HOS Two Country Model (Solver Version)

This is a Solver-based version of the Heckscher-Ohlin-Samuelson (HOS) model of production and trade in a two economy world (Home and Foreign). The model uses Cobb-Douglas functions for both production and final demand, and the initial setup has both economies identical. Exogenous variables and parameters are in white, endogenous variables in grey. As with the single economy model, the user can change endowments, technology or preferences in either economy. Prices are endogenously determined. The sheet actually contains two models on separate tabs. In one we have two autarkic economies. In the other we have the same two economies, but they are allowed to trade. A variety of the most commonly used geometric devices have been implemented. The primary purpose of he model is to illustrate the HOS model trade theorems. A description of how the model was built is in Gilbert (2004).

Model Layout Guide


Endowments and Trade (Heckscher-Ohlin Theorem)

The Heckscher-Ohlin theorem states that economies will have a comparative advantage in, and therefore export if trade is allowed, the good that uses relatively intensively in its production the factor found in relative abundance in that economy. In this sheet X is capital-intensive. Both countries have the same endowments of capital and labor initially. To simulate the Heckscher-Ohlin theorem, begin in the Autarky sheet. Increase the endowment of capital in Home (cell K5) and the endowment of labor in Foreign (cell K43). Home is now capital abundant by the quantity measure. Solving the model we find that output of X has risen by a greater proportion than output of Y in Home, and the opposite has occurred in Foreign (why? Rybczynski). The increase in relative supply drives the relative price of X down in Home and up in Foreign. This means that Home has a comparative advantage in X. Also note that the price of capital rises and the price of labor falls in Home, while the opposite occurs in Foreign (why? Stolper-Samuelson). We can therefore confirm that Home is capital abundant using the price definition.

Now switch to the Trade sheet and alter the endowments in the same pattern. We have established that this leads to a comparative advantage in X for Home. Solving the model reveals that Home exports X, while Foreign exports Y, just as the Heckscher-Ohlin theorem predicts.  

Trade and Factor Prices (Factor Price Equalization Theorem)

The simulation above reveals another important result. Once trade is allowed, the return to capital and labor in both countries is the same. This the called the factor price equalization theorem. The interpretation is that free international trade in the HOS model is the same as allowing the factors themselves to move. In a very real sense, international trade creates a single economic system as if capital and labor could move freely across border to where it is most valued. The mechanism is as described by Stolper-Samuelson. For further details see Samuelson (1949). The result depends critically on the assumptions of the model, in particular that technology is the same in both economies. To see this, try increasing the production shift parameters (cells C26 and E26) in Home by the same amount. This implies that Home has higher productivity than Foreign. Re-solve the model. The Heckscher-Ohlin result still holds, but now factor prices for both inputs are higher in Home than in Foreign. Hence, the HOS model does not override the fundamental insight from the Ricardian model on the importance of productivity to incomes.  

Country Size and the Terms of Trade

Within the Autarky model, retain a pattern of comparative advantage by keeping Home relatively capital abundant, but increase the size of Home relative to Foreign by increasing both endowments in Home and decreasing both in Foreign. For example, if you made Home's endowment K=150 and L=100, change in to K=300 and L=200 (don't worry about the spinners, you can always type a value directly into the cell), while making Foreign's endowment K=50 and L=75. This  keeps the pattern of abundance the same. Solving the model reveals no change in the relative autarky prices and hence in the pattern of trade. Now consider the same experiment in the Trade page. What happens? The world price is different. Compare it to the Autarky price in Home and Foreign. Which price is it closer to? It should be closer to the larger country autarky price (Home). The trade price must lie between the autarky prices for trade to be viable. But the larger an economy is the greater the influence it has on the world prices. If you make Home larger still (say K=450, L=300) the world prices will get closer still to Home's autarky price.
Growth and the Terms-of-Trade

The preceding analysis tells us that the world prices (terms of trade) depend on the relative sizes of the economies engaged in trade. What are the implications for growth? We break this into two questions: The effect of growth on the growing economy, and the effect of growth on the trading partner. To understand the implications of factor accumulation better, consider a scenario where trade is occurring and the endowments of Foreign remain constant, but the endowments of Home gradually increase. There are three patterns in which the endowments might grow to try: Capital could grow faster than labor, labor could grow faster than capital, or both could grow at the same speed. If capital and labor grow at the same speed, the pattern of abundance remains unchanged and trade continues to occur, but the terms-of-trade gradually deteriorate as Home gets larger, for the reasons discussed above. If capital grows faster than labor, Home's comparative advantage grows stronger. Trade will grow faster, and the deterioration in the terms-of-trade will be more rapid. If the growth of labor is faster, Home's comparative advantage will diminish, and it will trade less. The terms-of-trade will move in Home's favor. What are the welfare consequences? Home's productive capacity increases in all three cases. In the first two cases, the terms-of-trade deterioriate. In the second case (rapid growth of capital, it is even possible that welfare could fall (this is called immiserizing growth, see Bhagwati, 1958). 

Trading Partner Growth and Welfare

The above experiment also allows us to see the effect of having a rapidly growing trade partner. If the partner is growing in such a way that it wants to trade more, then this would have to improve the terms-of-trade for the slower growing economy (which is effectively becoming smaller), and therefore improve welfare. Only if the trading partner is growing in such a way that it wants to trade less (i.e., its pattern of factor abundance is becoming more similar) would the terms-of-trade effect on the trading partner be negative. Does this mean that not trading is preferable in this case? To see, simulate the same pattern of factor change in the Autarky model and compare the welfare indices with those in the trade model. What do we find? The autarky welfare level is the lowest that the trade welfare level can go, when the relative pattern of abundance is the same in both countries, otherwise the trade index is always higher. Hence, from an efficiency perspective, rapid growth in a trading partner could never make not trading the better option. 

Technology and Preferences and the Pattern of Trade

Students often feel that the assumptions of the HOS model make it unrealistic. It is useful to use the simulation model to emphasize that many of these assumptions are made only for the purpose of formalizing and isolating the effect of differences in factor endowments on the pattern of trade. One way to do so is to recast the model as an example of the 'no-trade' model. As initially set up, the two economies are identical in every respect. They have the same technology, the same endowments and the same preferences. Hence there is no pattern of comparative advantage and trade does not occur. To verify this solve the Trade model without making any changes to the sheet, the zero volume of trade is the solution. The HOS model emphasizes the role of endowments, but we can easily show that changes in technology or preferences would also lead to trade in this model. For example, in the Autarky sheet, change the preference parameters in cells C28 and C65 to 0.75 and 0.25, respectively. This is equivalent to saying Home now prefers good X relative to Foreign. Solve the model. The Home autarky price of X is now higher than in Foreign, indicating a Foreign comparative advantage in X. Now make the same change in the Trade sheet and solve. Foreign exports X. Next, trying restoring the preferences to their original state, and changing technology. We could increase the shift parameter in cell C26 in the Autarky sheet. This is equivalent to saying Home is now more productive (has superior technology) in X than Foreign. Solve the model. As we expect, Home now has a comparative advantage in X. Make the same change in the Trade sheet and solve, and Home now exports X. In short, differences in preferences, technology or endowments could all lead to trade. We assume that preferences and technology are the same only to emphasize the role of endowments in this toy model. In the real world, all these aspects will likely differ across economies.