Proving Comparative Advantage Made Easy

International Economics at “A” levels is what we, at JC Econs 101, would consider to be a “give-away” topic.

However, the explanation behind how the principle of Comparative Advantage drives trade often appears long and challenging, usually with need for numerical examples as proofs.

In particular, the most difficult explanation and proof lies with proving that comparative advantages can be mutually beneficial even if a trading partner has overwhelming absolute advantage in the production of all goods and services.

We therefore came up with a single comprehensive example, to help you understand easily why comparative advantages are often considered the main trade drivers in Economics.

Is the proof that comparative advantage can drive trade for a small country despite absolute disadvantages in production important?

One word – Yes!

Proving that comparative advantage can be attractive even for big countries to trade with small ones is considered to be the best proof that comparative advantage is a major driving force behind global trade.

As an extreme analogy, it is like saying the individual ant and an elephant find mutual benefit in trading.

If we can somehow prove this to be true, it will prove to be a very convincing argument!

Deriving the proof of the above is admittedly tricky in exams.

However we strongly feel that memorizing numerical examples is not the most efficient way to study Economics at all.

But not to worry! We have taken time to do the heavy lifting, and put together a suitable explanation for your understanding.

Start by setting the scenario up.

First, we begin by building the “story”:

  1. There are 2 countries, USA and Singapore;
  2. 2 commodities are being produced, Beef and Electronics;
  3. There are no barriers to trade and transport cost;
  4. Resources within the country can be easily transferred from one industry to another;
  5. There are constant returns to scale in both industries;
  6. All resources are fully employed in each country;
  7. In the absence of international trade, each country devotes half its resources to producing each product.

In the absence of trade, both countries will produce as such:

Bearing in mind that the aim of the exercise is to prove that trading based on the principle of Comparative Advantage is attractive to both countries despite size difference, we have chosen to compare between USA and Singapore, with USA having a clear absolute advantage in the production in both goods.

Determining comparative advantages.

We can deduce from above that the respective opportunity costs are as follows:

In the case of beef, Singapore sacrifices 2 units of electronics for every unit produced, whereas USA sacrifices 0.5 units of electronics.

Therefore USA has a more favourable opportunity cost related to producing beef (i.e. comparative advantage in producing beef).

On the other hand, in the case of electronics, Singapore sacrifices 0.5 units of beef for every unit produced, whereas USA sacrifices 2 units of beef.

Therefore Singapore has a more favourable opportunity cost related to producing electronics (i.e. comparative advantage in producing electronics).

Global output can be maximised by having each country specialise in the production of the good that they have comparative advantage in.

In the best case scenario, complete specialisation takes place (i.e. USA produces only beef, and Singapore produces only electronics), to take full advantage of the comparative advantages.

Both countries can then trade on terms that increase their consumption possibilities as compared to when they weren’t trading.

Determining the terms of trade.

A graph showing the consumption possibilities between the trading partners may also be drawn to intuit the comparative advantages:

In the above graph, the blue and green lines represent the consumption possibilities for Singapore and USA respectively before trade.

Let’s consider the case of complete specialisation (i.e. Singapore produces only electronics and USA produces only beef):

Since no country would engage in a trade that worsens its consumption possibilities, if both countries specialise completely, on the graph, trade would take place only if the consumption possibility pivots on either the x or y-intercept towards the right.

This allows for expansion of consumption possibilities, which is the desired outcome.

When countries trade, the ratio at which goods are traded for is referred to as the Terms of Trade.

Taken together, the terms of trade agreed between both countries can only be such that the new respective consumption possibilities for each country must be parallel and pivoted on either the x or y-axis to the right (i.e. both red lines on the graph).

In summary, the terms of trade must therefore lie between the opportunity costs of bother countries before trade (i.e. from the graph above, the gradient of the new consumption possibility must lie between the original consumption possibilities without trade).

Therefore in this example, both USA and Singapore will find trade mutually beneficial as long as 1 beef is traded for x electronic, where 0.5 < x < 2.

** Update: As of 10 July 2021, additional explanation to the graph and related content has been given here. Read that for further clarification. **

How do we know that comparative advantage is attractive to both countries?

Rationally, both countries would trade with each other if they mutually benefit from trade.

In the context of this example, this will mean both Singapore and USA consuming more beef and electronics at the same time.

But we have a problem.

Complete specialisation may be good from a global perspective since it maximises the global output for both goods.

But what about from the individual countries’ perspective?

Let’s try to make Singapore better off, and see if USA is better off with trade too. For convenience, let’s assume that the terms of trade = 1 beef :1 electronic (i.e. 1-to-1 exchange for both goods).

The minimum trade volume required to make Singapore better off conclusively, is to trade for 10 units of beef (which was the previous consumption point before trade):

Unfortunately, as you can see, it is difficult to conclude that USA is now better off, since the consumption of electronics had dropped from 100 to 10, based on the original pre-trade production figures below:

Let’s now try the maximum trade volume required to make Singapore better off conclusively, 20 units of beef (beyond which, the level of electronics would dip below the consumption point without trade):

Unfortunately the same problem in USA occurs too, since the consumption of electronics had dropped from 100 to 20 after trade!

Fortunately we have a solution.

Fundamentally, the issue lies with the fact that the USA is a much bigger country, and complete specialisation, but trading with a very small country like Singapore, will usually result in unacceptable constraints for the good to be traded for (i.e. electronics).

In fact, a solution can be found if the USA does not completely specialise.

Let’s try an example where the USA produces 90 units of electronics (“sacrificing” 180 units of beef in the process), while Singapore specialises completely. The production figures after specialisation (before trade) are then:

Let’s assume once again that the terms of trade = 1 beef :1 electronic, and Singapore imports 15 units of beef from USA. The consumption figures after trade would then be:

When we compare against the original consumption figures before trade as below, we can now conclude convincingly that both countries are indeed better off with trade as the consumption for both goods in both countries have increased. Voila!

So if you have understood this article well, there should no longer be any trouble proving that comparative advantage can trump even absolute disadvantage for the trading country.

As practice, you may try the same logical exercise using other figures too.

Lend your support!

I hope that you have enjoyed reading this article of mine. I am giving my time to sharing my knowledge and every bit of support means a lot to me! Do drop me a comment or share this article on social media with your friends.

To find out more about my services as a JC Economics tutor, visit my website here.

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