Editing Comparative advantage (section)

==Classical theory and David Ricardo's formulation==
{{More citations needed|section|date=July 2021}}
[[Adam Smith]] first alluded to the concept of ''absolute advantage'' as the basis for international trade in 1776, in ''[[The Wealth of Nations]]'':
{{quote|text=If a foreign country can supply us with a commodity cheaper than we ourselves can make it, better buy it off them with some part of the produce of our own industry employed in a way in which we have some advantage. The general industry of the country, being always in proportion to the capital which employs it, will not thereby be diminished [...] but only left to find out the way in which it can be employed with the greatest advantage.<ref>{{cite book|last=Smith|first=Adam|author-link=Adam Smith|title=An Inquiry into the Nature and Causes of the Wealth of Nations|title-link=The Wealth of Nations|date=1776}}</ref>}}

Writing two decades after Smith in 1808, [[Robert Torrens (economist)|Robert Torrens]] articulated a preliminary definition of comparative advantage as the loss from the closing of trade:
{{quote|text=[I]f I wish to know the extent of the advantage, which arises to England, from her giving France a hundred pounds of [[broadcloth]], in exchange for a hundred pounds of lace, I take the quantity of lace which she has acquired by this transaction, and compare it with the quantity which she might, at the same expense of labour and capital, have acquired by manufacturing it at home. The lace that remains, beyond what the labour and capital employed on the cloth, might have fabricated at home, is the amount of the advantage which England derives from the exchange.<ref>{{cite book|last=Torrens|first=Robert|author-link=Robert Torrens (economist)|title=The Economists Refuted and Other Early Economic Writings|year=1808|publisher=Kelley|location=New York|edition=1984|page=37}}</ref>}} In 1814 the anonymously published pamphlet ''Considerations on the Importation of Foreign Corn'' featured the earliest recorded formulation of the concept of comparative advantage.<ref name="ThompsonAllington2010">{{cite book | editor1 = Noel W. Thompson | editor2 = Nigel F. B. Allington | date = 13 December 2010 | title = English, Irish and Subversives Among the Dismal Scientists | publisher = Emerald Group Publishing | page = 101 | isbn = 978-0-85724-062-0 | url = https://books.google.com/books?id=6YPu0n04GfIC&pg=PA101}}</ref><ref>{{cite book |last=Maneschi |first=Andrea | editor1 = Shigeyoshi Senga | editor2 = Masatomi Fujimoto | editor3 = Taichi Tabuchi | date = 18 May 2017 | title = Ricardo and International Trade | publisher = Taylor & Francis | pages = 33 |chapter=Chapter 3: David Ricardo's Trade Theory Anticipations and later developments | isbn = 978-1-351-68616-7 | chapter-url = https://books.google.com/books?id=jTslDwAAQBAJ&pg=PA33}}</ref> Torrens would later publish his work ''External Corn Trade'' in 1815 acknowledging this pamphlet author's priority.<ref name="ThompsonAllington2010" />

[[File:David Ricardo (grey).jpg|upright|thumb|David Ricardo]]
In 1817, [[David Ricardo]] published what has since become known as the theory of comparative advantage in his book ''[[On the Principles of Political Economy and Taxation]]''.<ref>{{cite journal|author=Kalim Siddiqui|title=David Ricardo's Comparative Advantage and Developing Countries: Myth and Reality|journal=International Critical Thought|volume=8|issue=3|url=https://pure.hud.ac.uk/ws/portalfiles/portal/14132571/David_Ricardo_s_Comparative_Trade_Theory.pdf|via=[[University of Huddersfield]]}}</ref>

===Ricardo's example===
[[File:Ricardo example of comparative advantage.svg|thumb|upright=1.3|Graph illustrating Ricardo's example:<br />In case I (diamonds), each country spends 3600 hours to produce a mixture of cloth and wine.<br />In case II (squares), each country specializes in its comparative advantage, resulting in greater total output.]]
In a famous example, Ricardo considers a [[world economy]] consisting of two countries, [[Portugal]] and [[England]], each producing two goods of identical quality. In Portugal, the ''[[A priori and a posteriori|a priori]]'' more efficient country, it is possible to produce [[wine]] and [[cloth]] with less labor than it would take to produce the same quantities in England. However, the relative costs or ranking of cost of producing those two goods differ between the countries.

