Who usually sets and determines prices of products in a company?do competitors have anything to do with our strategy?what do we base our pricing on?

There are dedicated Product Managers who consults with Marketing and Sales team before setting a price for the new product. 

Yes if competitve analysis is not done there is always chances you may over quote which can be fatal for any product. 

A product pricing always depends on Manufacturing cost , Transportation,Marketing cost, profit margins (if distributros or channel partners involved there is cost calculated on it as well)

Then finally a price is decided.

If price of product is amazing and product adds value there can be huge demand. Some products are game changers for company specially some models in automotive has done well because of smart pricing strategies which give maximum value to customer. (VALUE for Money)

It depends on the company structure , if there is a pricing department or other but it is essential to take in consideration running costs, production costs, administrative costs, selling cost and any other costst relevant to that product. As for competitors the have nothing to do with our strategy that is something internal in our company which is supposed to be set to beat other companies out of the market, unless presence of any deals or contracts. Product pricing economicaly should be based on supply and demand of that product, but in real market depending on surrounding environment other benchmark's could be included but as long as that price is covering all costs and has profit margin.