Moped Army

I've been riding my moped alot lately. When I start it up, I usually have to give it some good throttle to keep her started. If I just let it idle the engine will die in about 10-20 seconds. If I go ride it around the block at full speed, it will idle for a few minutes. If I ride it for a long time, I dont have any problems with it idling at all. When the engine doesnt run hard enough, the generator doesn't produce enough electricity to run my turn signals etc. This is not good if I pull out of a parking lot and am ready to go into traffic. Like I said, I wont have any problems if I have been riding for ahwile, but if the engine isnt warmed up good it will want to die on me. Can anybody help me out? I think it might be my carb....not sure...