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What does it mean for a company to have its market cap larger than the market size?
You are comparing two things that are not comparable.  The "market size" would be the total annual revenue in one market, in this year.  The "market caps" of a company is the number of shares multiplied by the share price. This should be equal to the total profit that the company is going to make through its life time, taking into account that you would get interest on an investment, so future profits have to be counted less accordingly.  So if the "market size" is ten million dollars, and a company has four million revenue in that market with one million profit, and everyone thinks that company will continue making that profit for the next fifty years, then surely one million a year for the next 50 years is worth more than ten million.  That's if the market stands still. If the "market size" is ten million, and we expect that market size to double for the next three years, then the market size is still ten million, but a company having a 40% share of a market growing at that speed is going to be worth a lot more!