page_title: Comparative advantage
section_title: Ricardian model
hierarchical_section_title: Comparative advantage / Classical theory and David Ricardo's formulation / Ricardian model
context_page_description: The law of comparative advantage describes how, under free trade, an agent will produce more of and consume less of a good for which they have a comparative advantage.
  In an economic model, agents have a comparative advantage over others in producing a particular good if they can produce that good at a lower relative opportunity cost or autarky price, i.e. at a lower relative marginal cost prior to trade. Comparative advantage describes the economic reality of the work gains from trade for individuals, firms, or nations, which arise from differences in their factor endowments or technological progress.
  David Ricardo developed the classical theory of comparative advantage in 1817 to explain why countries engage in international trade even when one country's workers are more efficient at producing every single good than workers in other countries. He demonstrated that if two countries capable of producing two commodities engage in the free market, then each country will increase its overall consumption by exporting the good for which it has a comparative advantage while importing the other good, provided that there exist differences in labor productivity between both countries.
context_section_description: 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. The earliest test of the Ricardian model was performed by G.D.A MacDougall, which was published in Economic Journal of 1951 and 1952.
   In the Ricardian model, trade patterns depend on productivity differences.
  The following is a typical modern interpretation of the classical Ricardian model. 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 mobile domestically but not internationally; there may be migration between sectors but not between countries. We denote the labor force in Home by , the amount of labor required to produce one unit of wine in Home by , and the amount of labor required to produce one unit of cloth in Home by . The total amount of wine and cloth produced in Home are  and  respectively. We denote the same variables for Foreign by appending a prime. For instance,  is the amount of labor needed to produce a unit of wine in Foreign.
  We don't know if Home is more productive than Foreign in making cloth. That is, we don't know that . Similarly, we don't know if Home has an absolute advantage in wine. However, we will assume that Home is more relatively productive in cloth than Foreign:
  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:
  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  in Home and  in Foreign. With free trade, the price of cloth or wine in either country is the world price  or.
  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  will be determined uniquely by the intersection of world relative demand  and world relative supply  curves.
  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 , then Foreign specializes in wine, for the wage  in the wine sector is greater than the wage  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 , then both Home and Foreign specialize in wine, for similar reasons as above, and so the quantity of cloth supplied is zero.
  If , then Home specializes in cloth whereas Foreign specializes in wine. The quantity of cloth supplied is given by the ratio  of the world production of cloth to the world production of wine.
  If , 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 , then Home specializes in cloth while Foreign workers are indifferent between sectors. Again, the relative quantity of cloth supplied can take any value.
  As long as the relative demand is finite, the relative price is always bounded by the inequality
  In autarky, Home faces a production constraint of the form
  from which it follows that Home's cloth consumption at the production possibilities frontier is
  .
  With free trade, H
caption: The demand for cloth relative to wine decreases with the relative price of cloth in terms of wine; the supply 
    
      
        
          R
          S
        
      
      {\displaystyle RS}
    
   of cloth relative to wine increases with relative price. Two relative demand curves 
    
      
        
          R
          
            D
            
              1
            
          
        
      
      {\displaystyle RD_{1}}
    
   and 
    
      
        
          R
          
            D
            
              2
            
          
        
      
      {\displaystyle RD_{2}}
    
   are drawn for illustrative purposes.