David Ricardo points out the Ricardian Model in 1817. Different countries had differences in productivity and technology. Hence, those differences would cause comparative advantage trade. There are two mainly points of Ricardian Model; firstly, the different rates of labor productivity between different countries had important position in international trade. Secondly, the model of trade is dependent on comparative advantage, not absolute advantage. On the other words, According to Evans, H. D (1989), comparing two countries, a country had absolute advantage in the production of two goods, and the other on was in absolute inferiority. The assumption is: the two goods had different productivity in both countries (one goods productivity is more efficiency than the other one in a country). The advantage country got comparative advantage in one advantage good, and inferiority country got comparative advantage in one disadvantage good. Both countries produce their comparative advantage goods, moreover, both countries export the comparative advantage good and import comparative disadvantage good, then both countries could got benefits from this international trade. This is the principle of Ricardian comparative advantage trade theory.

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As lecture notes point out and Porter,M.E (1998) concluded, the Ricardian Comparative advantage trade theory is based on the assumptions followed: 1, there are only two countries, A and B. 2, both countries are only produced two goods. 3, when the goods were producing, there are different technology between two countries, A and B. Hence the different degrees of technology level affect different productivity and capital. 4, this model only got the goods to goods trade assumption. There is no complicate trading. (Both goods got same price, however the cost of production was not equal). 5, labor market supply was fixed. 6, labour can mobile inside the country, however, is not mobile across countries. 7, in countries, goods and markets are perfect competition. 8, there is no tariff and transportation cost. 9, productivity of labor is fixed. (Means the degree of technology would not increase during trading.)
The theory generally assumes that the relative supplies of these two particular commodities are based on their relative productivity and technology. Hence, every country got varies productivity or technology; the endowments were the factor of their relative the productivity. This theory presented two countries are endowed with different level or degree of the production factors, and the naturally determined endowments, country would follow the endowments to trade the comparative advantage goods to the other one. These affect the two countries international trade more efficient and decrease the cost of capital for both countries. Moreover, with constant productivity, both countries could benefit from the free international trade even one country is in absolute disadvantage. Takumi Naito (2012) concluded the Ricardian model of trade and growth. He concluded from the assumption and gets one results: if two countries got larger comparative advantage, the benefit for both countries are getting huger. We can easily contact the relationship between advance country and developing country. With the simple example, United Kingdom and India trade with the grains and textile during the law of comparative advantage coming out. Hence, the textile production in UK requires less labour hours required in the grains producing: UK got the comparative in producing cheese. Same as India, India has comparative advantage producing grains. Therefore, there are gain from international trade if UK product the textile and India product grains. The Ricardian Model really proved UK free international trade in grains.
Under those assumptions, Ricardian model ignores many product factors besides labor. David Ricardo explained the reason of international trade under different efficient of labor production. There are huge advantages for developing the international trade with this classic model. Firstly, this model comes from the law of comparative advantage, and help the United Kingdom got the solution to the grain crisis from 1815. Secondly, although Ricardian Model only showed its pedagogical importance, the classical emphasis on different productivity and the cost of labor has been utilized by the neoclassical focus on factor endowments. (Stephen S.G, 2000) thirdly, older tests, such as MacDougall, 1951 and Stern, 1962 were highly successful. Hence, it is valuable for us to know how this basic pedagogical model performs empirically with the large recent data.
The empirical Validity of the Model and the Relevance of the Empirical Work
In these parts, this paper would show the strengths and weaknesses of Ricardian Model, from the points of empirical. The core meaning as mention before: follow the law of comparative advantage; the country would to do specialized production for only one goods which is comparative advantage good. We cannot reject this theory points with the literature evidence; however, we could prove some empirical evidence to discuss the advantage and disadvantage for the international trade.
Basic Ricardian Model
The Ricardian Model focus on the technology and labour productivity. As the comparative advantage theory mentioned, the labour costs also is the important elements of this model. Now, based on the research of Stephen S.G (2000) we represent ‘Aa’ to the labor requirements of every single unit in country a, and ‘Qa’ is the value-added in country a. represent the ‘La’ as the labour employment in country a:

