A method of manufacturing an elevator includes installing a movable supporting platform and an elevator car in the elevator hoistway; taking the elevator car into use to serve passengers and/or to transport goods; removing the elevator car from use; changing the service range of the elevator car to reach higher up in the elevator hoistway by lifting the supporting platform higher up in the elevator hoistway; and taking the elevator car back into use. The elevator is reeved to include construction-time hoisting roping, which includes one or more ropes, the longitudinal power transmission capacity of which is based at least essentially on non-metallic fibers in the longitudinal direction of the rope. In the method, guide rails to be fixed with guide rail brackets can additionally be installed by the aid of an installation device. An elevator arrangement can be used to perform the method.