Discussion Topic

# Determining the production possibility frontiers for Brazil and the United States and analyzing which product each country should specialize in, based on their production capacities for clothing and soda

Summary:

The production possibility frontiers (PPFs) for Brazil and the United States illustrate the maximum possible output combinations of clothing and soda that each country can produce. To determine specialization, analyze the opportunity costs. The country with the lower opportunity cost for a product should specialize in that product. If Brazil has a lower opportunity cost for clothing and the U.S. for soda, then Brazil should specialize in clothing and the U.S. in soda.

What would be the production possibility frontiers for Brazil and the United States?Both Brazil and the U.S. produce clothing and soda. For Brazil the total cost to produce 100000 units of clothing per year and 50000 cans of soda is the same. For the U.S. the cost to produce 65,000 units of clothing per year and 250000 cans of soda is the same.

A production possibility frontier (PPF) is a way of showing the different possibilities that exist for the production of two goods, assuming that an increase in the production of one good requires a decrease in the production of the other. We are told that the cost for producing 100,000 units of clothing is Brazil is the same cost as producing 50,000 cans of soda. Dividing by 50 shows of that 2 units of clothing have the same cost as 1 can of soda. Thus, the opportunity cost of producing a can of soda is 2 units of clothing, and dividing by 2 shows us that the opportunity cost of producing a unit of clothing is half a can of soda.

Similarly, with the US, we can find the opportunity cost of producing one unit of each good by dividing the equivalence we're given by the coefficient of the other good.

That is: 65,000C = 250,000S.

Dividing by 65,000 tells us that 1 unit of clothing = 3.85 cans of soda.

Dividing by 250,000 instead tells us that 1 unit of soda = 0.26 units of clothing.

To graph the PPF, we would also need the maximum possible production for each country of one of these goods. Then we could create a linear graph starting from that maximum and showing all possible combinations of goods. The line would show combinations that produce as much as possible, and the area beneath the graph would show possibilities other than maximum production.

The formula for such a graph would be y = -OC(a) + b, where y is the production of good b, OC(a) is the opportunity cost of producing a unit of good a, and b is the maximum production of good b.

For example, if the equivalence we are given for Brazil represents maximum production, this graph would be y(units of clothing) = -2 * (cans of soda produced) + 100,000.

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What would be the production possibility frontiers for Brazil and the United States?Both Brazil and the U.S. produce clothing and soda. For Brazil the total cost to produce 100000 units of clothing per year and 50000 cans of soda is the same. For the U.S. the cost to produce 65,000 units of clothing per year and 250000 cans of soda is the same.

The production possibility frontier (PPF) gives an idea of the opportunity cost of producing a particular product. If there are two products A and B that can be produced using the same resources, producing more units of A comes with a decrease in the number of units of B that can be produced. Similarly producing more units of B comes with a decrease in the number of units of A that can be produced. The graph drawn with the number of units of A that can be produced on one axis and the number of units of B that can be produced on the other axis is the production possibility frontier. It is possible to produce a number of units that lies below the PPF but that would be an inefficient use of resources available. It is not possible to produce a number of units of both that lies outside the PPF.

In the question both Brazil and the U.S. produce clothing and soda. For Brazil the total cost to produce 100000 units of clothing per year and 50000 cans of soda is the same.

If by cost the resources utilized is implied, we have an opportunity cost for producing a unit of clothing as half a unit of a can of soda. On the other hand the opportunity cost of a can of soda is 2 units of clothing.

Similarly for the U.S. the resources used to produce 65,000 units of clothing per year and 250000 cans of soda is the same. The opportunity cost of a unit of clothing is approximately 3.846 units of cans of soda. The opportunity cost of a can of soda is 0.26 units units of clothing.

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What would the production possibility frontiers be for Brazil and the United States? Without trade, the United States produces and consumes 32,500 units of clothing and 125,000 cans of soda. Without trade, Brazil produces and consumes 50,000 units of clothing and 25,000 cans of soda. Denote these points on each country’s production possibility frontier. Using what you have learned and any independent research you may conduct, which product should each country specialize in, and why?