We can see easily, the Aa is unit labor requirements, that means the value of Aa get higher, the productivity of country a getting lower. Hence, the main points of ricardian model are increasing total productivity of whole country, the Aa needed to lower. Coming from the assumption of Ricardian Model, the labour is fixed and not crosses to the other country. Therefore, the La is fixed, we keep the La constant. So, the productivity is dependent on the totally value-added Qa. Hence, we can conclude: Ricardian Model would success, there would be a huge enough different productivity between two countries. Or there would not gain from the free trade.
We could also use b to represent the country b. hence, Ab, Lb, and Qb are all represent same means in country b. as the labour cost we can defined as the Ca and Cb. Then, Wa and Wb represent as the wage of employees in countries a and b. we assume the exchange rate between a and b is 1:1. We use ‘Rab’ as the rate of Ca and Cb. The function can be showed:

We can see, if Rab smaller than 1, that means country a cost lower than country b, country a got comparative advantage good that should export goods. If Rab bigger than 1, that means country a should import goods. (All the functions are all represent one same good between two countries) From this function, we can see one possible: Rab is equal to 1. Hence, there is no comparative advantage between country a and b (the absolute advantage country got same rate in both goods with the absolute disadvantage country), which means, there is equal disadvantage and equal advantage. This is one of the disadvantages of Ricartian Model.
Empirical work of Ricardian Model
With the basic Ricardian Model, we could learn from the empirical studies to find out the strengths and weaknesses. First of all, this paper would discuss the empirical theory from MacDougall (1951). This case study used the ratio of US exports to UK exports. The dependent variable can be presented as both exports. And he used the productivity as the main independent variable. He used the total exports between US and UK. He collected 25 industries from UK and US in 1937. With his findings, he set the hypothesis: the wage rate is the same level as the labour productivity between US and UK. He used the 1937 data; those data showed US wage rate is double to UK wage rate. And we can follow the function in top; there is same reason that US got the comparative advantage in exports. Then he used the simple measures, he found the results that 20 of the 25 products follow the ratio. There are bigger than one. Hence the results are support the Ricardian Model.
Secondly, the case study of Stern (1962) same as MacDougall, they both compare the totally exports between US and UK during different periods. And both used the productivity as the main independent variable. The results is 33 of the 39 sectors follow this ratios, as same as results of MacDougall could support for Ricardian Model. Thirdly, case study of Balassa (1963) points out the bilateral trade from UK and US to the third markets. Different with Stern and MacDougall, he relative both labor cost and productivity as explanatory variable. With the bilateral trade, there are three characteristics: speed fast, huger scope and sustainable sequencing. With the Song (1996) points out, there are some problem between the Balassa studies, which is the transportation cost and the tariffs. Under the developing countries, there are huge different between the tariffs and transportation cost. The only way is to fix the free trade strategy to bilateral trade. tariffs and transportation cost are against the assumption of Ricardian Model. With the bilateral trade, Balassa chose the data from 1950 to post 1970. As the results, this is also can prove the prediction of Ricardian Model. Although the bilateral trade is following the comparative advantage, this paper would use the overall export ratio of Stephen (2000) as in MacDougall and Stern. The radio is exports to third markets. Stehen choose 39 manufacturing sectors from 1970 to 1990. He got the database from OECD Structural Analysis Industrial (STAN) and Bilateral Trade (BT). Figure one and two are showed. He collected the purchasing-power-parity (PPPs) exchange rate. There are three PPPs shows on second Figure, frist is common PPPs, Second is sector-specific final expenditure PPPs from ICP, and last is sector-specific manufacturing PPPs from ICOP projects. (Stephen S.G ,2000).