Specific Factors Model and HOS Relationship (Transition) - Live Version 
This is a 'live' version of the model orginally designed to accompany Gilbert and Oladi (2008), although the focus of the paper was on the geometry of the problem not the numerical simulation. The sheet combines the live versions of the specific factors and HOS models into one sheet. The main purpose of the model is to show how an economy transitions from a short-run to a long-run equilibrium using simple transition dynamics as in the classic work of Mayer (1974) and Neary (1978), and thus demonstrate the close relationship between the specific factors and HOS models. The sub-models are the same as the separate single economy models, described here and here. The model allows the user to change any parameters and observe the short and long-run changes that result, then reallocate the capital stock to illustrate the transition. A Solver-based version is also available.
 
 
Model Layout Guide
 
 
Exercises

Because this sheet integrates the specific factors and HOS models of production into a single sheet, it can in principle be used for any of the exercises for those models. However, it is particularly suited to experiments involving a comparison of the two models, or simulations describing the connection between the two.

Prices and Factor Prices: Short vs Long Run

Prices for both the short and long-run equilibria are set in cells E13 and F13. Consider an increase in the price of X (increase the value in E13). Industry X is capital intensive, so Stolper-Samuelson tells us that in the long-run the return to capital will rise, and the return to labor will fall. In the short run, however, capital stuck in industry Y cannot benefit from the increase in its value in sector X. Hence, in the short run, the return to capital rises in sector X, but falls in sector Y as labor is drawn into sector X to increase output in response to the price rise (decreasing the marginal product of capital in Y). The return to labor rises, but by a smaller amount than the return to capital in X (and by proportionally less than the price of X, so whether or not labor is better off will depend on its consumption pattern, it may not be if it strongly prefers consumption of X). The difference between the two models suggests that industry based interests may be important in the short run, but factor based interests may be important in the long run.

Prices and Output: Short vs Long Run

Now consider what happens to output. We know that in both models an increase in the price of X causes an increase in production of X and a decrease in production of Y. In both models the PPF is concave and the supply functions upward sloping. But, comparing the output results for the same price change in cells E7 and F7 vs those in cells E41 and F41, we find that the output change is much bigger in the HOS model. Why? In the long run (HOS) both labor and capital can move to accomplish an increase in production, and in fact capital is most useful (since X is capital intensive). In the short run (specific factors) capital is stuck in each sector, and only labor can move. In effect, the economy is less flexible in the short run. The geometric interpretation is that the PPF in the short run is more concave than in the long run. 

Transition: How are the Short and Long Runs Related?

Would the equilibrium in the short run eventually coincide with the long run equilibrium? Consider a rise in the price of X of 10 percent (cell E13). We find that the return to capital in sector X is now 1.14, while in sector Y it is 1.02. In the short run this is an equilibrium, because capital cannot move it can be paid a differential return. Now consider the implications. Capital employed in Y has an incentive to move to X over time. The spinner next to cell E4 controls the allocation of capital across the sectors. Using it, shift a small amount of capital from Y to X. What happens? The returns to capital are driven closer together. How long would this process continue? Until the incentive to move disappears, i.e., when the returns to capital are equal. Keep shifting the capital into X. When does the process stop? When 83.25 units of capital are employed in X. Now, compare the equilibrium in the specific factors model with that in the HOS model. They are the same, the process leads the specific factors model to transition to the HOS equilibrium. You can use a similar experiment to confirm that the same results hold for changes in endowments (cells L4 and L5). Note that changes in capital are by default assumed to accumulate in sector Y in the short run, but you can change this by altering both L4 and E4 using the spinner if you wish.

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