## Wednesday, April 10, 2013

### A Numeric Example Of The Loss From Trade

 Ratio of the Value of Capital to Labor

This post summarizes a numeric example in which at least one country is unambiguously worse off under free trade. This example illustrates the model I developed in a draft paper. The example in this post differs from the one in my paper; interest rates of concern here are more reasonable values.

The model is of two small open economies facing identical technologies for producing two consumer goods. The model assumptions are:

1. Two countries, A and B, can produce the same two commodities, wine and silk, for consumption.
2. The entrepreneurs in each country know the given flow-input, point-output technology (Table 1). Wine and silk each require two years of labor input per unit output. For example, the grapes for a unit of wine require 10 person-years of unassisted labor to be expended in the first year. One hundred eighty eight person-years of labor work up these grapes into wine produced for consumption at the end of the second year.
3. Each country has a given endowment of labor, the only non-produced factor of production in each country. The labor force is fully employed in each country.
4. Only commodities produced for consumption can be traded internationally. Laborers neither immigrate nor emigrate. Capital cannot be traded internationally.
5. Wine and silk are produced with different factor-intensities, silk being more capital-intensive and wine being more labor-intensive. No factor-intensity reversals exist.
6. All consumers, in all countries, have identical homothetic utility functions.
7. Perfect competition obtains in all markets; transport costs are negligible; and free trade exists in all commodities produced for consumption, unless otherwise specified.

These are textbook assumptions. The numeric example proves mainstream textbooks are simply incorrect, since the opposite answer is obtained.

 Country A Country B Wine Production l1,A = 10 person-yrs per unit wine l1,B = 10 person-yrs per unit wine l2,A = 188 person-yrs per unit wine l2,B = 188 person-yrs per unit wine Silk Production l3,A = 100 person-yrs per unit silk l3,B = 100 person-yrs per unit silk l4,A = 89 person-yrs per unit silk l4,B = 89 person-yrs per unit silk Endowments lTotal,A = 4,158 person-years lTotal,B = 3,969 person-years

The firms in both countries face given prices of wine and silk on the international market, as shown in Table 2. The domestic interest rate and the corresponding wage vary between the two countries. As shown in my paper, one can use this price system to determine which commodity, if any, firms in each country would find it most profitable to specialize in the production of. If the interest rate were zero, each country would attempt to specialize in the producing silk. For the price of silk to be a switching price, where firms would find it profitable to specialize in the production of both wine and silk, the interest rate must be 10% for the example. For the interest rates shown, country A specializes in the production of wine, and country B specializes in the production of silk.

 Country A Country B Price of Silk: p = 1 units wine per unit silk Interest Rate: rA = 20% rB = 5% Wage: wA = (1/200) units wine per person-yr wB = (1/194) units wine per person-yr

Given the technology, endowments, an equilibrium price system, and tastes, one can calculate how much wine and silk will be produced and consumed in each country, both when neither country can trade consumer goods on international markets and when both can. Table 3 shows the resulting patterns of consumption among stationary states in the two countries. The consumers in country A are unambiguously worse off in a stationary state with specialization and free trade.

 Autarky Specialization Wine Consumption Country A 10 1/2 Units wine 10 1/2 Units wine Country B 10 1/44 Units wine 10 1/2 Units wine Total 20 23/44 Units wine 22 Units wine Silk Consumption Country A 11 Units silk 10 1/2 Units silk Country B 10 1/2 Units silk 10 1/2 Units silk Total 21 1/2 Units silk 22 Units silk

Figure 1, constructed for the example, shows that the endowment of capital cannot be taken as a parameter in the illustrated model. Because of price Wicksell effects, the quantity of capital varies with the interest rate, even for a given pattern of specialization. Yet confused textbook writers often present the Heckscher-Ohlin-Samuelson model in a two-country, two-commodity, two-factor framework, with the factors of production incorrectly labeled as "labor" and "capital".

So much for the orthodox theory of free trade. Neo-Ricardians proved, more than a third of century ago, that the neoclassical theory of international trade is defective in other ways, too.