Abstract
Much literature demonstrated the existence of general trade equilibrium in the Heckscher-Ohlin model, but no analytical solution has been reported yet. Dixit and Norman made a breakthrough showing that whole factor-price equalization set in integrated world equilibrium (IWE) shares the same world price. Helpman and Krugman enhanced the result, presenting the equal trade volume lines in the IWE diagram. Their ideas explored the new property and clue of trading equilibrium. Inspired by their ideas, this paper derives the price-trade equilibrium using Helpman and Krugman’s equal trade volume lines and shows that world prices are the function of world factor endowments. The current study finds that the relative price of two factors at equilibrium is inversely propositional to their world factor endowments, which simulates the law of demand. The study demonstrates that the equalized factor prices ensure gains from trade for both countries. With the equilibrium, the Heckscher-Ohlin theorem and factor-price equalization theorem are linked together by term of trade. They can explain each other. Trefler illustrated that the factor price equalization hypothesis and the Heckscher-Ohlin-Vanek theorem hold in his equivalent-productivities system (effective endowments). The integrated price-trade equilibrium will be helpful to understand the equilibrium of factor price non-equalization.
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Notes
Another approach is from the goods’ version or path of the Heckscher-Ohlin theorem, which analyzes goods equilibrium.
This assumption is relaxed in the analyses when using the IWE diagram.
One can describer \(\alpha ={s}^{H}-{\lambda }_{L}\) as the redistributed share of GNP formed by trade in country H. Similarly, \(\beta ={{\lambda }_{K}-s}^{H}\) is the redistributed share of GNP formed by trade in country F.
This paper interprets the trade volume as the value of net factor content of trade, for simplicity.
If one assumes \({\gamma }_{K}=1,\) then \({\gamma }_{L}=-{K}^{W}/{L}^{W}\). The equivalent result can also be obtained.
The length of the horizontal border of the trade box is \(\left({\lambda }_{K}-{\lambda }_{L}\right){L}^{W}\).
More strictly, we need to express \(VT=2{\left|{F}_{K}^{H}\right|r}^{*}\), where \(\left|{F}_{K}^{H}\right|\) is absolute value of \({F}_{K}^{H}\).
This assumption is the same condition of Eq. (12), which leads to Eqs. (22) and (28). It implies that the Walras law was only used once. No matter how one assigns a value to a price (such as alternatively \({r}_{}^{*}=1\), then \({w}^{*}={K}^{W}/{L}^{W}\)), the relative factor price and relative goods price will be same. The \({s}^{H}\) will be the same, the factor content of trade will be the same, and goods trade flow will be same.
Feenstra (2018) identified three sources for the gains from trade: variety, creative destruction, and markup in the real economy analyses.
McKenzie (1987) described the task of general trade equilibrium and mentioned that equilibrium is a pre-condition to show the equilibrium change (or trade effect).
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Guo, B. Integrated Price-Trade Equilibrium by World Factor Endowments. Int Adv Econ Res 29, 193–205 (2023). https://doi.org/10.1007/s11294-023-09876-9
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DOI: https://doi.org/10.1007/s11294-023-09876-9
Keywords
- Factor content of trade
- Factor price equalization
- General trade equilibrium
- Integrated world equilibrium
- Gains from trade
- Autarky price