The AC loss measurements of the high temperature superconductor (HTS) cable prototype in the EDIPO test facility motivated detailed investigations of the loss contributions from the tape, strand and cable stages of the HTS fusion conductor design proposed at the Swiss Plasma Center. As an initial step of the task, magnetization tests of soldered stacks of HTS tapes were carried out at temperatures of 5 and 77 K and magnetic fields up to 12 T using the vibrating sample magnetometer technique. The influence on the magnetization loss of the number of tapes, width of the tape, field's orientation and tape's manufacturer is studied experimentally performing both the major and minor magnetization loops with different ramp rates of the applied magnetic field. In order to validate the test results, a numerical model is developed and presented in this work. From the numerical model we also deduced an analytical approach for the magnetization loss in the stacks of tapes with arbitrary number of tapes in the critical state model. Comparison between the measured and estimated magnetization loss of the cable prototypes is reported as well.