Fares themselves are rarely raised or lowered. Usually, airlines publish a slew of fares, each with various restrictions as to routing, travel days/dates, advance purchase, minimum/maximum stay, booking inventory, etc., and continually adjust booking inventory availability (for individual flights and for connecting flights). EF can show all available fares and currently available booking inventory, but it isn't designed to price itineraries. For that, I use Matrix (for the fine-grain control it offers), while many use Google Flights (for the speed and simplicity). These tools match available flights and available fares to price them.

If you really want to find the cheapest fares or cheapest fares that aren't basic economy or some such, you can use EF to do it, but it takes some work. First, do a Fare Information query for fares for your origination and destination, being sure to check the box for "Show Fares for All Travel Dates" and uncheck "Validate Fares". That shows all published fares for the starting and ending cities. Then, pick the cheapest fare you want to buy and read through the routing rules and fare rules to see if you could use that fare. If so, make note of the booking inventory required, and do a Flight Availability query to see if there are flights that have the available inventory. If not, set an EF alert to notify you if the required inventory becomes available.