{| class="wikitable"
|+ Hours of work necessary to produce one unit
|-
! {{diagonal split header|Country|Produce}}
! scope="col" | Cloth
! scope="col" | Wine
! scope="col" | Total
|-
! scope="row" | England
|100||120||220
|-
! scope="row" | Portugal
|90||80||170
|}

In this illustration, England could commit 100 hours of labor to produce one unit of cloth, or produce {{sfrac|5|6}} units of wine. Meanwhile, in comparison, Portugal could commit 100 hours of labor to produce {{sfrac|10|9}} units of cloth, or produce {{sfrac|10|8}} units of wine. Portugal possesses an ''absolute advantage'' in producing both cloth and wine due to more produced per hour (since {{sfrac|10|9}} > 1). If the capital and labour were mobile, both wine and cloth should be made in Portugal, with the capital and labour of England removed there.<ref>{{cite book |last1=Ricardo |first1=David |author1-link=David Ricardo |title=On the Principles of Political Economy and Taxation |date=1817 |publisher=J. Murray |pages=160–162 |quote=It would undoubtedly be advantageous to the capitalists of England, and to the consumers in both countries, that under such circumstances, the wine and the cloth should both be made in Portugal, and therefore that the capital and labour of England employed in making cloth, should be removed to Portugal for that purpose}}</ref> If they were not mobile, as Ricardo believed them to be generally, then England's ''comparative advantage'' (due to lower opportunity cost) in producing cloth means that it has an incentive to produce more of that good which is relatively cheaper for them to produce than the other—assuming they have an advantageous opportunity to trade in the marketplace for the other more difficult to produce good.
{{Stack begin}}
{| class="wikitable"
! {{diagonal split header|Country|Produce}}!!scope="col"|Cloth!!scope="col"|Wine!!scope="col"|Saved
|-
!scope="row"|England
|200||–||20
|-
!scope="row"|Portugal
|–||160||10
|}
{{Stack end}}
In the absence of trade, England requires 220 hours of work to both produce and consume one unit each of cloth and wine while Portugal requires 170 hours of work to produce and consume the same quantities. England is more efficient at producing cloth than wine, and Portugal is more efficient at producing wine than cloth. So, if each country specializes in the good for which it has a comparative advantage, then the global production of both goods increases, for England can spend 220 labor hours to produce 2.2 units of cloth while Portugal can spend 170 hours to produce 2.125 units of wine. Moreover, if both countries specialize in the above manner and England trades a unit of its cloth for {{sfrac|5|6}} to {{sfrac|9|8}} units of Portugal's wine, then both countries can consume at least a unit each of cloth and wine, with 0 to 0.2 units of cloth and 0 to 0.125 units of wine remaining in each respective country to be consumed or exported. Consequently, both England and Portugal can consume more wine and cloth under free trade than in [[autarky]].

===Ricardian model===
The '''Ricardian model''' is a [[general equilibrium]] mathematical model of [[international trade]]. Although the idea of the Ricardian model was first presented in the ''Essay on Profits'' (a single-commodity version) and then in the ''Principles'' (a multi-commodity version) by [[David Ricardo]], the first mathematical Ricardian model was published by [[William Whewell]] in 1833.<ref>{{cite book |title= David Ricardo: Critical Assessments|last= Wood |first= John Cunningham|year= 1991 |publisher= Taylor & Francis |isbn= 9780415063807|page= 312 |url= https://books.google.com/books?id=h5GzUUfTL4sC&q=Ricardian+model&pg=PA312}}</ref> The earliest test of the Ricardian model was performed by [[Donald MacDougall|G. D. A. MacDougall]], which was published in ''[[The Economic Journal]]'' of 1951 and 1952.<ref>{{cite book |title= International Economics: A European Focus|last= Ingham |first= Barbara|year= 2004 |publisher= Pearson Education |isbn= 9780273655077|page= 22 |url= https://books.google.com/books?id=zIaS9R7HUGIC&q=international+economics}}</ref> In the Ricardian model, trade patterns depend on productivity differences.

