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For a typical negative externality market graph, with Demand curve (also labelled private value), and supply curve (private cost) and a social cost curve above the supply curve. What is the optimal quantity that maximizes total economic well being? Is it where the social cost curve and demand intersect or is it at zero?

The reason i am confused is because of the demand curve (private value), does this mean the society have no benefits from it at all, so the optimal quantity is at zero? What if the demand curve does not label as private value, the optimal will be where it intersects? So i treat that demand curve as the social demand curve?

optimal quantity is where the demand curve intersects the social cost curve. With this economic model, ALL social costs of the externality are reflected in the social cost curve. That is, the social cost curve represents the sum of the private cost of the supplier and the social cost of the externality. The demand curve represents the private value of various levels of consumption -- any additional "social" value to a person's private consumption would, if present, be reflected in the supply. curve adjustment. So, yes, you could think of the private demand curve as the social demand curve as well.

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