From an economic standpoint, it makes sense for the United States and Brazil to specialize in the product with the most consumers. The United States should specialize in soda as that attracts almost four times as many consumers. Brazil should specialize in clothes as that attracts double the consumers.

However, one could make the case that the country should specialize in the product with the least amount of consumers in an effort to expand that industry and bring it up to par with the industry that attracts the larger pool of consumers. As all 32,500 units of clothing are consumed in America, and all 25,000 cans of soda are consumed in Brazil, perhaps each country should see what happens to the consumption rate when production of these goods is ramped up.

From a health point of view, the United States might want to try to move away from increasing its production of cans of soda regardless of economic benefits. Soda contains a significant level of added sugar. The added sugar has been linked to obesity and an array of health issues. To encourage its citizens to embrace healthier choices, America could cut back on soda production and invest in beverages that are better for a person’s body.

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What would the production possibility frontiers be for Brazil and the United States? Without trade, the United States produces and consumes 32,500 units of clothing and 125,000 cans of soda. Without trade, Brazil produces and consumes 50,000 units of clothing and 25,000 cans of soda. Denote these points on each country’s production possibility frontier. Using what you have learned and any independent research you may conduct, which product should each country specialize in, and why?

Each country ought to specialize in making whichever product costs its economy relatively the least. We can define such a cost in many terms; popular definitions include the lost opportunity to make other things of value to the economy or an economy's allocation and production efficiencies.

The United States, at its most efficient economic state, is utilizing soda at a rate nearly four times greater it does clothing: 125,000 sodas : 32,500 units of clothing = ~3.846:1.

Brazil, on the other hand, is said to utilize soda only half as much as clothes at its own optimal PPF state: 25,000 sodas : 50,000 clothes = 1:2.

Sometimes these ratios are expressed as the "slope" of the respective nations' PPF functions, but more generally, they represent the relative value each commodity has to one another within said country. If each nation ought to specialize in producing that which it values the most under optimum economic conditions, then Brazil ought to specialize in making clothes and the US should specialize in making soda.

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What would the production possibility frontiers be for Brazil and the United States? Without trade, the United States produces and consumes 32,500 units of clothing and 125,000 cans of soda. Without trade, Brazil produces and consumes 50,000 units of clothing and 25,000 cans of soda. Denote these points on each country’s production possibility frontier. Using what you have learned and any independent research you may conduct, which product should each country specialize in, and why?

You do not have enough information here to answer any of these questions.

In order to find the production possibility frontiers (PPFs) for the two countries, you would need to have at least two ordered pairs for each country.  Right now, we have only one ordered pair for each.  We know that the US can produce and consume 32,500 units of clothing and 125,000 cans of soda.  We know that Brazil can produce and consume 50,000 units of clothing and 25,000 cans of soda.  The problem is that we do not have any other points.  For example, we do not know how many cans of soda Brazil could produce if it only produced 40,000 units of clothing.  We do not know how many units of clothing the US could produce if they only produced 100,000 cans of soda.  We need more points so that we can draw PPFs through those points.  As it is, you could denote those points, but you would not be able to draw any curves to show the PPFs.

As far as what product each country should specialize in, you do not know enough because you cannot determine opportunity cost.  The idea of comparative advantage says that a country should specialize in the good for which their opportunity cost is lower than that of their trading partner.  The problem here is that you do not know the opportunity costs for either country because you only have one data point for each.  I would guess that the US should specialize in soda because rich countries rarely have a comparative advantage in something as labor-intensive as the garment industry, but I have no numbers to back this up.

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What would be the production possibility frontiers for Brazil and the United States in this scenario? There are two products: clothing and soda. Both Brazil and the United States produce each product. Brazil produces 100,000 units of clothing per year and 50,000 cans of soda. The United States produces 65,000 units of clothing per year and 250,000 and cans of soda. Assume that costs remain constant.  http://www.economicsonline.co.uk/Competitive_markets/Production_possibility_frontiers.html

In Economics studies, exercises in production possibility frontiers (PPF) can be conducted with minimal details such as provided in this question. To illustrate, EconomicsOnline.co.uk (UK)--sponsored by Pearson Education, OCR (Oxford Cambridge RSA or The Royal Society for the Encouragement of Arts) and AQA (Assessment and Qualifications Alliance)--provides a teaching example very much like this one but with computers and textbooks produced in Mythica. So, assuming that this is the kind of exercise you are aiming at, we'll apply the procedure provided in the EconomicsOnline example set up for Mythica.

