It is an object of the present invention to provide a high pressure discharge lamp capable of shifting to arc discharge without going out at initial lighting. The object of the invention is achieved by a high discharge lamp in which mercury of 0.15 mg/mm.sup.3 is enclosed, and a power supply apparatus. The power supply apparatus comprises a chopper circuit including a switching element, and a smoothing circuit including at least one smoothing capacitor connected to an output terminal of the chopper circuit, and a feedback system control circuit which drives the switching element of the chopper circuit, wherein a parallel circuit comprising a resistor and a second switching circuit is in series connected to an output terminal of the smoothing circuit, and at least at time of initial lighting, the second switching circuit is turned off, and when the lamp is stabilized, the second switching element is turned on.