Agnapostate
Well-Known Member
I've recently completed reading Robin Hahnel's Panic Rules, and one of his appendices contains a simple but sound model indicating that free trade necessarily increases global inequality and deliver's the lion's share of efficiency gains to wealthier nations, as opposed to fair trade, which can eliminate both income inequality and inefficiency. Such insight is especially welcome when advocates of trade liberalization often resort to (mis)quoting Smith and Ricardo and babbling on about comparative advantage.
Hahnel's Models of International Trade
First, suppose that there are two varieties of countries, some in the "North" and some in the "South." We also assume that the international trade markets between Northern and Southern countries are perfectly competitive. (A concession to free market theory.) All countries have 1,000 citizens who must consume one unit of corn annually. There are two methods of corn production. One uses pure labor and the other uses a combination of labor and machines. There is one method of machine construction that requires both labor and machines. These are the technologies:
5 units of labor + 0 machines yields 10 units of corn
2 units of labor + 1 machine yields 10 units of corn
1 unit of labor + 2 machines yields 10 machines
Now, machines function for one year and must be replaced annually. Since machines are created from other machines, a certain number must be placed aside and utilized for the purpose of machine production rather than corn production, which will obviously result in greater long-term efficiency. Northern countries begin with 200 machines, whereas Southern countries begin with only 50 machines.
We will examine three models, a model in which Northern and Southern countries are not permitted to trade with each other, called the autarkic model, and two models in which trade is permitted but to different extents, the free trade and fair trade models. Recall that equality is measured through labor expenditures, as greater labor expenditures function as greater impositions on each respective population.
The Autarkic Model
Due to Northern countries' high surplus of machines, it is clear that making corn through the use of machines and labor will be far more productive than corn production through the sole use of labor. Corn production through the sole use of labor is entirely unnecessary in a Northern country, as a result of their machine supply. Let X(1) be the number of times that corn is produced through the sole use of labor, X(2) be the number of times corn is produced through a combination of machines and labor, and X(3) the number of times machines are produced using other machines. The most efficient production plan for a Northern country would be the following.
A Northern Country's Optimal Production Plan Under Autarky
X(1) = 0 using M(1) = 0 and L(1) = 0 to get 0 C
X(2) = 100 using M(2) = 100 and L(2) = 200 to get 1,000 C
X(3) = 12.5 using M(3) = 25 and L(3) = 12.5 to get 125 M
Such a plan necessitates the following in terms of machinery:
M(1) + M(2) + M(3) = 0 + 100 + 25 = 125 machines
This would replace the 125 machines used in the optimal production plan.
This is the amount of labor that would be necessary:
L(1) + L(2) + L(3) = 0 + 200 +12.5 = 212.5 units of labor
The 1,000 units of corn would thus be acquired. Now, this plan minimizes labor expenditures, but it only uses 125 of the 200 machines available for production purposes. And if trade is prohibited, and this is the most efficient manner of corn production, efficiency cannot be maximized inasmuch as 75 machines lie dormant.
Now, as for Southern countries, their 50 machines are not sufficient to produce 1,000 bushels of corn, especially considering that machines must be replaced. Since they must replace machines, the maximum amount of corn production through machine use must be X(2) = 40, and machine production must be X(3) = 5. But this yields only 400 bushels of corn, a 60% shortage. Hence, Southern countries must also resort to the less efficient method of corn production through the use of pure labor, so X(1) = 60. This would result in this plan:
A Southern Country's Optimal Production Plan Under Autarky
X(1) = 60 using M(1) = 0 and L(1) = 300 to get 600 C
X(2) = 40 using M(2) = 40 and L(2) = 80 to get 400 C
X(3) = 5 using M(3) = 10 and L(3) = 5 to get 50 M
600 C + 400 C thus yields the necessary 1,000 bushels of corn for consumption, and uses this in machine-based production.
M(1) + M(2) + M(3) = 0 + 40 + 10 = 50 machines
Hence, all machines are replaced, and the minimum expenditure of labor involved is this:
L(1) + L(2) + L(3) = 200 + 80 +5 = 385 units of labor.
