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Suppose that oil is perfectly divisible (you can buy non-integer quantities)

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Suppose that oil is perfectly divisible (you can buy non-integer quantities). The marginal cost curve is given by MC=1.8Q+4MC=1.8Q+4. The demand curve is given by P=39−1.8QP=39−1.8Q, which gives MR=39−3.6QMR=39−3.6Q In the most efficient outcome (which perfectly competitive markets achieve), P=MCP=MC. Solve the equilibrium price and quantity in that case.

The most efficient equilibrium quantity is _____.

The most efficient equilibrium price is _____.

Now suppose that, for each unit of oil consumed, $5.84$5.84 worth of environmental damage is done. Solve the optimal Pigouvian tax (per unit) that would obtain the socially-efficient outcome where less oil is produced and sold. The optimal tax per unit is $_____.