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...

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. 


Asked on by littlemay

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

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.

kplhardison's profile pic

Karen P.L. Hardison | College Teacher | eNotes Employee

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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).
fturegano's profile pic

fturegano | In Training Educator

Posted on

While the question gives us limited insight into the optimal PPF, it does inform us about other aspects of their economies. 

The point of the PPF is to determine the optimal quantity produced within a given marketplace. Based off this (limited) information, it'd be best for the USA to focus their production on soda, while Brazil would focus their efforts on clothing. Very simply, this is indicated by the large differences in the quantities each nation is production. The key to a PPF is the find the optimal efficiencies; in other words, what is easiest and most efficient for the countries to produce. Generally speaking, focusing production on goods that the nation excels in is the best answer. While both countries produce soda and clothing, one would say that Brazil has a comparative advantage in clothing production, while the USA has a comparative advantage in soda production. To ensure efficiency within these markets, each country would focus on specialization, wherein they allocate all their resources towards the most efficent production of goods. This means USA focused on soda; Brazil on clothing. By concentrating their efforts into their optimum manufacturing capabilities, they can maintain an advantage within that industry, allowing them better trade opportunities. Many times, nations attempting to produce all their own goods leads to an ineffective allocation of resources, all the while they could just concentrate their production on what they excel in. However, due to massive difference in soda produced between the nations, one could say with some certainty that the USA has an absolute advantage in soda production. This means they are just more efficent at soda production (many factors determine this). 

Graphically, each axis would represent a good (e.g. X-Axis is soda, Y-Axis is clothing), while the graph as a whole represents the nation's production possibilities. Connecting the maximum quantities produced on either axis would allow you to determine the optimal quantity produced, relative to other goods being produced. This means that, if you were to increase soda production X amount, clothing production would decrease by X amount. This unknown amount is the opportunity cost: what is being given up for the production of something else. 

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writer-edwin | College Teacher | In Training Educator

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No country has an absolute advantage over the other as neither of them produces more than the other in the two commodities: soda and clothing. The United States has a comparative advantage in the production of soda as Brazil has a steeper production possibility frontier relative to the United States. This means Brazil has a higher opportunity cost in the production of soda relative to the United States. Consequently, Brazil has a comparative advantage in the production of clothing. Given their comparative advantages, the United States should specialize in production of soda while Brazil should specialize in production of clothing. Based on Ricardo’s theory of comparative advantage, the countries would significantly benefit from Brazil exporting clothing to the United States and conversely the United States exporting soda to Brazil.

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