# L consider the finite horizon bargaining model with

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l) Consider the finite horizon bargaining model with alternating offers. Assume for simplicity that there are only two periods and that both players have the same dis- count factor. Would you rather be the player who makes the offer in the first period or the player that makes the offer in the second period? Explain your answer. m) Suppose you live in a city that has a public pension plan that is underfunded by 50 percent. Why should you be concerned about this? What can do you to protect yourself? n) Consider the model of corruption discussed in class in which the highest bidder wins the government contract, but both bidders have to pay the bribes. Explain why you bid less aggressively when there are more players in the game?

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Problem 2: Regional Transfers (40 percent) Consider a model with two cities 1 and 2. Each city can invest in a public good that improves the welfare of the households living in the city. Let g j denote the level of public good provision in city j = 1 , 2. There are some spill-over effects, i.e city 1 receives some benefits from the provision of g 2 . Similarly, city 2 benefits from the provision of g 1 . We assume that preferences over public goods can be represented by the following welfare functions: W 1 ( g 1 , g 2 ) = 2 [ a g 1 + b g 1 g 2 ] - c g 1 (1) W 2 ( g 1 , g 2 ) = 2 [ a g 2 + b g 1 g 2 ] - c g 2 (2) where a > 0 and 0 < b < c . a) Find the Nash equilibrium levels of g 1 and g 2 when public good investments are taken simultaneously. (Hint: Note that the equilibrium will be symmetric since both regions are identical.) b) Why do you need to the restriction that a > 0 and 0 < b < c ? c) Suppose that public good provision is now centralized. Compute the efficient allocation of g 1 and g 2 by maximizing the sum of the welfare functions, W 1 ( g 1 , g 2 ) + W 2 ( g 1 , g 2 ). What other restriction do you need? d) Suppose we introduce linear subsidies, denoted by s 1 g 1 and s 2 g 2 , so that the new welfare functions are given by: W 1 ( g 1 , g 2 ) = 2 [ a g 1 + b g 1 g 2 ] - c g 1 + s 1 g 1 (3) W 2 ( g 1 , g 2 ) = 2 [ a g 2 + b g 1 g 2 ] - c g 2 + s 2 g 2 (4) What level of the subsidies, s 1 and s 2 , would induce each city to choose non- cooperatively in a Nash equilibrium an even higher level of public good investments as in part (c)?
Problem 3: Tiebout Sorting and Income Segregation (40 percent) Consider the model of fiscal competition discussed in class. Assume that the indirect

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