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ECON43915

Public Choice

2021

1. Assume that there are three individuals, A, B, and C. Consider four (two-dimensional) policy proposals: a, b, c, and d. The preference orderings (>) are as follows:

Individual A: a > d > c > b

Individual B: b > d > c > a

Individual C: c > b > a > d

a) Show that there is no Condorcet winner.                                                (20 marks)


b) Limit the number of proposals to be the set of ideal points (i.e. each individual's most preferred alternative). Show that there is a Condorcet winning proposal.   (20 marks)

 

c) Draw a graph in two-dimensional space that gives the preference ordering above.

(20 marks)

 

d) Suppose candidates A, B, C, can run for election, and the winning candidate implements their own preferred policy. Discuss whether a political equilibrium can be reached.

(20 marks)

 

e) Discuss direct democracy and indirect democracy in light of part a), b) and d) above and their equilibria.                                                                                      (20 marks)


 

2. Consider two-stage legislative bargaining, with three politicians in the legislature, indexed L, M, and R, with most preferred policies (ideal points) gL  > gM > gR  > ̅ , where ̅ is the default policy if there is no agreement in the second stage. An (exogenous) agenda setter can choose a coalition partner in stage one and make an offer of policy. If an agreement is not reached the game moves to stage two. In stage two, another agenda setter (different from the one in stage one) is chosen at random (with probability p). The new agenda setter chooses coalition partner and makes an offer of policy. If there is no agreement, the default policy is implemented. You can assume there is no discounting of utility going into stage two (i.e. there is no impatience).

a) Assume the  (exogenous) agenda setter  in stage one  is R.  Derive  an  expression characterising the equilibrium policy. Mark the policies on a line and point out where the equilibrium policy is (approximately) located.                                            (30 marks)

b) Assume that there is a second time period, where the legislative bargaining takes place again. The default policy is now the equilibrium policy of the previous time period (i.e. the one in part a)). For each agenda setter in stage one (L, M, and R), derive the expression characterising equilibrium policy. Mark the policies on a line and point out there the period two equilibrium policies are (approximately) located.                               (50 marks)

c) In light of the results in part a) and b), what will happen if time goes on and the default policy in each time period becomes the default policy in the next period? Discuss.

(20 marks)


 

3.   Assume there are two candidates (A and B) running for election. Each candidate can make a binding commitment to policy prior to the election. Policy is a level of a tax, τ , and a level of public goods spending, g. The public good g is financed through proportional income taxes. A continuum of citizens of measure one, indexed by i, all have the same income 1. The government’s budget constraint is τ = g + r, where r are the rents the elected politician can  divert for own  consumption. Assume that the  citizens’  preferences  over  private consumption, ci , and the public good, g, are given by the utility function ui = ci + H (g), with the budget constraint ci = (1 − τ).

The citizens have intrinsic bias towards one of the candidates. Citizen i will prefers candidate A if

 >  +   +

 

where

 

 ≝ (1 −   ) + ( )

  ≝ (1 −   ) + ( )

 

The parameters σi  and δ are stochastic and describe the citizen’s bias in favour of party B. They are uniformly distributed on [- 1/(2ϕ), 1/(2ϕ)] and [- 1/(2φ), 1/(2φ)], with density ϕ and φ ,  respectively.

a)  Show that the probability of candidate A of winning the election is   = ( ) +

(30 marks)

 

b)   The politicians maximise their expected rents. A maximises   and B maximises

 

(1 −  ) with respect to  ,  and  ,  , respectively. Assume the two politicians announce  their  policies  at  the  same  time,  i.e.  they  play  Nash  in  policy announcements. Derive the equilibrium proposals and the equilibrium election probabilities, as well as the expected rents, both from the individual politicians’


point of view and from the voters’ point of view.                                      (30

 

marks)

 

c)   Assume the objectives for the two politicians are as in part b) above. Suppose

 

that politician B announces policy first, and politician A second, observing what B did. Derive the optimal choice,  ,  , of politician A, taking politician B’s choice as given. Substitute A’s choice into the election probability function    to obtain a new probability function, say  . Solve for B’s choice of  ,  , by maximising (1 −  ) . Derive the equilibrium proposals and the equilibrium election probabilities, as well as the expected rents, both from the individual politicians’ point of view

and from the voters’ point of view.                                                (30 marks)

 

d)   Discuss how the result in c) differs from that in b), and in particular who (A, B, and

 

the citizens) will have higher expected utility.                               (10 marks)

 

4.    Discuss  the  findings  of the  empirical  literature  regarding  the  effect  of  constitutional differences on central government spending, and how they can be explained by public choice theory.

 

5.    How can it be explained that individuals go to the polling stations to vote, when the probability of being the pivotal voter appears to be low? Discuss.