Specific Factors Model (Live Version)
This is a 'live' version of the specific factors model of production (see Jones, 1971). The model uses Cobb-Douglas functions for both production and final demand, and is very similar in structure to the HOS model. Exogenous variables and parameters are in white, endogenous variables in blue. The user can change endowments, prices, technology or preferences. The model incorporates the common VMPL diagram, and the quadrant PPF diagram. A Solver-based version of the model is also available. Another version of the model, which emphasizes the relationship between the specific factors model and the HOS model is also available, and focuses instead on the Edgeworth box representation. A description of how the model was built is in Gilbert (2009c).
Prices and Factor Returns
Consider an increase in the price of X (cell E13). When you solve the model you will find that the return to capital in X has risen, along with the return to labor, while the return to capital in Y has fallen. A rise in the price of Y (cell F13) will yield a symmetric result. Capital can be paid a differential return in the specific factors model because it is prevented from moving across sectors. Alternatively, the specific factors employed in each sector can be thought of as completely distinct factors (e.g., capital and land), which have different prices as a consequence. Overall, it appears that price increases will benefit one specific factor and the mobile factor (labor) and hurt the other specific factor. In fact, however, things are not so clear cut for the mobile factor. Notice that while the wage has risen, it has risen by less in percentage terms than the increase in the price of X. So, the real wage in terms of Y has risen, but the real wage in terms of X has fallen. Is labor better off? It depends on how much X and Y it likes to consume. This result is called the neoclassical ambiguity.
Prices and Output
When you increase the price of X output of X also expands, and output of Y contracts. As in the HOS model, the supply curves in the specific factors model are upward sloping, and the PPF is concave. In fact, it is more concave than in the HOS model. See the HOS-Specific comparison.
Endowments and Factor Returns
In the HOS model when endowments change the factor prices remain constant provided that both goods are produced and prices remain constant (as they would be for a small, open economy). To confirm, recall the Rybczynski simulation. What about the specific factors model? Unlike with HOS, the factor prices will depend on the factor endowments. First consider an increase in the endowment of one of the specific factors. Try increasing capital of type X in cell E4. After we solve the model we find that the return to capital has fallen in both sectors, while the return to labor has risen. Why? As we increase the amount of capital in sector X, the marginal product of labor in X must rise (since it has more capital to work with), and so must the wage (the value of the marginal product) at constant prices. Since labor is mobile, it must be paid a higher wage wherever it works, so the wage rises for sector Y also. Since prices are constant, the return to capital in Y must be squeezed down. The same pattern occurs for a rise in the endowment of capital of type Y.
What if the endowment of the mobile factor rises? To see increase the endowment in cell L5. We find that the return to labor falls, while the returns to both specific factors (which now have more labor to work with) both rise.
Endowments and Output
The Rybczynski result shows how biased factor accumulation leads to a biased expansion of the PPF, and hence to a pattern of trade. Can similar results be obtained here? First consider the implications of expanding the endowment of specific factors. For an expansion of the stock of capital of type X (cell E4) we find that the output of X expands, while output of Y contracts. As capital increases in X, more labor is drawn in to work with it. Since it must come from Y production, output of Y declines. A symmetric result holds for capital of type Y. In terms of the PPF, accumulation of a specific factor will expand the PPF along the axis of the good that uses the factor, making it steeper or flatter, similar in spirit to the HOS result.
For the mobile factor things are different. Increasing the amount of labor in the economy will increase the output of both sectors. In terms of identifying a pattern of comparative advantage then, things are a bit murkier than with the HOS model. If we compare two economies that are similar with respect to the size of their labor stocks, but where one has a larger endowment of capital of type X and the other has a larger endowment of capital of type Y, for example, we can show that the former will have a comparative advantage in X. This can help us to understand the pattern of comparative advantage of countries with large resource endowments.