Comparative Advantage

An important concept in economics is comparative advantage. It helps to illustrate the importance of trade between countries. Though one country may produce a number of goods more efficiently and at a lower cost than another, it is beneficial to trade if the other country has a comparative advantage.

Imagine that countries A and B both produce tractors and wheat. However, the number of hours needed to produce them is different in both countries. For one tractor, Country A needs 12 hours and Country B needs 4. For one tonne of wheat, Country A needs 4 hours and Country B needs 2. Here is a chart to summarize:

Country A tractor- 12 hours wheat- 4 hours
Country B tractor- 4 hours wheat- 2 hours

By comparing these numbers, it is clear that Country B can produce both tractors and wheat in less time than Country A. In other words, Country B is more efficient in the production of these goods and can produce both at a lower cost. It may thus seem that it is unnecessary for Country B to trade these goods with Country A.

However, trade is beneficial because the ratios spent on the production of the two goods are different in the two countries. If we compare opportunity cost, we notice that it is beneficial for both to specialize in the good which they produce most efficiently.

What does Country A give up if it produces a tractor? For every tractor that Country A produces, it gives up the opportunity to produce 3 tonnes of wheat.

What does Country B give up if it produces a tractor? For every tractor that Country B produces, it gives up the opportunity to produce 2 tonnes of wheat.

Likewise, we can also analyze what each country gives up in tractor production to produce one tonne of wheat. What does Country A give up if it produces one tonne of wheat? It gives up the opportunity to produce 1/3 of a tractor.

What does Country B give up if it produces one tonne of wheat? It gives up the opportunity to produce 1/2 a tractor.

It is clear that when the two countries produce tractors, Country A gives up more in wheat production. However, when the two countries produce wheat, Country B gives up more in tractor production. It is clear that trade can benefit both countries. Country A should specialize in wheat production and Country B should specialize in tractor production.

Though Country A can produce both tractors and wheat at a lower cost than Country B, it is beneficial for the two countries to trade with one another. Country A has a tractor-wheat ratio of 3:1 but Country B has a tractor-wheat ratio of 2:1. Viewed in a different light, Country A has a wheat-tractor ration of 1/3 and Country B has a wheat-tractor ratio of 1/2.

Country A can focus on the good which it produces most efficiently, wheat, and trade it for tractors from Country B. Country B can focus on the good which it produces most efficiently, tractors, and trade them for wheat from Country A. As a result, both countries benefit.

Irish Numbers

Irish is an Indo-European language of the Celtic language family. Though it is an Indo-European language, it is nevertheless quite different from languages such as English and French. To demonstrate, here are the numbers from one to ten:

1) a haon
2) a dó
3) a trí
4) a ceathair
5) a cúig
6) a sé
7) a seacht
8) a hocht
9) a naoi
10)a deich

All of these numbers are written as two words. The number one has the "o" and "n" of English. The number two looks similar. It has a "d" instead of the "t" of English. The number three also looks similar to English. The number four does not look similar to the number four in English, but looks a little like the French number "quatre." The number five does not look similar to English but shares some similarity with the French number "cinq." The numbers six and seven both start with an "s", the same as English. The number eight also ends with a "t" and actually looks closer to the French word for eight which is "huit." The numbers nine and ten do not look so similar to English but nine also starts with a nasal and ten has a "d" instead of a "t" as in English.

Most of the Irish numbers from one to ten are not so similar to those of English, but a few, two and three, share many similarities. In a number of cases such as four and eight, the Irish numbers are actually more similar to those of French than those of English. From an analysis of the Irish numbers, one can see that Irish is an Indo-European language, but not a language that is very similar to English. For this reason, it is a Celtic language and not a closely-related Germanic language such as German, Dutch and Danish.

Adjective Order in English

Attributive adjectives usually precede nouns in a specific order. English speakers know that "new wooden table" is acceptable but "wooden new table" is not. They also know that "big red hat" sounds correct but "red big hat" does not. Though they may not be familiar with the rule for adjective order in English, they know which order sounds best on the basis of intuition.

English adjectives usually precede nouns in the following order: opinion, size, age, shape, colour, origin, material and purpose. However, speakers usually do not use too many adjectives in a phrase because this can be difficult to process. Opinion adjectives such as "beautiful" and "exciting" precede factual adjectives.

Here are examples of adjective phrases with different kinds of adjectives:

1. I bought a nice black silk tie.
2. He has a beautiful new red sports car.
3. You must try these delicious dark Belgian chocolates.
4. They have a comfortable long brown leather sofa.
5. She has gorgeous long curly black hair.

This adjective order applies to adjectives which precede a noun. If they follow, the adjective order is more flexible. It is also possible to use a relative clause such as "I bought a nice silk tie which is black." Sentence 3 uses a different adjective order when the adjectives follow the noun: "These Belgian chocolates are dark and delicious." Here the adjective "dark" precedes "delicious." Adjective order is relatively fixed for attributive adjectives but rather flexible for predicate ones.

Quick Loss

I played a game of speed chess which only lasted 12 moves. Fortunately, I usually do not lose so quickly. My opponent was Ceres Macaraeg from the Phillipines who played black. Here are the moves of the game along with my commentary.

1. e4 e5
2. f4 Nc6

Black usually plays fxe or d6 here.

3. Nf3 exf
4. d4 d5
5. e5 Bg4
6. h3 Bxf3

A better move for me is Nd2. The problem with my move is that now my kingside is weak and the black queen can check on h4.

7. gxf Qh4+
8. Ke2 Nge7

All of my pieces are on the back rank. Black is clearly better.

