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What is the theory behind a free market and planned economies and what is the difference between them?

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1. Ignoring externalities and market failures, each person acting in their own self interest can be shown to create the highest welfare for the entire group because prices serve as signals of marginal scarcity. Price allows producers to determine how much to produce, how many people to hire and how much money to borrow from otherwise unused savings at the smallest amount of waste. Average wages are higher under free market economies over any other. In a perfectly free system, under perfect competition and in perfect markets (everything has a price), all people get their fair wage, plus or minus an error of judgment factor on the part of employers. Planned economies begin with a different concern, those least well off are felt to be so disadvantaged that they cannot arrive at any fair resolution through anything other than government controlling all principal transactions. The concern isn't that the society is as well off as possible, it is that the weakest have some minimum level of well being. The trade is that all are worse off, except the very weakest. In either extreme, they are both bad systems. Free markets are bad due to externalities, completely planned economies trigger very substantial poverty because the waste is so high and resources are misallocated.