Imagine there is an economy with two individuals: one smoker and one non-smoker. The smoker decides how many cigarettes she smokes comparing her Marginal Cost and her Marginal Benefit. Given by the following expressions:

MB= 220-3Q MC= 20+Q

Q: number of cigarettes she decides to smoke.

However, every cigarette generates a marginal damage to the non-smoker equal to Q.

Find:

1. The number of cigarettes that the smoker will smoke without any government intervention.
2. The number of cigarettes that the smoker will smoke in the social efficient equilibrium.
3. If there will be a way of forcing the smoker to smoke the social efficient quantity which will be the loss for the smoker, the benefit for the non-smoker and the total social gain?