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Ec101F10HW3_101118

# Ec101F10HW3_101118 - Economics 101 UCLA Fall 2010 Jernej...

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Economics 101, UCLA Fall 2010 Jernej Copic Homework 3, 11/19/2010; Due Tue 11/30/2010, 1230pm. This homework refers to a problem of providing a public good. The second part is about social enforcement in a small community when the public good is provided year after year during many years. The public good problem is somewhat similar to the one in the attempted experiment. Remember that you should appropriately cite any sources you end up using. In this problem, there is a city, called Gotham, where there are N inhabitants. They each have a budget of money; call ω i the endowment of money for agent i . Gotham city is plagued with a gremlin infestation problem – gremlins live in the catacombs under the city. Depending on how many gremlins there are, everyone in Gotham city is affected by the problem, hence what matters is the density of gremlins under Gotham city. Let y be the density of gremlins under the city. We normalize y , so that if no action is taken against the gremlins, y = 1, and if there is no gremlins at all, then y = 0; in general, y [0 , 1]. Each inhabitant has a utility function, which depends on how much money he has available for consumption, but is also negatively affected by the gremlins, which harass him at night. Some inhabitants, however, are more immune to gremlins than others. In other words, inhabitant i has a weight v i in their utility function, describing how affected they are by the gremlin problem. Denote by x i

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Ec101F10HW3_101118 - Economics 101 UCLA Fall 2010 Jernej...

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