Again, labor expenditures are the inequalities that must be measured, since both Northern and Southern countries have the same levels of corn consumption. Now, the degree of global inequality as measured through labor expenditures must be defined as the ratio of the number of average work days in Southern countries divided by the ratio of the number of average work days in Northern countries. If Northerners and Southerners have equivalent average labor amounts, the ration will be 1, but the ration and according degree of inequality will rise through greater labor expenditures by Southern workers than Northern workers. Hence, since Southerners work an average of 0.385 units of labor, whereas Northerners work an average of 0.2125 units of labor, the degree of inequality is measured as 0.385/0.2125 = 1.81. Now, the cause of this inequality is clearly different initial access to machine technology. But there is no method of rectifying this inequality since Northern and Southern countries are not permitted to trade with each other.
The Free Trade Model
The free trade model involves opening international trade for exchange of corn and machines and permitting trade conditions to be determined by the law of supply and demand in the international marketplace.
Machines are desired because they allow countries to produce corn more efficiently and easily. Hence, corn is the ultimate goal, and machines function as means to that end, which means that the number of corn bushels anyone would be willing to trade for machines can be calculated thusly: Assume that 17 units of labor existed. Without machines, only labor could be utilized in the process of corn production, which would mean that 34 C could be produced with 17 L. If, however, 10 machines were available, they could be utilized as a more efficient method of corn production, although the ten machines would obviously have to be replaced. 1 unit of labor and two machines is sufficient for this purpose. 16 units of labor and 8 machines are left to produce corn through the machine technology. 16 L and 8 M will produce 80 bushels of corn. Hence, if machines are available, this permits production of 80 - 34 = 46 more units of corn than pure labor, which amounts to 46/10 = 4.6 more units of corn per machine than would have been possible through pure labor.
Now, paying more than 4.6 units of corn for a machine is obviously inadvisable, since any country that did so would end up with less corn than its labor expenditures were worth. However, if machine prices were below 4.6 units of corn, countries would purchase them indefinitely since they would expend less labor per unit of corn by doing so. Hence, the equilibrium price of a machine, P(M), is 4.6 units of corn, and left to pure market forces, machines would sell for 4.6 units of corn. Now, let us examine the process of Northern and Southern countries' optimal production and trade plans under this scheme.
Hahnel's Models of International Trade
First, suppose that there are two varieties of countries, some in the "North" and some in the "South." We also assume that the international trade markets between Northern and Southern countries are perfectly competitive. (A concession to free market theory.) All countries have 1,000 citizens who must consume one unit of corn annually. There are two methods of corn production. One uses pure labor and the other uses a combination of labor and machines. There is one method of machine construction that requires both labor and machines. These are the technologies:
5 units of labor + 0 machines yields 10 units of corn
2 units of labor + 1 machine yields 10 units of corn
1 unit of labor + 2 machines yields 10 machines
Now, machines function for one year and must be replaced annually. Since machines are created from other machines, a certain number must be placed aside and utilized for the purpose of machine production rather than corn production, which will obviously result in greater long-term efficiency. Northern countries begin with 200 machines, whereas Southern countries begin with only 50 machines.
We will examine three models, a model in which Northern and Southern countries are not permitted to trade with each other, called the autarkic model, and two models in which trade is permitted but to different extents, the free trade and fair trade models. Recall that equality is measured through labor expenditures, as greater labor expenditures function as greater impositions on each respective population.
The Autarkic Model
Due to Northern countries' high surplus of machines, it is clear that making corn through the use of machines and labor will be far more productive than corn production through the sole use of labor. Corn production through the sole use of labor is entirely unnecessary in a Northern country, as a result of their machine supply. Let X(1) be the number of times that corn is produced through the sole use of labor, X(2) be the number of times corn is produced through a combination of machines and labor, and X(3) the number of times machines are produced using other machines. The most efficient production plan for a Northern country would be the following.
