The population of Outbacktown is 1,000 people. Each of them has a marginal benefit curve for fireworks given by M B = 10 2Q dollars, where Q is the number of minutes of the fireworks display. The marginal cost is constant, each extra minute costs 5,000 dollars; thus M C = 5, 000. Outbacktown is sparsely populated, and the terrain is very flat, so it is fairly safe to assume that fireworks over there are both nonrival and nonexcludable. (a) Obtain the optimal number of minutes that the show should last. What is the Lindahl price for each individual? (b) Now suppose that the usual provider is unavailable to offer the firework display this year and the major has to go with a new provider, Mr. Smoke. Fortunately, Mr. Smoke's marginal cost is the same as the usual provider. However, the environmental quality of Mr. Smoke's display is not that great; it generates a negative externality in the health of the population that has been estimated to be 2 dollars per each minute of the show, and for each individual in the population. Obtain the optimal number of minutes that Mr. Smoke's show should last. What is the Lindahl price for each individual once that the externality has been taken into account?