I have the model in my electronic spreadsheet (created by me) and its results quite suprised me. In short, complete specialization (I just call it specialization) in good where a country has comparative advantage CAN lead to inefficiency, to decrease of production of one of the goods (cheese in this case). This result suprised me and I would like it checked in case a mistake (in my reasoning or calculations) was made. (I can also share the spreadsheet if you want)
Suppose there are two countries, USA and France. Each country has industries: cheese production industry and wine production industry. Each industry in each country has exactly 1000 workers(the top is the American workforce, the bottom is the French workforce)
France has comparative advantage in cheese, while USA hold comparative advantage in wine. So France should concentrate all its laborforce in its chesee industry while USA should concentrate all its labor force in wine industry.
... except it will be bad news for world cheese production.
Production of cheese and wine in both countries before trade and (complete) specialization (the top is the American production, the bottom is the French production):
Production of cheese and wine in both countries after trade and (complete) specialization (the top is the American production, the bottom is the French production):
Now France produces all cheese in the world. But its cheese production technologies are too labor-intensive to produce enough cheese to compensate for fall of cheese production in USA. In order to avoid this USA will have to employ at the least 500 of its workers in cheese production, despite it beign American comparative disadvantage.
Thus we can conclude that in this case full specialization in cheese is a bad idea.