The following is a typical modern interpretation of the classical Ricardian model.<ref>{{cite book|last1=Krugman|first1=Paul|author1-link=Paul Krugman|last2=Obstfeld|first2=Maurice|author2-link=Maurice Obstfeld|title=International Economics: Theory and Policy|year=1988|publisher=Prentice Hall|location=New York|pages=27–36|edition=2008}}</ref> In the interest of simplicity, it uses notation and definitions, such as opportunity cost, unavailable to Ricardo.

The world economy consists of two countries, Home and Foreign, which produce wine and cloth. Labor, the only factor of production, is [[labor mobility|mobile]] domestically but not internationally; there may be migration between sectors but not between countries. We denote the labor force in Home by <math>\textstyle L</math>, the amount of labor required to produce one unit of wine in Home by <math>\textstyle a_{LW}</math>, and the amount of labor required to produce one unit of cloth in Home by <math>\textstyle a_{LC}</math>. The total amount of wine and cloth produced in Home are <math>Q_W</math> and <math>Q_C</math> respectively. We denote the same variables for Foreign by appending a [[prime (symbol)|prime]]. For instance, <math>\textstyle a'_{LW}</math> is the amount of labor needed to produce a unit of wine in Foreign.

We do not know if Home can produce cloth using fewer hours of work than Foreign. That is, we do not know if <math>a_{LC}<a'_{LC}</math>. Similarly, we do not know if Home can produce wine using fewer hours of work. However, we assume Home is ''relatively'' more productive than Foreign in making in cloth vs. wine:
:<math>a_{LC}/a'_{LC}<a_{LW}/a'_{LW}.</math>

Equivalently, we may assume that Home has a comparative advantage in cloth in the sense that it has a lower opportunity cost for cloth in terms of wine than Foreign:
:<math>a_{LC}/a_{LW}<a'_{LC}/a'_{LW}.</math>

In the absence of trade, the relative price of cloth and wine in each country is determined solely by the relative labor cost of the goods. Hence the relative autarky price of cloth is <math>a_{LC}/a_{LW}</math> in Home and <math>a'_{LC}/a'_{LW}</math> in Foreign. With free trade, the price of cloth or wine in either country is the world price <math>P_C</math> or<math>P_W</math>.

Instead of considering the world demand (or supply) for cloth and wine, we are interested in the world ''relative demand'' (or ''relative supply'') for cloth and wine, which we define as the ratio of the world demand (or supply) for cloth to the world demand (or supply) for wine. In general equilibrium, the world relative price <math>\textstyle P_C/P_W</math> will be determined uniquely by the intersection of world relative demand <math>\textstyle RD</math> and world relative supply <math>\textstyle RS</math> curves.

[[File:World relative supply and demand in the classical Ricardo model of one-factor international trade between two countries.svg|thumb|upright=1.3|The demand for cloth relative to wine decreases with the relative price of cloth in terms of wine; the supply <math>RS</math> of cloth relative to wine increases with relative price. Two relative demand curves <math>RD_1</math> and <math>RD_2</math> are drawn for illustrative purposes.]]
We assume that the relative demand curve reflects substitution effects and is decreasing with respect to relative price. The behavior of the relative supply curve, however, warrants closer study. Recalling our original assumption that Home has a comparative advantage in cloth, we consider five possibilities for the relative quantity of cloth supplied at a given price.