The economic elements concerned in developing a PPF for a country with two goods to produce are:

• opportunity cost and increasing opportunity cost
• production possibilities
• given output and change in output
• Pareto production efficiency (including efficient, inefficient and impossible production)

The objective of a PPF (production possibility frontier) is to establish graphically (on a graph) the efficient allocation of resources for production, or, to put it a little differently, the efficient level of production of competing goods to maximize utilization of scarce resources (remembering that all resources are scare for an industry, country, production of a particular good, etc). What you want a PPF to show (using the question example of clothing and soda) is efficient levels of production--and a plot line gradient reflecting increasing opportunity cost--with maximized resources for the two competing goods.

The central step, as shown in the Mythica example, is to determine all the production possibilities for the two goods. For example, in Mythica, for computers and textbooks, they can produce (among all other combinations):

• 0 computers     70 million (m) textbooks
• 1m computers     69m textbooks
• 2m computers     68m textbooks
• 3m computers     65m textbooks

You would form a similar chart showing all production possibilities for clothing and soda, first for Brazil and again for the United States (you'll have two charts for all production possibilities, one labeled "Brazil" and one "United States"). In Brazil, production is at 50,000 and 100,000 for soda (50,000) and clothing (100,000). If soda production reduces by some unit of quantity, say 10,000 units, then clothing production will increase correspondingly because the production relationship between the two goods is inverse: if soda decreases, then, inversely, clothing increases; if soda increases (goes up), then clothing decreases (goes down).

You'll note, though, that the inverse relationships between production possibilities of the two goods is not static. Since the PPF is a graph with an outward bowed line, concave to the 0 point of origin (the 0 point where both axes meet), the opportunity cost gradient between amounts produced at varying levels becomes steeper after the mid-point of the concave graph curve: there is an increasing opportunity cost for producing more of one good and less of another; the increasing opportunity cost shows as an increasingly steep PPF gradient between production points.

On the graph, you can plot production points, beginning with the known points of 50,000 and 100,000 (or 50k and 100k). You can then plot output changes by some unit, e.g., 10,000 (10k) units, of production, either reducing or increasing (the PPF graph will run both directions) soda production by 10k and correspondingly inversely increasing or reducing clothing production to the amount indicated by the correlated plot point.
The resultant outward bowing concave plot line is the line of Pareto efficiency (an efficiency usually not possible in the real world because of rigidities and imperfections in micro- and macro-economies, such as non-productive in a resource as from unemployment or unavailability, e.g., an employee on leave or an oil shortage). Points on this concave plot line are efficient production possibilities that maximize scarce resources, although the opportunity cost (that which is sacrificed of one product to gain more of another product) becomes steeper as the line curves downward. Points inside this line (between the axis lines and the plot line) do not demonstrate Pareto efficiency but rather inefficiency, with production not maximizing scarce resources. Points outside this line are impossible because of the nature of scarce resources: resources are not existent, at the time of the composition of the PPF, to support production at a point beyond the Pareto line (advances in technologies or the discoveries of substitute resources may change the impossibility at a future time).

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What would be the production possibility frontiers for Brazil and the United States in this scenario? There are two products: clothing and soda. Both Brazil and the United States produce each product. Brazil produces 100,000 units of clothing per year and 50,000 cans of soda. The United States produces 65,000 units of clothing per year and 250,000 and cans of soda. Assume that costs remain constant.  http://www.economicsonline.co.uk/Competitive_markets/Production_possibility_frontiers.html

The data given here is not sufficient to create a PPF for each country.  This is because we only have one data point for each country and we need at least two data points in order to create a PPF.

One thing a PPF shows is opportunity cost.  It shows us how many (in this example) cans of soda the US would have to give up in order to produce an extra unit of clothing.  With the data given here, we only know about one possibility for each country.  We do not know how many, for example, cans of soda either country could produce if it produced no clothing whatsoever.

In order to create a PPF for either country (or for both combined) we would need to have at least one more data point for each country.