HOS Model (Live Version)
This is a 'live' version of the Heckscher-Ohlin-Samuelson (HOS) model of production in a single economy. The model uses Cobb-Douglas functions for both production and final demand. The solution is embedded directly in the sheet, making the use of Solver unnecessary. The model should work in any version of Excel. Exogenous variables and parameters are in white, endogenous variables in blue. The user can change endowments, prices, technology or preferences. A variety of the most commonly used geometric devices have been implemented. Aside from the method of implementation and minor cosmetic differences, the model can be used in the same way as the Solver-based version. A description of how the model was built is in Gilbert (2009).
Price-Factor Price Relationship (Stolper-Samuelson Theorem)
The Stolper-Samuelson theorem underlies analysis of political economy of protection. It states that an increase in the price of a good will result in a magnified increase in the price of the factor used intensively in the production of that good, and a decrease in the price of the other factor. In this model good X is capital intensive. Increasing the price of X (in cell E13) results in a rise in the price of capital (cell I4) and a fall in the price of labor (cell I5). The unit value isoquant and isoprice diagrams are the most commonly used textbook geometry. See Stolper and Samuelson (1941).
Endowment-Output Relationship (Rybczynski Theorem)
The Rybczynksi theorem is an important component of the Heckscher-Ohlin theorem of the international trade pattern, in addition to helping us to understand the consequences of new resource discovery, immigration, etc. It states that an increase in the endowment of a factor will result in a magnified expansion of the output of the good that uses that factor intensively, and a contraction of the other sector. With Y labor-intensive in the sheet, we can increase the endowment of labor by increasing the value in cell L5. The consequence is a proportionally greater increase in output of Y (cell F7), and a decrease in output of X (cell E7). Geometrically, the result is usually described using the output isoquants, the Edgeworth box, or the transformation locus. See Rybczynski (1955).
Price-Output Relationship (Concavity of the PPF)
The price-output relationships in the HOS model are very difficult to establish formally using algebra (see Gilbert and Oladi, 2008, for a geometric approach), and misunderstanding the unit isoquant diagram often leads to confusion over the implications of an increase in prices for output. The Stolper-Samuelson experiment should make clear that when the price of a good rises, the amount worth $1 shrinks (hence the inward shift of the unit value isoquant), but the output rises. Output of the other good falls. Because the supply curves are upward sloping, this is one way of formalizing the concavity of the PPF (another way is to use Samuelson's heuristic described below).
Factor Intensities and the PPF
The technology can be altered in this model by altering the cost shares (cells L15 and M15). These directly affect the factor intensities, and have a close relationship with the shape of the PPF. As you make the cost shares more similar across industries, the PPF will become less and less bowed out. The further apart the cost shares become the greater the degree of curvature in the PPF. The reason can be explained using Samuelson's heuristic. Consider the endpoints of the PPF. These reflect full allocation of the resources of the economy to one sector or the other. Now suppose the economy decided to produce both goods. It could simply split the resources fifty-fifty. This would result in half the maximum output of X and half the maximum output of Y. But suppose one factor is relatively better suited to one industry than another, and the opposite is true (by definition) for the other. Then a different split should be able to result in higher output of both goods. The greater the difference in the factor intensities, the greater the benefits of a reallocation of factors across industries.
No Money Illusion (Numeraire Shock)
The numeraire in this implementation of the HOS model is implicitly the foreign exchange rate. To simulate a numeraire shock, change both prices by the same proportion (cells E13 and F13). The consequence will be an increase in the prices of labor and capital, and an increase in income by the same proportion, but no changes in the rest of the economic system. The economic meaning of the result is that in a general equilibrium model like this one agents do not suffer from money illusion, they recognize that an increase in all prices by the same proportion changes nothing real in the economy.
Technological Change and Output/Income
A rise in productivity can be simulated by increasing the technology shift parameters (cells L18 and M18). Interesting technology shifts can be made in one sector only, or both. Consider an unbiased increase in productivity, by increasing the values in both L18 and M18 by the same proportion. The result is in some ways similar to the no money illusion simulation, both factor prices rise by the same proportion, and factor allocations do not change. However, welfare increases, as does output and consumption. More goods are now being produced with the same resources, and society is better off. Try the same experiment after first inducing trade by changing the initial prices, endowments or preferences. Does this matter? The answer is no. The important lesson is that changes in productivity increase income, and this is no less true for an open economy than a closed one.