If it will increase your profit. Lets say that both you and the guy across the street sell a product for $100 that costs both of you $70 wholesale, and that you each sell 100 of them a month. So you're making $3,000 profit on $10,000 sales. Now if you believed that by dropping your price to $95, you could get 75% of the 200 units sold each month, that would amount to $3,750 profit on $14,250 sales.
You might even do a little better, because lowering the price brings in 10 more customers who will buy at $95 but not at $100, and you might be able to make a deal with your wholesaler to get the items for $67.50 because of the increase in your volume. This would net you $4,400 profit on $15,200 sales.
The only thing the guy across the street can do is lower his price to $95 too, or he might even go you one better and cut his price to $92.50. This can go on until the margin is barely enough to cover your overhead or all but one of you decides he's unwilling to sell for less than X profit.
If you are goping to do this, you need to know a)where you are on the supply and demand curves for your products, and b)the exact slope of those curves, and c) how both of those might change over time.
Can you be sure of these in a quantifiable way?
Glad to see someone is ‘still thinking’. Yes, market forces work.