Is it necessary to regulate crowding on recreation sites ? A random utility model with participation[Faut-il réguler l'encombrement des sites récréatifs ? Un modèle de choix discret avec participation]

Open-access is probably the main cause of crowding on recreational sites, especially when they are attractive and close to urban areas. In this case, theory predicts equilibrium and optimum differ due to externality of congestion. Whereas Fisher and Krutilla, 1972, caracterized optimum and equilibrium in monosite models, recent works on congestion in multiple sites models (Random utility models) only study equilibrium and the repartition of visits between sites in an empirical way. Our theoritical framework allows us to go further and derive visitation equilibrium and visitation optimum in a two sites random utility model with participation. Sites differ by quality. We use a recent measure of welfare (Erlander, 2005), essential to calculate optimum. At equilibrium, we show that participation is too high and that the high quality site is too much visited. We introduce optimal taxes to resolve this issue. Because this solution does not appear very realistic in the French case, we also examine impacts of improvements of quality on welfare. Our model is finally applied with a multinomial logit model estimated with data on recreational fishing.