Imagine that you are a manufacturer of inflatable rubber ducks. Unfortunately, the manufacture of ducks involves damaging water pollution. You have computed that your marginal savings in millions of dollars from emitting pollution is linear: \(M S(e)=10-e\), where \(e\) is the amount of emissions in tons. The Ministry of the environment has decreed that your emissions should not exceed 2 tons.

a. How much money does it cost you to obey the regulation rather than emit as much as you want?

b. The Ministry has just instituted a program whereby it will audit you with a probability of 0.01 . If you are found in violation, you must pay a fine of \(\$ 10\) million per ton of emissions in excess of the limit. How much is optimal for you to emit (optimal from your point of view)?