Any majority is free to form. If the proposal is approved by at least two politicians, it is implemented. Otherwise an exogenous status quo tax rate, ts, in enacted. Next, ae proposes an allocation of expenditure, subject to the budget determined in the previous node of the game. Again, a vote is taken, and any majority can form. An exogenous default allocation (unattractive for the voters) is implemented if the proposal is rejected. Finally, having observed everything that has taken place before, voters decide whether or not to reappoint the incumbent politician in their district.
This game has a unique subgame-perfect equilibrium. We now discuss its properties, without formally deriving any of the results. In doing so, we focus on the central trade-offs that must be resolved by the optimal choices of incumbent legislators and voters. A formal derivation is provided in Persson and Tabellini (1998) and, for a more general infinite horizon model, in Persson, Roland and Tabellini (1998a).
Consider the allocation of spending proposed by ae, for a given budget size. Getting the support from a legislator typically requires spending additional resources, either on rents for him, or on transfers for his district (so that he can satisfy his re-election constraint), or both. Hence, ae seeks a minimal winning majority, namely the support of only one legislator for his spending proposal. Moreover, he seeks the support of the legislator who is ’’cheapest to buy”, namely whoever demands the least either for himself or for his voters. This pits the other two voting districts against each other: the voters in the districts i = ae pay taxes anyway, but receive zero transfers if they are left out of the winning coalition. Hence, they become engaged in a ”Bertrand competition” for the spoils allocated by ae. To increase the chance of their representative being included in the winning coalition, they reduce their reservation utilities down to the point where they drive the demand for redistribution down to zero. Any equilibrium thus has:
The right-hand side of (4.3) is the maximum joint payoff to ae and his coalition partner if they go for the short-run option of allocating the entire budget to rents for themselves, only to be kicked out of office. The left-hand side of (4.3) is the joint payoff to ae and his coalition partner if they decide to seek reappointment and please their voters. In this case, they get current rents °r plus future exogenous rents 2R (as both politicians are re-elected). Thus, voters cannot push the endogenous rents r below the value implied by (4.3). If the value of reappointment R is not very high, then by (4.3) equilibrium rents can be positive. Intuitively, such positive equilibrium rents reflect the contract incompleteness and the resulting discretion enjoyed by politicians, once they are in office. Concerning the allocation of rents among politicians, it is optimal for ae to exploit his agenda-setting power, nailing the junior coalition partner to his status-quo payoff. internet payday loans