Technological di¤erences and trade equilibrium:
                                                   Ricardian Theory of Trade
                                                         Karen Helene Ulltveit-Moe
                                                                    Fall 2010
                           Contents
                           1 Ricardo’s model (1817)                                                                   2
                               1.1  Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     2
                               1.2  Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    3
                                    1.2.1   Production possibility frontier . . . . . . . . . . . . . . . . . . .     3
                               1.3  Autarky equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . .       4
                                    1.3.1   Equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . .      4
                                    1.3.2   Solving the autarky equilibrium . . . . . . . . . . . . . . . . . .       5
                               1.4  Trade Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       6
                                    1.4.1   Solving the trade equilibrium . . . . . . . . . . . . . . . . . . .       6
                               1.5  The gains from trade . . . . . . . . . . . . . . . . . . . . . . . . . . . .      9
                               1.6  Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   11
                           2 Ricardian model with a continuum of goods                                              12
                               2.1  Characteristics of the model . . . . . . . . . . . . . . . . . . . . . . . .     12
                                    2.1.1   Technology and Production . . . . . . . . . . . . . . . . . . . .        12
                                    2.1.2   Relative good prices . . . . . . . . . . . . . . . . . . . . . . . .     13
                                    2.1.3   Preferences and demand . . . . . . . . . . . . . . . . . . . . . .       13
                               2.2  Trade equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    14
                               2.3  Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   16
                                    2.3.1   The e¤ect of an increase in relative size L =L       . . . . . . . . .   16
                                                                                          F    H
                                    2.3.2   The e¤ect of technological progress . . . . . . . . . . . . . . . .      18
                                                                        1
                                         1 Ricardo’s model (1817)
                                               Ricardo’s classic model of international trade attributes trade to di¤erences in
                                                  technogoly across countries.
                                               Di¤erences in technology give rise to di¤erences in relative costs, and are a
                                                  source of comparative advantage.
                                               These technological di¤erences are re‡ected in di¤erences in the productivity of
                                                  labor. This model can be used also to explain wage disparities across countries.
                                              Assumptions of the model
                                               Labor is the only factor of production.
                                               Only two goods (say Wine and Cloth) are produced.
                                               The supply of labor is …xed in each country.
                                               The productivity of labor in each good is …xed.
                                               Perfect competition prevails in all markets.
                                         1.1       Preferences
                                         Suppose that preferences in each country (of the representative consumer ) are of
                                         Cobb Douglas type. Consumer will choose consumption to maximize
                                                                                                       I
                                                                                                     Xlogc
                                                                                                              i        i
                                                                                                      i=1
                                         subject to the budget constraint
                                                                                                    I
                                                                                                  Xpc w L
                                                                                                          i i        n n
                                                                                                  i=1
                                         where p is the price of good i, w is the wage in country n, and L the country size.
                                                     i                                         n                                                      n
                                         Cobb Douglas preference implies that expenditure of good i is a constant share i of
                                         income, ie
                                                                                                  p c =  w L .
                                                                                                    i i         i   n n
                                              For simplicity condider two goods (ie: I = 2) C and W and two countries (n=1,2)
                                         home H and foreign F.
                                                                                                              2
                         1.2   Technologies
                             Assume constant return to scale technologies in the production of both goods.
                             With only one factor of production, technology can be described in terms of the
                               number of workers required to produce one unit of commodity i in country n
                                   i
                               as a .
                                   n
                                                        i
                             Labour productivity: 1=a
                                                        n
                             We say that country H has absolute advantage in producing C if
                                                                   C     C
                                                                 a