Let us imagine that we have three types of individuals in

Question

1. Let us imagine that we have three types of individuals in the electorate (each with same population), with the following preferences.

1: a > b > c

2: b > c > a

3: c > b > a

(a) Simple majority:

(i) Which policy wins a simple majority in a vs b?

(ii) Which policy wins a simple majority in a vs c?

(iii) Which policy wins a simple majority in b vs c?

(b) Imagine a world in which individuals all vote and they all vote truthfully. Moreover, imagine that voting happened in the following way.

First, electorate votes for policy i vs alternative j.

Second, if i wins, run i vs alternative j'. But if j wins, call j the new i and repeat. Therefore, for a policy to win, it needs to beat all other alternatives in pair-wise simple majority run-offs.

(i) If we implemented this voting scheme, what happens in the world with the above preferences?

(c) Imagine a world in which all individuals vote and the voting commences in the fol-lowing manner.

First there is a run-off between policies a and b.

Second, voters pick between c and the winner of the first round.

(i) If all voters vote truthfully (according to their preferences) in every round, which policy wins?

(A) Which policy wins round 1?

(B) Now, using that, which policy wins round 2?

(ii) Imagine type-3 voters know that type-2 and -1 voters will vote honestly.

(A) What is the best move for type-3 voters in round 1?

(B) In round 2?

2. Suppose individuals pay income tax at rate τ. Moreover, assume that income y is distributed log-normally. That is, y = e^μ+σZ where Z is a standard normal. (Hint: Notice that the mean is y = e^μ+σ2/2. What is the median?)

(a) Compute the average revenue per person in the population.

(b) An individual's consumption is

c = y (1 - τ) + τy_avg - δτ².

Justify this expression.

(c) What is an individual's preferred tax rate if she has consumption y?

(d) What is the median voter's preferred tax rate?

(e) Compare the equilibrium tax rates between two societies facing parameters (μ, σ²) and (μ, σ^'2) where σ' > σ. Interpret your finding.

(f) Compare the equilibrium tax rates between two societies facing parameters (μ, σ²) and (μ', σ²) where μ' > μ. Interpret your finding.