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.

Table 1: The Technology
Country ACountry B
Wine Productionl1,A = 10 person-yrs per unit winel1,B = 10 person-yrs per unit wine
l2,A = 188 person-yrs per unit winel2,B = 188 person-yrs per unit wine
Silk Productionl3,A = 100 person-yrs per unit silkl3,B = 100 person-yrs per unit silk
l4,A = 89 person-yrs per unit silkl4,B = 89 person-yrs per unit silk
EndowmentslTotal,A = 4,158 person-yearslTotal,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.

Table 2: The Selected Price System
Country ACountry 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-yrwB = (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.

Table 3: Results for the Numeric Example
Wine ConsumptionCountry A 10 1/2 Units wine10 1/2 Units wine
Country B10 1/44 Units wine10 1/2 Units wine
Total20 23/44 Units wine22 Units wine
Silk ConsumptionCountry A11 Units silk10 1/2 Units silk
Country B10 1/2 Units silk10 1/2 Units silk
Total21 1/2 Units silk22 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.

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