There is less and less heat in the outside air as the temperature drops, and thus, the heat pump has less and less to actually move from outside to inside. SO, depending on its efficiency, at some point, it will not be able to extract any heat, so yes, at some point it becomes cheaper to just use the emergency heat, as the cost to run the compressor and the heat extracted starts (eventually) to become a negative factor - i.e., you'd get more heat by just running the resistance heater strips for the power expended. Now, the newer units are more efficent than older ones, and the point at which they no longer are capable of running and extracting heat is lower than older ones. Somewhere in the spec sheets of the unit you have, they will discuss that cross-over point, and it becomes more efficient to just run the emergency heating. They may also have some charts. You have to figure in your local electrical rates, too. Some places give you a break on electricity if used for heating verses 'general' use, so there may be a tiered structure that makes the calculation harder.