The marginal cost of a college education is given by the equation MC = ½ Qs + 2, where Qs represents the national student enrolment in millions each year. The demand for a college education is given by the inverse demand function P = -½ Qd + 18. In addition to the private benefit for each student from a college education, the increased education level of the society creates external, spillover benefits that improve national economic growth. Those spillover benefits that can be represented by the equation EMB = -1/4Q + 9. In order to ensure the efficient level of student enrolment, the government decides to provide a tuition break for all college students. Calculate the efficient level of enrolment, the optimal size of the tuition break using a Pigouvian subsidy, and the deadweight loss that is created without the government program.