3. By installing a smoke detector in a university residence, a student confers a positive external benefit on other students because the detector reduces the chance that other students will be harmed in a fire. An economist has estimated the likelihood of a fire in the school's residences and the harm that a fire might cause. The economist also estimates that each smoke detector installed generates an external benefit of $10. She also reports that the school can buy smoke detectors for $40 each, which reflects the marginal cost of production. The economist estimates the market demand curve for smoke detectors, which reflects the private benefits the students enjoy from having a smoke detector. The estimated demand curve is Qa = 60 - P. (a) Without any intervention on the part of the university, how many smoke detectors would students buy? Explain. What is the resulting deadweight loss. Illustrate using a suitable diagram that shows the private marginal benefit, the social marginal benefit, the private marginal cost and the social marginal cost of installing smoke detectors. (b) If the university decided to buy smoke detectors and provide them free of charge to every student who wanted one, would there be a deadweight loss? If so, how large