If the company's stock is traded publically, then they CAN NOT set the price for their stock. The price of the stock is set by the market place and the company has nothing to do with it.
If the company is going public with their stock, they along with the underwriter decide on what is a decent price to offer the stock to the public or what the public is willing to pay, But once the stock is issued, they company has no say in the price of the stock
Might be a dumb question but is it based on the volume?