Students receive two types of benefits from standardized test preparation services: first, they learn useful material; second, they score better on the test relative to other students. Because relative performance matters, their improved performance creates a negative externality for other students. Suppose that the market demand function for test preparation services is Qd = 30 - P/2, where Qd is millions of hours of services and P is the price per hour. Suppose also that the market for these services is competitive and that the market supply function is Qs = 2P - 30.
Finally, suppose that the external cost of test preparation is given by EC = 5Q + 0.75Q2. Find the socially efficient level of test preparation, the competitive equilibrium, and the deadweight loss created by the externality. Draw a figure to illustrate your answer.