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Political Economy
Say's law is that "production is the source of demand" (Investopedia, 2015). The idea is that when an individual produces a work, they receive payment for it, and then use that payment to purchase other goods and services. Say's law conveniently ignores savings, but even more importantly assumes that all goods have equal demand, and that demand will arise from nowhere for any good on the basis that it has been produced.
Say's law would fail to hold on these accounts. While there is some argument that Say's law may hold in the long run, in the short run there are all kinds of issues with its logic (EconLib, 2015). In a monetary economy, savings is certainly going to be one of those problems. Savings represent a drain on the economy, in that money is not being put into productive use. In the modern era, savings might be put into investments, the capital markets, and that would not represent a diminishment of Say's law. However, any money that is basically taken off the table is money that has been earned but is not being spent. If someone puts their paycheck under the mattress, proverbial or otherwise, that is a drain on capital...
Banks have done this, too. For example, in 2009 and 2010, even when the Federal Reserve was pumping money into the economy like a sailor on shore leave, banks were not lending at pre-recession rates. They simply held back more money, which took that money out of the economy. Say's law does not adequately account for savings.
In addition, Say's law assumed the production equals sales. This has long been a bone of contention with the theory -- one cannot simply produce any old thing. People need to produce things for which they can earn. Arguably, in the long run everybody will need to do this in order to finance their ongoing existence, such that while people can indulge themselves in the short run on unproductive ventures, in the long run they must gravitate towards that which will pay -- allowing Say's law to hold in the long run. But there is still a drag any time someone produces something for which they do not earn -- such production does not inherently create demand.
2. Comparative advantage definitely has some limitations. The theory is used as an argument in favor of free trade, because…
References
EconLib (2015). Jean-Baptiste Say. Library of Economics and Liberty. Retrieved May 14, 2015 from http://www.econlib.org/library/Enc/bios/Say.html
Investopedia (2015). Say's law of markets. Investopedia. Retrieved May 14, 2015 from http://www.investopedia.com/terms/s/says-law.asp
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