An economical elevator additionally arranged outside a building comprises an old building, an old stair, an elevator shaft, a shaft door, a car, a car door, an elevator door platform, a newly-built walkway, a newly-built stair, an elevator machine room, a harmonic speed reduction traction machine, a traction wheel, a traction guide wheel, a steel wire rope, a car guide wheel, a car guide rail, counterweight iron plates, counterweight guide wheels, counterweight guide rails, Hall sensors, strip-shaped permanent magnets, an intelligent controller and operating buttons; the harmonic speed reduction traction machine is a hub type traction machine integrating a harmonic speed reducer, a two-pole outer rotor brushless permanent magnet direct current motor and the traction wheel; when the two-pole outer rotor brushless permanent magnet direct current motor is shut down, large magnetic resistance exists between a rotor and a stator, a speed reduction ratio of the harmonic speed reducer is large; when the harmonic speed reduction traction machine is shut down, the harmonic speed reduction traction machine has a strong self-locking function which is equivalent to a braking state, a braking system of the traction machine is omitted, the harmonic speed reduction traction machine is simple and cheap, and the safety and the reliability meet the standard requirements.