50 pounds of meatballs and no spaghetti, or any combination in between. The Frivoli, by themselves, each month can produce 40 pounds of spaghetti and no meatballs, or 30 pounds of meatballs and no spaghetti, or any combination in between. a. Assume that all production possibility frontiers are straight lines. Draw one diagram showing the monthly production possibility frontier for the Tivoli and another showing the monthly production possibility frontier for the Frivoli. Show how you calculated them. b. Which tribe has the comparative advantage in spaghetti production? In meatball production? In A.D. 100 the Frivoli discover a new technique for making meatballs that doubles the quantity of meatballs they can produce each month. c. Draw the new monthly production possibility frontier for the Frivoli. d. After the innovation, which tribe now has an absolute advantage in producing meatballs? In producing spaghetti? Which has the comparative advantage in meatball production? In spaghetti production?

Short answer

Answer: After the technological innovation, Tivoli has the comparative advantage in both spaghetti and meatball production.

Step-by-step solution

Identify the endpoints for Tivoli's PPF

The Tivoli can produce either 30 pounds of spaghetti and no meatballs, or 50 pounds of meatballs and no spaghetti. These endpoints represent the bounds of production possibilities for the PPF.

Plot the PPF for Tivoli

On a graph with spaghetti on the x-axis and meatballs on the y-axis, use the endpoints (30,0) and (0,50) to draw a straight line between them. This represents the production possibility frontier for the Tivoli.

Identify the endpoints for Frivoli's PPF

The Frivoli can produce either 40 pounds of spaghetti and no meatballs, or 30 pounds of meatballs and no spaghetti. These endpoints represent the bounds of production possibilities for the PPF.

Plot the PPF for Frivoli

On a separate graph with spaghetti on the x-axis and meatballs on the y-axis, use the endpoints (40,0) and (0,30) to draw a straight line between them. This represents the production possibility frontier for the Frivoli. #b. Identifying Comparative Advantages#

Calculate Opportunity Costs

Calculate the opportunity cost of producing one unit of spaghetti for each tribe. Tivoli: \[Opportunity\;Cost(Spaghetti)=\frac{50}{30}=\frac{5}{3}\] meatballs. Frivoli: \[Opportunity\;Cost(Spaghetti)=\frac{30}{40}=\frac{3}{4}\] meatballs.

Identify Comparative Advantages

Frivoli has a lower opportunity cost of producing spaghetti, so they have the comparative advantage in spaghetti production. Conversely, Tivoli has a lower opportunity cost of producing meatballs, so they have the comparative advantage in meatball production. #c. Drawing the New Monthly PPF for Frivoli#

Identify New Endpoints for Frivoli's PPF

The Frivoli discover a new technique that doubles their meatball production. Now, they can produce either 40 pounds of spaghetti and no meatballs, or 60 pounds of meatballs and no spaghetti. These endpoints represent the bounds of the new production possibilities for the PPF.

Plot the New PPF for Frivoli

On a separate graph with spaghetti on the x-axis and meatballs on the y-axis, use the new endpoints (40,0) and (0,60) to draw a straight line between them. This represents the new production possibility frontier for the Frivoli. #d. Comparing Advantages After Innovation#

Identify Absolute Advantages

Now, Tivoli can produce a maximum of 50 pounds of meatballs while Frivoli can produce a maximum of 60 pounds of meatballs. Thus, Frivoli has an absolute advantage in producing meatballs. Tivoli can produce a maximum of 30 pounds of spaghetti, while Frivoli can produce a maximum of 40 pounds of spaghetti. Thus, Frivoli has an absolute advantage in producing spaghetti.

Calculate New Opportunity Costs

Calculate the new opportunity cost of producing one unit of spaghetti for Frivoli: \[Opportunity\;Cost(Spaghetti)=\frac{60}{40}=\frac{3}{2}\] meatballs.

Identify New Comparative Advantages

Now, Frivoli's opportunity cost of producing spaghetti has risen to \[\frac{3}{2}\] meatballs, while Tivoli's opportunity cost remains at \[\frac{5}{3}\] meatballs. Tivoli now has a lower opportunity cost for producing spaghetti, so they have the comparative advantage in spaghetti production after the innovation. Tivoli still has the comparative advantage in meatball production, as their opportunity cost remains lower.

Key concepts

Comparative Advantage

The concept of comparative advantage is all about determining which tribe should focus on producing which good to maximize efficiency. It compares the opportunity costs between groups to determine who can produce a particular good at a lower opportunity cost. In the case of the Roman tribes, comparative advantage is a crucial concept in determining whether the Tivoli or the Frivoli should specialize in producing spaghetti or meatballs each month.

Originally, the Frivoli tribe had the comparative advantage in producing spaghetti because their opportunity cost was lower at \( \frac{3}{4} \) meatballs for every pound of spaghetti. Meanwhile, the Tivoli tribe had a comparative advantage in creating meatballs due to their lower opportunity cost for producing meatballs at \( \frac{3}{5} \) pounds of spaghetti per pound of meatball. This concept helps determine how resources are best utilized, ensuring that each tribe is focusing on what they do best to increase overall production and possibly trade between them.

Opportunity Cost

Opportunity cost represents the benefits or products that are foregone when one alternative is chosen over another. It is essential because it helps tribes like the Tivoli and Frivoli make informed decisions about what to produce. For example, every unit of one good produced means sacrificing some production of the other good. It quantifies what each tribe gives up to produce more of the other good and is vital in determining comparative advantage.

The opportunity cost of producing spaghetti for the Tivoli is calculated as \( \frac{50}{30} = \frac{5}{3} \) meatballs. Similarly, the Frivoli have an opportunity cost of \( \frac{30}{40} = \frac{3}{4} \) meatballs for each pound of spaghetti. Understanding these opportunity costs allows each tribe to evaluate where their efforts should be concentrated to minimize loss of potential output from producing other goods.

After the Frivoli discovered a new technique and doubled their meatball production efficiency, this changed their opportunity costs. Despite their new capabilities, it was revealed that they still had a higher cost of producing spaghetti relative to meatballs compared to the Tivoli. Thus, knowing and analyzing opportunity costs allows each tribe to strategize and utilize their resources efficiently.

Absolute Advantage

Absolute advantage is a term used for one tribe's outright capacity to produce more of a good compared to another tribe using the same resources. It basically measures raw productivity without considering the relative cost of production. After the Frivoli's technological innovation that upped their meatball production, understanding absolute advantage became especially relevant.

Because the Frivoli can now produce 60 pounds of meatballs compared to the Tivoli's 50 pounds, the Frivoli have clear absolute advantage in meatball production. Likewise, Frivoli have always had absolute advantage in spaghetti production since they can produce 40 pounds compared to Tivoli's 30 pounds.

This concept is essential, but knowing an absolute advantage doesn't imply that a tribe should necessarily specialize in the same product. It's understanding the comparative advantage that helps make better decisions in specialization for mutually beneficial trade. Even if Frivoli can produce more of both, deciding based on comparative advantage allows them to focus on what minimizes their sacrifice, optimizing overall gains for both. Only after evaluating comparative advantage, can tribes make informed choices that maximize their overall productive capacities.