Battery creates a negative externality of $3 each. A city has a demand for batteries given by :P=200-0. The supply of batteries is perfectly elastic...

Battery creates a negative externality of $3 each. A city has a demand for batteries given by :P=200-0.003Q.

The supply of batteries is perfectly elastic at $50.

Please answer with a graph: What is the social optimal level of batteries? If there is a tax on batteries, what will it be?

P.S. does the supply of batteries is perfectly elastic at $50 means the supply curve is a horizontal line at $50?