9. Qd2 Nf5

I want to force an exchange of queens. Black now threatens Ng3+, Ncxd4+ and Nfxd4+.

10. Qxf4 Nxd4+

11. Kd3 Qf2

Black plays aggressively and now threatens Qxc2#. I should play Nd2.

12. Na3 Bxa3

Black removes my defender of c2 and I resign.

I lose quickly because my sixth move leads to the weakening of my kingside and a check by the black queen on h4 which exposes my king. The final nail in the coffin is my twelfth move. My knight fails to protect my c2 square after black captures it with his bishop. My exposed king and lack of development result in my quick downfall.

Powerful Bishops

I recently won a game of speed chess with a pair of powerful bishops. My opponent was Asmadhu of the USA who played white. Here are the moves of the game along with my commentary:

1. e4 c5
2. c3 d6

White's second move is unusual.

3. d4 cxd
4. cxd Nc6

White has a powerful pawn centre but no piece development.

5. d5 Ne5
6. f4 Nd7
7. Nf3 e6
8. dxe fxe
9. Nc3 Ngf6
10. Bd3 Be7
11. 0-0 0-0
12. h3 b6
13. e5 dxe

White plays aggressively.

14.fxe Nd5

White has an advanced pawn on the e-file but it is isolated.

15. Qc2 g6
16. Nd4 Rxf1+
17. Kxf1 Qf8+
18. Kg1 Qg7

Here I should play Nxe5.

19. Nxe6 Qxe5
20. Nxd5 Qxe6

My queen can capture either of the white knights but I capture on e6 because I want to play Qe1+ on my next move. I expect white to play Nc7 on his next move.

21. Nc7 Qxe1+
22. Kh2 Bd6+

My dark-squared bishop now controls the b8-h2 diagonal.

23. g3

White blocks the check and then resigns. He sees that I can play Qxg3+. Then white must play Kh1. On my following move I activate my light-squared bishop with b7+. This gives my light-squared bishop control of the b7-h1 diagonal. My powerful bishops dominate the board. In reply black must play Qg2 and I then play Qxg2#.

In this game my bishops turn the game in my favour. White also has two bishops on the board but they are not nearly as dominant as mine. This game illustrates the power of the bishop pair.

Forever

Lucy Maud Montgomery is one of Canada's most famous writers. She wrote the novel "Anne of Green Gables." However, she also wrote poems. One is the poem "Forever" which I wish to share with you.

Forever

I

With you I shall ever be;
Over land and sea
My thoughts will companion you;
With yours shall my laughter chime,
And my step keep time
In the dusk and dew
With yours in blithesome rhyme;
In all of your joy shall I rejoice,
On my lips your sorrow shall find a voice,
And when your tears in bitterness fall
Mine shall mingle with them all;
With you in waking and dream I shall be,
In the place of shadow and memory,
Under young springtime moons,
And on harvest noons,
And when the stars are withdrawn
From the white pathway of the dawn.

II

O, my friend, nothing shall ever part
My soul from yours, yours from my heart!
I am yours and you mine, in silence and in speech,
Death will only seal us each to each.
Through the darkness we shall fare with fearless jest,
Starward we shall go on a joyous new quest;
There be many worlds, as we shall prove,
Many suns and systems, but only one love!

This poem is full of imagery such as stars, moons, dusk, dew, land and sea. It also has alliteration in dusk and dew, suns and systems and silence and speech. "Forever" is my favourite poem by Lucy Maud Montgomery.

Phonological Rules

Though phonological rules can be written in prose, they can also be written in rule notation. The use of rule notation is often more concise than the use of sentences. I will provide a few examples to illustrate.

In English and many other languages, a vowel is nasalized when it is followed by a nasal in the same syllable. This is the case with words such as "sand" and "camping." This rule can be expressed with the following rule notation:

V ---> [+nasal]/_ [+nasal]$

This rule states that a vowel is nasalized in the environment before a nasal in the same syllable.

Another rule of English is the nasal assimilation rule. This states that an alveolar nasal becomes a velar nasal before a velar plosive. This is the case with words such as "ink" and "singer." Here is the rule in rule notation:

[+alveolar][+nasal] --> [+velar]/_ [+velar][-continuant]

This rule states that an alveolar nasal becomes a velar nasal in the environment before a velar plosive.

The vowel lengthening rule of English is also easy to express in rule notation. This rule states that a word-final vowel becomes long as in "see" and "yellow." This is the rule in rule notation:

V --> [+long]/_#

This rule states that a vowel becomes long in the environment word-final.

English also has a rule which deletes laterals before bilabial nasals. This is the case in words such as "calm," "palm" and "salmon." This is not true in all cases. The word "helmet" does not follow this rule, but nevertheless it applies in many cases. This can thus be called a variable rule as opposed to a categorical rule. In rule notation, the rule can be expressed as follows:

[+lateral] --> 0/ _ [+bilabial][+nasal]

This rule states that a lateral is deleted before a bilabial nasal.

Aspiration is another well-known rule in English. This states that a voiceless plosive is aspirated before a stressed vowel. This is the case in words such as "take," "party," "cold," "please," "prince" and "appear." Here is the rule in rule notation:

[-voice][-sonorant][-continuant]--> [+SG]/ _ ([+sonorant])([-nasal])V [+stress]

This rule states that a voiceless plosive is aspirated in the environment before an optional liquid or glide and a stressed vowel.

Rule notation is common in phonology. It is used as an alternative to prose in the expression of phonological rules. The examples demonstate the use of rule notation to express common phonological rules of English.