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I heard that profit of all firms in long-term becomes zero. But I am not convinced of why it is like that. Can anyone explain this mathematically?

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    You'd have to give us more mathematical definition of the model and the problem for this to qualify as a math problem suitable for this site.2012-12-12
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    At least the average profit should be zero.2012-12-12
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    It doesn't sound like a claim that would be true under even unrealistically simplified macroeconomic assumptions (such as a finite money supply). It's easy to imagine a toy economy where all businesses continually make profits and pay out dividends; the income of each business comes from private individuals buying services from it with money they were paid in dividends from their owning other businesses. In such a world, a single unit of money can keep generating profits again and again as it circulates.2012-12-12
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    I suspect the reason is that any company making a profit will necessarily engender competition, until the profits are whittled to zero.2012-12-12
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    @HenningMakholm: Your argument holds water in terms of accounting profit. I suspect what OP concerns is economic profit.2012-12-16

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