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4 Mathematical Externality Problem Paper is sold in competitive markets. The private marginal benefit from paper: PMB = 200 - Q, where Q is the quantity of paper consumed in the market. The private marginal cost of paper production is PMC=20. However, there is an externality in paper produc- tion, equal to the quantity produced, i.e. production of paper causes marginal damage to society in Q. a) Solve for equilibrium price and quantity of paper sold in the market. Solve for the socially efficient quantity. Calculate the deadweight loss. b) If the government wanted to achieve the socially efficient outcome using a tax of sub- sidy, which should it use? Calculate the optimal per unit tax or subsidy