Consider the model of political accountability by Persson where the discount factor is δ = 0.5, the status quo payoffs for the executive and legislature are x^S = 0.04 and l^ S = 0.04 respectively, and the utility functions for both the executive and the legislature are v(x) = √ x in each period.
(1) Suppose one-player-veto checks and balances is used, namely the executive proposes (x, l) and the legislature chooses to veto or not. If the executive tries to grab as much as it can in the current period (and not being re-elected afterwards), how much it must offer to the legislature so that the legislature will not veto?
(2) Under one-player-veto checks and balances, what is the voters' equilibrium consumption level in each period?
(3) If two-stage budgeting is used instead, what is the voters' equilibrium consumption level in each period?