A Dynamic Model of Democratization 195 revolution starting in state S {L , H }. This value is naturally given by: V p(R, S) = (1 S) y (1 )(1 ) (6.11) which is the per-period return from revolution for the innite future discounted to the present. Also, because the elites lose everything, V r (R, S) = 0 whatever is the value of S. Moreover, recall that we have assumed L = 1, so V p(R, L ) = 0, and the citizens would never attempt revolution when t = L . In the state (N, L ), the elites are in power and there is no threat of revolution; therefore, in any Markov perfect equilibrium, = = 0 and N = r = 0. This says simply that when the elites are in power and the citizens cannot threaten them, the elites do not repress and set their preferred tax rate, which is zero. Therefore, the values of the citizens and the elites, i = p or r , are given by: (cid:12) q V i (N, H ) + (1 q )V i (N, L ) (cid:13) V i (N, L ) = yi + (6.12)

Now, (6.12) says that the value to an agent of type i in a nondemocracy when there is no threat of revolution is equal to a payoff of yi today, plus the expected continuation value discounted back to today (which is why it is multiplied by ). The payoff today is yi because taxes are set at zero and everyone simply consumes their income. The continuation value consists of two terms; the second, (1 q )V i (N, L ), is the probability that L arises tomorrow times the value of being in that state V i (N, L ). In this case, tomorrow is the same as today, which is why the same value recurs. The rst term, q V i (N, H ), is the probability that H arises tomorrow multiplied by the value of that state V i (N, H ). This value is different because now there is a potential threat to the regime. To see how this plays out, we need to understand what the value V i (N, H ) looks like.

Consider the state (N, H ), where there is a nondemocracy but it is relatively attractive to mount a revolution. Suppose that the elites play = = 0 and N = r ; that is, they neither create democracy nor repress nor redistribute to the citizens. Then, we would have: V p(N, H ) = y p 1 The revolution constraint is equivalent to V p(R, H ) > V p(N, H ), so that without any redistribution or democratization, the citizens prefer to initiate revolution when t = H . This is equivalent to > , which is identical to (6.3) in the previous section, and says that revolution becomes attractive when is sufciently high (i.e., when inequality is sufciently high). Because revolution is the worst outcome for the elites, they will try to prevent it. They can do this in three different ways. First, the elites can choose to maintain political power, = 0, but redistribute through taxation. In this case, the poor P1: JtR 0521855268c06.tex CB919-Acemoglu.cls 0 521 85526 8

September 29, 2005 20:49 196 Democratization obtain V p(N, H , N) where N is the specic value of the tax rate chosen by the elites. Second, the elites can create democracy. Third, the elites can use repression. Let V i (O, | ) be the value function of agent i = p, r in state when the elites pursue the strategy of repression and the cost of repression is . We condition these values explicitly on to emphasize the importance of the cost of repression and to simplify notation when we later dene threshold values. If the elites create democracy or attempt to stay in power by redistributing, the citizens may still prefer revolution; thus: V p(N, H ) = V p(O, H | ) + (1 ) max {0,1} (cid:17) (cid:18) V p(R, H ) + (1 )(V p(D)+(1 )V p(N, H , N))