A 2 kW air to air heat pump with a SCOP of 4 is about 2.2 kUSD installed here in Norway (Samsung Nordic Extreme 09 varmepumpe AR09BXFYDWKEE). This is reckoned to be big enough to heat room of 170 m2. Quite a lot of people here have one air to air heat pump on the ground floor and another for the upper floor.
Even down at -30°C it has a heat transfer capacity of 2.5 kW.
You didn't say how much your has heater costs so I have no idea how this compares but it seems reasonably priced to me.