Recreation centers offer a place for young people to play sports and do 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.
a. Without government intervention, how many people use the recreation centers?
b. Derive the social demand curve for recreation centers.
c. What is the socially optimal number of entrants?
d. Explain how the government could use a price-based intervention to achieve the socially optimal number of entrants.

Question

Quizplus · Accepted Answer

The Answer of Recreation centers offer a place for young people to play sports and do 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.
a. Without government intervention, how many people use the recreation centers?
b. Derive the social demand curve for recreation centers.
c. What is the socially optimal number of entrants?
d. Explain how the government could use a price-based intervention to achieve the socially optimal number of entrants.

Recreation Centers Offer a Place for Young People to Play