A new chain of garages specializing in quick (under 5 minutes) oil-changes for automobiles has opened in the county. It charges $25 per oil change and currently sells 10,000 oil changes per year. It appears that the marginal cost of the firm is approximately $25 per oil change and independent of the number of changes sold. Unfortunately, the chain uses a process that results in considerable leakage of hydrocarbon emissions into the air. No state or federal regulations prevent these emissions, and the county does not have direct regulatory authority. It can, however, impose a tax on oil changes using this process. An analysis presented by an expert panel indicates that the social cost of the emissions is $10 per oil change. Economists have estimated that the price elasticity of demand for the quick oil changes is -.5 at the current price and quantity assuming a linear demand schedule. a. Illustrate the market in a fully labeled graph. b. Imagine that the county imposes a $10 tax per oil change on the chain. What are the annual net benefits of this tax? c. What would be the annual net benefits of the $10 tax if the county faced a marginal excess tax burden of 10 percent? d. Imagine that, as a result of the tax, 50 percent of those who no longer purchase oil changes from the chain get oil changes at garages using traditional (30 minute) processes that emit no pollutants. Assume that the extra business does not affect the price these garages charge. The other 50 percent of former customers, however, do their own oil changes. Of the do-it-yourselfers, 80 percent follow procedures that result in no pollutants, while 20 percent dump oil illegally into storm sewers at a social cost of $20 per oil change. What are the annual net benefits of the tax assuming zero marginal excess tax burden? e. Now imagine that all those who no longer purchase oil changes from the chain go to the garages using the slower but pollution-free process. Discuss whether, and if so how, you would recalculate your answer to part b if the price charged by the garages increased substantially as a result of the increased demand for their services that resulted from the tax?