What happens to price of stocks when a corporation reduces authorized amount of stocks?

I believe what you are referring to is when a corporation buys back it's own stock resulting in less authorized shares in the marketplace. This doesn't have a direct effect on a stocks price but can typically indirectly cause a stocks price to increase. The reason that it is not direct is that the company must spend it's own money to buy back the stock. This results in less shares and each shareholder now holds a larger stake in the company but the resulting company now either has less cash in it's reserves or has issued debt to pay for the stock. Indirectly this can help the price of the stock. The fact that a company is buying it's own stock back would indicate that the company feels it's own shares are a bargin at the current price. It also adds support to a stocks price in that if the price begins to fall due to market conditions the company can step in and buy shares to prevent or limit continued stock depreciation.