2. (20 points) 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 will eventually 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).
a. (5 pts) Without government intervention, how many batteries will be purchased each year? What will the price of a battery be?
b. (5 pts) 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?
c. (5 pts) Graphically illustrate the situation before and after the tax is imposed. Be sure to indicate the efficiency gain.d. (5 pts) What is the numerical value of the efficiency gain from part c?How much revenue does the tax raise? What is the percentage reductionin lead pollution?