A power source apparatus includes a controller that carries out horsepower control to determine a flow rate of a hydraulic pump in accordance with a discharge pressure of the hydraulic pump detected by a pump pressure determination sensor. In horsepower control, the controller determines the flow rate such that a maximum input setting for the hydraulic pump defined by the discharge pressure and the flow rate is greater than a maximum output of the engine when the discharge pressure is a first discharge pressure, gradually becomes smaller as the discharge pressure changes from the first discharge pressure towards a higher pressure, and becomes smaller than the maximum output of the engine when the discharge pressure is a second discharge pressure.