In representative democracies where legislators represent geographic districts in legislative bodies (such as the U.S. House of Representatives), we often hear of “pork barrel spending”. Typically, this refers to special projects that legislators include in bills that pass the legislature — projects that have direct benefits for the legislator’s district but not outside the district. In this exercise we will think of these as publicly funded private goods whose benefits are confined to some fraction of residents of the geographical boundaries of the district. (In exercise 27.12, we will consider the case of different types of local public goods.)
A: Suppose that there are N different legislative districts, each with an equal proportion of the population. Suppose for simplicity that all citizens are identical—and that tax laws affect all individuals equally. Suppose further that all projects cost C, and that the total benefits B of a project are entirely contained in the district in which the project is undertaken.
(a) How much of the cost of a project that is passed by the legislature do the citizens in district I pay?
(b) How much of a benefit do the citizens in district i receive if the project is located in district i? What if it is not?
(c) Suppose the possible projects that can be brought to district i range in benefits from B = 0 to B = B where B > C. Which projects should be built in district i if the legislature cares only about efficiency?
(d) Now consider a legislator who represents district i and whose payoff is proportional to the surplus his district gets from the projects he brings to the district. What projects will this legislator seek to include in bills that pass the legislature?
(e) If there is only a single district—i.e. if N = 1, is there a difference between your answer to (c) and (d)?
(f) How does the set of inefficient projects that the legislator includes in bills change as N increases?
(g) In what sense do legislator’s have an incentive to propose inefficient projects even though all of their constituents would be better off if no inefficient projects were located in any district? Can you describe this as a prisoners’ dilemma? Can you also relate it to the Tragedy of the Commons (where you treat tax payer money as the common resource)?
B: Consider the same set of issues modeled slightly differently. Instead of thinking about a number of different projects per district, suppose there is a single project per district but it can vary in size. Let yi be the size of a government project in district i. suppose that the cost of funding a project of size y is c(y) = Ayα where α > 1, and suppose that the total benefit to the district of such a project is b(y) = Byβ where β≤ 1.
(a) What do the conditions α > 1 and β≤ 1mean? Do they seem like reasonable assumptions?
(b) Suppose all districts other than district i get projects of size y and district i get a project of size yi. Let district i ’s legislator get a payoff πi that is some fraction k of the net benefit that citizens within his district get from all government projects. What is πi (yi, N) assuming that the government is paying for all its projects through a tax system that splits the cost of all projects equally across all districts?
(c) What level of yi will legislator i choose to include in the government budget? Does it matter what y is?
(d) What level of yeq will all legislators request for their districts?
(e) What is the efficient level of y∗ per district? How does it differ from the equilibrium level?