I'll offer up a different perspective to the other answers which hopefully will make clear why a small investor can't ever make a noticeable difference. This will use a fictional example with made up numbers, but the principle is the same for the real markets.
Imagine we have Foobar Ltd, a company listed on a stock exchange. At any given time there is an order book which contains a list of all buy/sell (technical term: bid/offer) orders. The order book is essentially a list which summarises for each given price, how many shares are being offered for sale or purchase at that price. For example, at a given moment of time the order book might look like this:
Bids: [1,000,000 @ $100.00] [2,000,000 @ $ 99.99] [1,500,000 @ $ 99.98]
Offers: [1,300,000 @ $100.01] [2,100,000 @ $100.02] [1,800,000 @ $100.03]
Now, you, as an ordinary investor, might try do one of the following to lower the price of Foobar Ltd:
- Sell some shares to use up the existing orders and force the price to the next set of orders.
- Place a bid order at a new, lower, price.
Let's try scenario 1. You, being a small investor, decide to sell 100 shares using the available orders. The best price you can currently get (from the bid offers on the order book above) is $100. So you sell your shares and now the order book looks like this (changed entry tagged with < >):
Bids: < 999,900 @ $100.00> [2,000,000 @ $ 99.99] [1,500,000 @ $ 99.98]
Offers: [1,300,000 @ $100.01] [2,100,000 @ $100.02] [1,800,000 @ $100.03]
There are simply too many other bids at $100.00 for your sale to have made any noticeable difference. You'd have had to sell 1,000,000 shares for $100,000,000 to reduce the bid price to $99.99.
Now let's try scenario 2. You decide you're not happy about the fact that you have to pay $100.01 to buy 100 shares of Foobar Ltd (using available orders) or $100.00 (placing an order of your own at the current price), so you decide to place a bid at $99.99. Now the order book looks like this (changed entry tagged wtih < >):
Bids: [1,000,000 @ $100.00] <2,000,100 @ $ 99.99> [1,500,000 @ $ 99.98]
Offers: [1,300,000 @ $100.01] [2,100,000 @ $100.02] [1,800,000 @ $100.03]
Your tiny order has marginally increased the orders available at $99.99, but there are still the 1,000,000 bids at $100.00. Anyone selling their shares will sell the first 1,000,000 at $100.00 before they even look at your order. So again, your action has made no noticeable difference.
But, throw in a few 10,000s of other small investors all making the same decision as you (or a few large institutional investors) and now the price will change because collectively the action is large enough to make a difference.
In summary:
"They say the stock price is determined by what the public is willing to pay for a given security."
This means that the price is determined by what the "public" is willing to pay collectively, not what you, by yourself, are willing to pay. Note that "public" here includes what you are thinking of as public (ordinary investors) but also institutional investors who buy/sell in bulk, and market makers (those that profit from placing simultaneous bid/offer orders with a price spread, and help to create liquidity by making sure there are always orders available).