1. Consider country A. In this country, 20% of the people are from ethnicity α, 40% from ethnicity β, and the other 40% are from ethnicity γ. In the same country, 1/3 of the people

revolution. from ethnicity α speak language BLUE, 2/3 of the people from ethnicity β speak

revolution. language BLUE, and 1/5 of the people from ethnicity γ speak language BLUE. a) Suppose that there is a threat of revolution. What is the optimal policy for a leader if W ⇥ a) Suppose that there is a threat of revolution. What is the optimal policy for a leader if W ⇥

w1? What is the logic behind this strategy? b) Suppose that there is a threat of revolution. What a) Suppose a person is speaking language BLUE. What is the probability that this person is from ethnicity γ? Provide your answer in fractions and not in decimal places. Failure to

w1? What is the logic behind this strategy? b) Suppose that there is a threat of revolution. What is the optimal policy for a leader if w1 ⇥ W ⇥ w2? What is the logic behind this strategy? c)

do so will result in the loss of points. is the optimal policy for a leader if w1 ⇥ W ⇥ w2? What is the logic behind this strategy? c) Using the argument of Bueno de Mesquita and Smith discussed in class, why is there not a threat of

2. Consider the model by Hollyer and Rosendorff (2011). Write down the autocrat's Using the argument of Bueno de Mesquita and Smith discussed in class, why is there not a threat of

revolution when W is large (say, if W ⇤ w2)? d) On the figure, highlight a leader's optimal policy expected utility function for e=0; this is the level of effort put into deposing the

government. Interpret this function in 30 words or less. revolution when W is large (say, if W ⇤ w2)? d) On the figure, highlight a leader's optimal policy along W assuming that for W ⇥ w2 there is a threat of revolution, but no threat of revolution for along W assuming that for W ⇥ w2 there is a threat of revolution, but no threat of revolution for W >w2.

3. You are an advisor to the ruler of a big country that is surrounded by smaller nations. Your boss is considering whether to invade one of the smaller neighboring nations W >w2.

3. We want to explore the effect of international treaties on countries' behavior. Suppose because its citizens have demonstrated capacity for independent thought. You explain to your boss that he can do that and obtain a single payoff of $100. You also explain to your

3. We want to explore the effect of international treaties on countries' behavior. Suppose that signing a treaty can be considered as a treatment. Countries that signed the treaty are in the

boss that he can also encourage the citizens of the small nation to continue developing that signing a treaty can be considered as a treatment. Countries that signed the treaty are in the independent thought and with it a dynamic population that might buy your country's

treatment group and countries that did not sign the treaty are in the control group. Suppose that products. If this is the case, he will obtain a payoff of $10 in this current year (i.e. period

treatment group and countries that did not sign the treaty are in the control group. Suppose that countries were assigned to groups randomly. The following table presents the results of the treaty.

0), $10 next year (i.e. period 1), $10 in two year time (i.e. period 2), $10 in three years time (i.e. period 3), and so on for an infinite number of years (i.e. infinite periods). The countries were assigned to groups randomly. The following table presents the results of the treaty. a) Calculate the mean causal effect of the treaty (i.e. E[Yi(1) # Yi(0)] = μ1 # μ0). Remember discount factor of your boss is δ.

a) Calculate the mean causal effect of the treaty (i.e. E[Yi(1) # Yi(0)] = μ1 # μ0). Remember that, since countries were randomly assigned to groups, we can divide the sample by group and cal- culate the mean (i.e. average) effect for each group. Does the effect of the treaty look significant?

a) Under what conditions do you recommend the promotion of independent thought in that, since countries were randomly assigned to groups, we can divide the sample by group and cal- culate the mean (i.e. average) effect for each group. Does the effect of the treaty look significant?

the small nation as opposed to an invasion? 4. Following Downs et al., the utilities for pairs of countries engaged in trade depend on

3. Consider the following utility function for country A: levels of protection. Consider the following utility function for country A, where PA is

3. Consider the following utility function for country A: level of protection in country A and PB is level of protection in country B: UA(PA, PB) = #(P B # P B

UA(PA, PB) = #(P B # P B Assume that the utility function for country B is

Assume that the utility function for country B is: Assume that the utility function for country B is UB(PA, PB) = #(P A # P A

UB(PA, PB) = #(P A # P A Assume that the non-cooperative tariffs are P A

Assume that the non-cooperative tariffs are P A 0 ) # (P A # P A

0 ) # (P A # P A 2 + (1/2)(P B # P B 0 )

2 + (1/2)(P B # P B 0 )

0 )(P A # P A 0 )(P A # P A

0 )+(P B # P B 0 )+(P B # P B 0 )

0 ) 0 ) # (P B # P B 0 ) # (P B # P B

2 + (1/2)(P A # P A 0 ) 2 + (1/2)(P A # P A

0 )

1 0 = P B 0 = P B

2 0 )(P B # P B 0 )(P B # P B 0 = 1 and cooperative tariffs are P A = 0 = 1 and cooperative tariffs are P A = 0 )+(P A # P A 0 )+(P A # P A

0 ) 0 )

Assume that the non-cooperative tariffs (i.e. the status quo) are P0

cooperative tariffs are PA =PB =1/2. Countries can either choose to implement non- cooperative tariffs or cooperative tariffs. a) Write down the matrix with payoffs for both players.

b) What is the Nash equilibrium in pure strategies? A = P0 = 1 and B