Assuming that you are referring to purchases made in the game... you can purchase as little as you wish, as leed0g says, but keep in mind that each trade costs you $10, If you purchase 1 share, it has to make over $20 before you make a profit on it... because it cost you $10 for buying, and another $10 for selling it. There is a limit in the game of 25% of your portfolio value for each stock, so if you spend 20% on a particular stock, you cannot spend another 10% on the same stock...
So while there is no actual minimum, you don't want to buy so little that your stock will never make that $20 cost, and there is a maximum.
HTH ...
GOOD LUCK and HAPPY TRADING!