Recreation centers offer a place for young people to play sports and engage in other activities at a marginal cost of MC = 0.25Q. 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 externalities because they help get young people off the street and engaged in productive activities. The external marginal benefits are EMB = 1 + 0.06Q. Without government intervention, ____ people will use the recreation centers.

Question

Quizplus · Accepted Answer

Without government intervention, the equilibrium is found where marginal cost (MC) equals the marginal private benefit (demand curve). Setting MC = 0.25Q equal to the inverse demand curve P = 10 - 0.25Q, we solve for Q: 0.25Q = 10 - 0.25Q, which gives Q = 2,000 (since Q measures hundreds of entrants, this corresponds to 2,000 people).

Recreation Centers Offer a Place for Young People to Play