Consider a market where demand is p10-2q and supply is pq2

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Consider a market where demand is P=10-2Q and supply is p=Q/2. There is a consumption positive externality of $2.5/unit of consumption.

a. What is the social optimum quantity and price?

b. If the government uses a tax to get producers to internalize their externality, what is the net price received by producers?

c. Calculate the total surplus in the market equilibrium, at the social optimum and with the tax.

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