Chapter 43: The Four-quadrant Diagram for the Two-sector Heckscher-Ohlin Model
Arvind Panagariya The four-quadrant diagram is remarkable for its ability to represent succinctly and precisely the full equilibrium in the two-good, two-factor, two-country Heckscher-Ohlin (H-O) model. With four factor allocations, two outputs and two factor prices in each country and the common goods price, the model has 17 variables in all. The diagram manages to show the equilibrium value of the key variables explicitly, with the remaining ones determined indirectly. I first introduce the basic diagram as applied to the autarky equilibrium. I then extend it to the two-country equilibrium and briefly mention further applications. In the penultimate section, I give a brief history of the diagram. 1. THE BASIC DIAGRAM Consider an economy producing two goods, 1 and 2, using two factors, labor (L) and capital (K). Production functions exhibit the standard properties, including constant returns to scale and diminishing returns to each factor. Cost minimization under these assumptions leads to a positive relationship between optimal capital–labor ratio and the wage–rental ratio in each good. Measuring the wage–rental ratio, w, along the horizontal axis and the capital–labor ratio in sector i, ki, along the vertical axis, I depict the relationship for each good in the first quadrant of Figure 43.1. The H-O model further assumes that one of the goods, say, good 2, is unambiguously capital intensive. This means that for each set of factor prices, the cost-minimizing capital-to-labor ratio is higher in good 2 than good 1. This is the reason I have drawn...
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