It is impossible to do it under 50 $, but quite possible to do it under 150 $... which is quite cheaper than many battery systems.

1. Get a Shimano dynohub. Given the difference between the lower end and the other ones, I would recommend the DH-3N7x or DH-3N8x (or the disk version if needed). That's about 100 $, and you need to rebuild your front wheel.
Or you get a good bottle generator such as the Dymotec 6 (50 $). It's a great alternative, but there is a slight buzz when riding at night and the generator is prone to some slippage if you ride in foul weather (tires with a generator strip help)

2. Get a Lumotec headlight. The Lumotec Fly costs between 35 and 50 $ depending on whether or not you want a standlight. It provides very good lighting to be seen, is very effective in the city (i.e. left-turners stop and don't try to ride through me), but I would not recommend it for long rides in total darkness. Still, it is brighter than the Planet Bike 1 W Blaze, and because the beam is well patterned, it is much more effective than that.
The Lumotec IQ Fly is about 3 times as bright as the Lumotec Fly (no IQ). Great on dry pavement, not as bright as I would want on semi-urban areas, with dark sections and stray light, when the pavement is wet. Still at 100 $, I think it is a great investment for most.
The Lumotec IQ Cyo and the Schmidt Edelux take care of that last bit, but they make a bigger dent in your wallet.