By not offering an artificial incentive to stay in business (the subsidy), product would not have been over-produced and wasted (perhaps an environmental impact), new and in-demand skills would have been acquired, real demands would have been met, and the price for those demands would have fallen (helping the consumer). Thus, by removing the artificial barrier to real and free trade (perhaps influenced by political pressure), economic well-being is ensured for all parties.
Now, consider labor, itself to be a similar commodity as the milk. Perhaps a certain software company employed 5000 employees to write code for a popular program. However, due to better education, increased drive, and longer work days in another country, the company could instead employ 1000 employees abroad (i.e. through "outsourcing"). Given the right political and legal conditions, the company could either allow fewer foreign employees to do the same work, or allow more employees to do the work at a higher price. Clearly, the market has changed and less labor is now in demand for the same work. Yet the company may be forced to stay with the higher priced labor regardless due to artificial barriers (much like the subsidy above). Prices on the product will be unnaturally high, the consumer will suffer, and resources (in this case the labor) will be wasted and misdirected.
Although free trade as represented in the outsourcing question is by nature emotional, the truth is the artificial barrier to trade in labor is counterproductive in many senses. Not only does it keep prices high for consumers, but it waists resources, and perhaps stifles innovation. Much like a dairy farmer could instead produce an "in demand" crop, thusly benefiting society at large (of course, unintentionally), the misdirected labor in the United States (which could be more efficiently provided elsewhere to the eventual benefit of all), could be redirected to new industries and applications as yet unimagined. Just as this is more in keeping with the self-image of the United States as a "world leader" in many areas, it is also in keeping with the economic theories of the earliest thinkers economics. As Adam Smith wrote in "The Wealth of Nations:"
It is the maxim of every prudent master of a family, never to attempt to make at home what it will cost him more to make than to buy...What is prudence in the conduct of every private family, can scarce be folly in that of a great kingdom. If a foreign country can supply us with a commodity cheaper than we ourselves can make it, better buy it of them with some part of the produce of our own industry, employed in a way in which we have some advantage. (Book IV Chapter II)
In the end "freedom" comes at a price, whatever the form. Yet the fruit of its practice has always been great. Let, then, the vine of labor be "pruned back," allowing it to bloom again in an even greater variety. Who knows what wonderful form it will take?
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