The private marginal benefit for commodity \(X\) is given by \(10-X\), where \(X\) is the number of units consumed. The private marginal cost of producing \(X\) is constant at \(\$ 5\). For each unit of \(X\) produced, an extemal cost of \(\$ 2\) is imposed on members of society. In the absence of any government intervention, how much \(X\) is produced? What is the efficient level of production of \(X\) ? What is the gain to society involved in moving from the inefficient to the efficient level of production? Suggest a Pigouvian tax that would lead to the efficient level. How much revenue would the tax raise?