Question

A large number of tourists choose between two holiday resorts: Ecoheaven and Beachfun. Ecoheaven is located in an environmentally fragile area, and the payo§ to tourists visiting this resort is negatively a§ected by the number of visitors. The payo§ from visiting Beachfun, by contrast, is independent of the number of tourists. Formally, let II(E) and II(B) denote the payo§s from visiting Ecoheaven and Beachfun, and let x denote the percentage of tourists who visit Ecoheaven (i.e. 0<x<100). With this notation, the payo§s are

II(E) = 100-x

II(B) = 40

(a) Draw a diagram illustrating the payoffs from choosing Ecoheaven and Beachfun as functions of x.

(b) Find the Nash equilibrium/ equilibria in this ëvacation-choiceígame. What are the equilibrium values of x and the payo§s II(E) and II(B)?

(c) Now assume that a social planner wants to maximize the sum of the touristsípayo§s.

i. Find the value of x that maximizes x(E) + (100-x) II(B):

ii. Discuss how the social planner could use taxes to bring about the desired outcome from your answer to (i). Find the required tax rate on vacations in E:

iii. What are the payo§s to the tourists in the new equilibrium? Does the new equilibrium represent an improvement over the nonintervention equilibrium from question (b) above? Explai

Answer 1