Problem
Consider the Tapeline-Alexia model in the case where α can only take on the values 0 and 1. Suppose that the amount of debt to be issued, D, is determined before the preferences of the period-1 median voter are known. Specifically, voters vote on D at a time when the probabilities that α1MED = 1 and that α2MED = 1 are equal. Let π denote this common value. Assume that the draws of the two median voters are independent.
(a) What is the expected utility of an individual with α = 1 as a function of D, π, and W?
(b) What is the first-order condition for this individual's most preferred value of D? What is the associated value of D?
(c) What is the most preferred value of D of an individual with α = 0?
(d) Given these results, if voters vote on D before the period-1 median voter is known, what value of D does the median voter prefer?
(e) Explain briefly how, if at all, the question analyzed in part (d) differs from the question of whether individuals will support a balanced-budget requirement if it is proposed before the preferences of the period-1 median voter are known.