Assume that the indirect utility function is now

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Consider the model of fiscal competition discussed in class. Assume that the indirect utility function is now given by: V ( g, p, y ) = -{ αg ρ + [ y p - B ] ρ } (5) where ρ < 0, α > 0 and 1 > B > 0. Remember households differ in income y which is distributed with density f ( y ). a) Using Roy’s identity derive the housing demand for each household type. What are the price and income elasticities of housing demand? b) Derive the condition which characterizes boundary indifference between two adja- cent communities. c) Suppose households not only differ in income, but also tastes for public goods denoted by α . Derive the new condition which characterizes boundary indifference between two adjacent communities. d) Consider a model with 2 communities. Provide a graph that illustrates household sorting for the model in (c) (Hint: graph the boundary indifference condition in the ( α, y ) space and explain who lives in which community.)
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Problem 4: Externalities and Global Warming The newly elected mayor of an city has pledged to reduce air pollution. The city has no close neighbors. The only source of air pollution are the two domestic plants run by firm A and firm B. Firm A has pollution abatement (=reduction) costs of x 3 , where x is a unit of pollution. Firm B has a pollution abatement cost of x 2 . Assume that neither firm is initially engaging in pollution abatement. The per unit benefit to a unit of pollution abatement experienced by the island’s citizen is constant at $300. a) What is the socially optimal level of pollution abatement? How is the socially optimal level of abatement split between the two firms? b) The mayor considers engaging in command and control style quantity regulation and declares that each firm must engage in 80 units of pollution abatement. Is this optimal? Why or why not? c) Alternatively the mayor considers providing a subsidy of $300 per unit of pollution abatement. What is the per firm and total level of pollution abatement? Is this socially optimal? d) The mayor also considers issuing pollution permits and establishing a market for these permits. For reasons associated with the relative generosity of the firms to his recent election campaign, firm A is given permits such that is must engage in 100 units of pollution abatement if it fails to enter the market. Firm B is given permits such that it must engage in 60 units of pollution abatement if it fails to enter the market. Each unit allows the firm holding the unit to produce one unit of pollution.
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