* If <math>\textstyle P_C/P_W = a_{LC}/a_{LW}<a'_{LC}/a'_{LW}</math>, then Foreign specializes in wine, for the wage <math>P'_W/a'_{LW}</math> in the wine sector is greater than the wage <math>P'_C/a'_{LC}</math> in the cloth sector. However, Home workers are indifferent between working in either sector. As a result, the quantity of cloth supplied can take any value.
* If <math>\textstyle P_C/P_W < a_{LC}/a_{LW}<a'_{LC}/a'_{LW}</math>, then both Home and Foreign specialize in wine, for similar reasons as above, and so the quantity of cloth supplied is zero.
* If <math>\textstyle a_{LC}/a_{LW}<P_C/P_W < a'_{LC}/a'_{LW}</math>, then Home specializes in cloth whereas Foreign specializes in wine. The quantity of cloth supplied is given by the ratio <math>\textstyle \frac{L/a_{LC}}{L'/a'_{LW}}</math> of the world production of cloth to the world production of wine.
* If <math>\textstyle a_{LC}/a_{LW}<a'_{LC}/a'_{LW}<P_C/P_W</math>, then both Home and Foreign specialize in cloth. The quantity of cloth supplied tends to infinity as the quantity of wine supplied approaches zero.
* If <math>\textstyle a_{LC}/a_{LW}<a'_{LC}/a'_{LW}=P_C/P_W</math>, then Home specializes in cloth while Foreign workers are indifferent between sectors. Again, the relative quantity of cloth supplied can take any value.

[[File:Consumption possibilities in the classical Ricardo model of one-factor international trade between two countries.svg|thumb|upright=1.3|The blue triangle depicts Home's original production (and consumption) possibilities. By trading, Home can also consume bundles in the pink triangle despite facing the same productions possibility frontier.]]
As long as the relative demand is finite, the relative price is always bounded by the inequality
:<math> a_{LC}/a_{LW}\leq {P_C/P_W}\leq {a'_{LC}/a'_{LW}}.</math>

In autarky, Home faces a [[production–possibility frontier|production constraint]] of the form
:<math> a_{LC}Q_C+a_{LW}Q_W\leq L,</math>
from which it follows that Home's cloth consumption at the production possibilities frontier is
:<math>Q_C=L/a_{LC}-(a_{LW}/a_{LC})Q_W</math>.

With free trade, Home produces cloth exclusively, an amount of which it exports in exchange for wine at the prevailing rate. Thus Home's overall consumption is now subject to the constraint
:<math>a_{LC}Q_C+a_{LC}(P_W/P_C)Q_W\leq L</math>
while its cloth consumption at the ''consumption possibilities'' frontier is given by
:<math>Q_C=L/a_{LC}-(P_W/P_C)Q_W\geq L/a_{LC}-(a_{LW}/a_{LC})Q_W</math>.

A symmetric argument holds for Foreign. Therefore, by trading and specializing in a good for which it has a comparative advantage, each country can expand its consumption possibilities. Consumers can choose from bundles of wine and cloth that they could not have produced themselves in closed economies.

There is another way to prove the theory of comparative advantage, which requires less assumption than the above-detailed proof, and in particular does not require for the hourly wages to be equal in both industries, nor requires any equilibrium between offer and demand on the market.<ref>{{cite book |title= Mathematical methods for Economic analysis|last= L. |first= G.|year= 2021 |url= https://bookdown.org/praxeolab/mathematics-for-economics/chapter1.html}}</ref> Such a proof can be extended to situations with many goods and many countries, non constant returns and more than one factor of production.

=== Terms of trade ===
Terms of trade is the rate at which one good could be traded for another. If both countries specialize in the good for which they have a comparative advantage then trade, the terms of trade for a good (that benefit both entities) will fall between each entities opportunity costs. In the example above one unit of cloth would trade for between <math>\frac 56</math> units of wine and <math>\frac 9 8</math> units of wine.<ref>{{Cite web|url=http://www.reviewecon.com/comparative-advantage.html|title=AP Economics Review: Comparative Advantage, Absolute Advantage, and Terms of Trade|date=2016-09-28|website=www.reviewecon.com/comparative-advantage.html}}</ref>