A Northern Country's Optimal Production Plan Under Autarky
X(1) = 0 using M(1) = 0 and L(1) = 0 to get 0 C
X(2) = 100 using M(2) = 100 and L(2) = 200 to get 1,000 C
X(3) = 12.5 using M(3) = 25 and L(3) = 12.5 to get 125 M
Such a plan necessitates the following in terms of machinery:
M(1) + M(2) + M(3) = 0 + 100 + 25 = 125 machines
This would replace the 125 machines used in the optimal production plan.
This is the amount of labor that would be necessary:
L(1) + L(2) + L(3) = 0 + 200 +12.5 = 212.5 units of labor
The 1,000 units of corn would thus be acquired. Now, this plan minimizes labor expenditures, but it only uses 125 of the 200 machines available for production purposes. And if trade is prohibited, and this is the most efficient manner of corn production, efficiency cannot be maximized inasmuch as 75 machines lie dormant.
Now, as for Southern countries, their 50 machines are not sufficient to produce 1,000 bushels of corn, especially considering that machines must be replaced. Since they must replace machines, the maximum amount of corn production through machine use must be X(2) = 40, and machine production must be X(3) = 5. But this yields only 400 bushels of corn, a 60% shortage. Hence, Southern countries must also resort to the less efficient method of corn production through the use of pure labor, so X(1) = 60. This would result in this plan:
A Southern Country's Optimal Production Plan Under Autarky
X(1) = 60 using M(1) = 0 and L(1) = 300 to get 600 C
X(2) = 40 using M(2) = 40 and L(2) = 80 to get 400 C
X(3) = 5 using M(3) = 10 and L(3) = 5 to get 50 M
600 C + 400 C thus yields the necessary 1,000 bushels of corn for consumption, and uses this in machine-based production.
M(1) + M(2) + M(3) = 0 + 40 + 10 = 50 machines
Hence, all machines are replaced, and the minimum expenditure of labor involved is this:
L(1) + L(2) + L(3) = 200 + 80 +5 = 385 units of labor.
Again, labor expenditures are the inequalities that must be measured, since both Northern and Southern countries have the same levels of corn consumption. Now, the degree of global inequality as measured through labor expenditures must be defined as the ratio of the number of average work days in Southern countries divided by the ratio of the number of average work days in Northern countries. If Northerners and Southerners have equivalent average labor amounts, the ration will be 1, but the ration and according degree of inequality will rise through greater labor expenditures by Southern workers than Northern workers. Hence, since Southerners work an average of 0.385 units of labor, whereas Northerners work an average of 0.2125 units of labor, the degree of inequality is measured as 0.385/0.2125 = 1.81. Now, the cause of this inequality is clearly different initial access to machine technology. But there is no method of rectifying this inequality since Northern and Southern countries are not permitted to trade with each other.
The Free Trade Model
The free trade model involves opening international trade for exchange of corn and machines and permitting trade conditions to be determined by the law of supply and demand in the international marketplace.
Machines are desired because they allow countries to produce corn more efficiently and easily. Hence, corn is the ultimate goal, and machines function as means to that end, which means that the number of corn bushels anyone would be willing to trade for machines can be calculated thusly: Assume that 17 units of labor existed. Without machines, only labor could be utilized in the process of corn production, which would mean that 34 C could be produced with 17 L. If, however, 10 machines were available, they could be utilized as a more efficient method of corn production, although the ten machines would obviously have to be replaced. 1 unit of labor and two machines is sufficient for this purpose. 16 units of labor and 8 machines are left to produce corn through the machine technology. 16 L and 8 M will produce 80 bushels of corn. Hence, if machines are available, this permits production of 80 - 34 = 46 more units of corn than pure labor, which amounts to 46/10 = 4.6 more units of corn per machine than would have been possible through pure labor.
Now, paying more than 4.6 units of corn for a machine is obviously inadvisable, since any country that did so would end up with less corn than its labor expenditures were worth. However, if machine prices were below 4.6 units of corn, countries would purchase them indefinitely since they would expend less labor per unit of corn by doing so. Hence, the equilibrium price of a machine, P(M), is 4.6 units of corn, and left to pure market forces, machines would sell for 4.6 units of corn. Now, let us examine the process of Northern and Southern countries' optimal production and trade plans under this scheme.