Consider a manufactured good whose production process generates pollution.

The annual demand for the good is given by Qd $=1202$P $.$ The annual

market supply is given by QS $=2$P $.$ For every unit of output produced,

the industry emits polution causing marginal damage equal to $2$Q $($in dollar

values$).$

$($a$)$ Find the equilibrium price and quantity produced in a competitive

market with no government intervention.

$($b$)$ Find the socially optimal quantity of output in this market $($taking into

account the externality$).$

$($c$)$ Suppose an emissions fee is imposed on producers. What is the socially

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optimal level of the fee?