Author: Humberto Bernal,
Economist,
e-mail: zhumber@gmail.com
Twitter: Humberto_Bernal.
This note is to broadcast my research on General Equilibrium Model under two firms and two consumers GE 2x2. There are huge of information about it such as Debreu (1972), Arrow and Hahn (1984), Arrow and Intriligator (1986) and text books such as Kreps (1990), Varian (1992), Mas-Colell, Whinston and Green (1995) and Jehle and Reny (2011), Nicholson and Snyder (2011). However, they do not show how to solve this type of models in detail, they work through generalizations such as Arrow, Hahn and Debreu did. Therefore, the contribution of this document is to work on this GE 2x2 through uses of values; moreover, at the end of this contribution, I found a novel theorem about relative prices under trade.
To show how GE 2x2 works, there are three models taken into account. First, it is a model under diseconomies of scale; second, it is a model under constant returns to scale; finally, it is the Heckscher-Ohlin model. Solution of these models can be interesting for those who want to understand in easy way GE 2x2 models such as researchers, teachers and students. Moreover, a novel theorem about relative prices under trade is presented at the end of document. This theorem is important because says that in the long run (the Heckscher-Ohlin model) there will not be labour and capital migration between countries no matter political restrictions or transport restrictions because of relative prices are equal between countries; it happens because at end all countries will enjoy equal technology for producing goods; moreover, internet can be taken as media to broadcast this technology.
In this research you will find how to plot Possibility Production Frontier and Contract Curves as figure 1, 2, 3 show.
Figure 1. Production Possibility Frontier GE 2x2
Figure 2. Production Possibility Frontier HO model Autarky
Figure 3. Production Possibility Frontier HO model Trade
Hopefully, the myth about GE 2x2 and its weaknesses can be mitigate although I am aware of its restrictions such as scenarios of market failures.
Bernal, Humberto. 2014. "General Equilibrium Model 2x2 under Cobb-Douglas functions". Public Access.
