PUBLIC GOODS A small island, known as Dark Island, does not have a lighthouse. The citizens of Dark Island are trying to persuade the governor of the island to build one. This would help those in the shing trade return home safely after a night of work on their boats (which is the most popular activity among Dark Island's workers). However, not everyone shares the same interest in the creation of a lighthouse: there is a group of citizens (denoted as Group 1) who own a farm and do not value the use of the lighthouse for work. They will only use the lighthouse for leisure boating. The rest of the population (Group 2) does not have any other work activity and is in desperate need of a lighthouse for their livelihood. Given the relevance of the request, the governor decides to accommodate it and to start the construction of a lighthouse. However, having it running all night is too expensive for a small island, so the governor has to compare the benets and costs of the activity and choose the socially optimal amount of hours of lighting to provide. Denote by Q the amount of hours in which the lighthouse works at night. The marginal cost the governor has to pay for every extra unit of Q is constant and equal to 5$. The marginal benet of an extra hour for Group 1 is described by the function 5 M 31(Q) : a while the one for Group 2 is given by 10 M 32(Q) = 5 1. What kind of good is the lighthouse? Explain. 2. Given the marginal benets of the two population groups and the marginal costs faced by the governor, how many hours the lighthouse should work at night? [Hint: You should look for the efficient level of Q, 62*] 3. Due to an unexpected heat wave, the farm activity becomes less valuable in Dark Island. This changes Group 1's marginal benet function, which becomes the same as Group 2 (i.e., M Bl(Q) = M B2(Q) = 220). Do you expect a change in the level of provision of the good? Will Q increase or decrease? Explain and compute the new efficient level of Q, Q**. 4. Due to an increase in the price of electricity, the marginal cost of running the lighthouse goes from 5$ to 10$. Even if the heat wave is still devaluing the farm activity (i.e the marginal benets of the group are as in part (3)) the governor is forced to revise his previous decision about the hours of operation of the lighthouse. Do you expect an increase or a decrease in Q compared to part (3)? Explain and compute the new efficient level of Q, Q***