Putting aside the social problems that communism causes, the most basic economic problem with communism economically is that it would eliminate risk taking, which is what drives any economy. A person could only fare as well as their community. I understand that some communists want to eliminate money, so I'll refer to economic "units" for the sake of convenience. If, by my efforts, I can make 1 economic unit in communism while I could make 100 economic units in capitalism (let us say a commune had 100 people in it), I am likely to work much harder under capitalism. Of course, there is more potential for loss in the short-term, but most people think the risk is worthwhile. There are rare circumstances (e.g. the Great Depression), in which modestly increasing government control of the economy is justified, since most have abandoned such risk taking, but even those measures should be cautious and temporary.

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"I am a Tory Anarchist. I should like every one to go about doing just as he pleased- short of altering any of the things to which I have grown accustomed." (Max Beerbohm)