61. Recreation centers offer a place for young people to play sports and do other activities at a marginal cost of MC = 0.250. The inverse demand curve for recreation centers is given by P = 10 0.25Q, where P is the price of entry and Q measures hundreds of entrants. Recreation centers generate positive extemalities because they help get young people off the street and engaged in productive activities. The external marginal benets are EMB = 1 + 0.06Q. 'Wlthout government intervention, how many people use the recreation centers? Derive the social demand curve for recreation centers. What is the socially optimal number of entrants? Explain how the government could use a price-based intervention to achieve the socially optimal number of entrants. P'PP'P