Used automobile batteries can be a serious environmental problem. When dumped into landfills, batteries can leak lead and contaminate nearby water supplies, a negative externality. To explore this issue, consider the following scenario. A small city has a demand for car batteries given by: P = 200 - (3/1000)Q Please note that this is the ordinary market demand before any consideration of externalities. The supply of batteries is perfectly elastic at $50. However, each new battery eventually will be discarded and will contribute to the contamination of the town's water supply. An economist has estimated that the damages are equal to $3 per new battery (that is, all future damages caused by the battery are equivalent to $3 at the time of purchase).

What is the socially efficient number of batteries? Be sure to show your work. Suppose the government wanted to address the problem by imposing a tax on batteries. What should the tax be?