Question 1. Consider the model of corruption explored by Shleifer and Vishni's where there is one government-produced good X. There is a demand for that good described by the inverse demand equation Q_d = 10 - P. The official government price for the good is P_g = 3. The government pays the cost of producing the good. A bureaucrat can restrict the supply of
X. Since there is no risk of detection, the public official has incentives to ask for a bribe to supply the good.

Assume that the official's marginal revenue for selling the good in this context is given by Q_c = (7/2) - (1/2)P.

a) Consider the model of "no theft" where the consumer pays the official government price plus a bribe in order to obtain X. What is the number of government- produced good X that will maximize the bureaucrats income?

b) In the model of "no theft," what is the amount of the bribe that the corrupt official will charge?

c) Now consider the "model with theft" where consumers only pay a bribe but not the official government price. In this model what is the number of government -produced X that will maximize the bureaucrats income?

d) In the "model of theft," what is the total amount consumers will pay in order to obtain good X?

Question 2. When we discussed McGillivray's argument about industry protection, we said that firm location was exogenous. Continue to consider McGillivray's argument on industry protection but now suppose that firms can choose their geographical location within a country.

a) In the US, and all else equal, circle the only location that a firm would choose in order to obtain government protection, say, from foreign competition.

- In a marginal district
- In a republican district
- In a safe district
- In a district represented by an influential member of congress
- In a district where local taxes are lowest across the country
- In the district that is represented by the Prime Minister

b) In the UK, and all else equal, circle the only location that a firm would choose in order to obtain government protection, say, from foreign competition.

- In a marginal district
- In a conservative district
- In a safe district
- In a district represented by an influential member of congress
- In a district where local taxes are lowest across the country
- In the district that is represented by the Prime Minister

Question 3. The government of a certain country has installed a new device that monitors the activity of public officials working for an agency prone to corruption. There are only two types of public officials: corrupt and honest. The device called "Fire Alarm" indicates officials to be either corrupt or honest; with the device, the probability that an official is charged with corruption is 1/2. The probability that an official is charged with corruption given that the official is actually corrupt is 2/5. The probability that an official is honest is 7/9. Based on the results provided by the device, an official has been charged with corruption. Use Bayes' Theorem to find the probability that the official is actually honest given that the device indicates that the official is corrupt.

Question 4. Consider two drug cartels, C1 and C2. The cartels have a dispute over market share, represented by X=[1,0]. C1 would prefer to control all the market, so it's ideal point is 1 while C2's ideal point is 0 (ie, C1 controls 0% of the market). The cartels' utility functions for a point x ∈ X are U_c1 = x and U_c2 = 1-x. Assume that for i={C1,C2}, u_i(1)=1 and u_i(0)=0. These cartels can negotiate the proportion of the market they control, or they can fight over who controls the market. If the cartels fight, C1 wins with probability "0<q<1." The cartel that wins the fight gets to choose it's ideal point. However, fighting is costly and therefore C1 must pay k₁>0 while C2 must pay k₂>0 if they choose to fight.

a) What are the expected utilities for fighting for both cartels? Show your calculations.

b) Assume that there is a set of negotiated settlements x* ∈ X that both cartels prefer to fighting. What are the upper and lower bounds of this set x*? Label the bounds accordingly.

Question 5. Consider the model of industry protection of Grossman and Helpman discussed in lecture. There are two industries A and B, each producing good X and Y respectively. All other things being equal, the demand for good X is inelastic while the demand for good Y is elastic (or more simply, the demand for good Y is more elastic than the demand for good X). The country where these two industries are located is considering to open up its border to foreign companies that will bring competition and reduce the domestic prices of goods X and Y. In this context, and using the G-H model, explain

which industry will seek protection against international competition and why. Do not write more than 30 words.

Question 6. Suppose that economic outcomes can be classified as either good or bad. Governments differ in ability and this affects the likelihood of good outcomes. There are two types of governments: high ability or low ability. The prior probability that a government is high ability is 1/2. The probability that the economy is good given that the government is high ability is 3/4 while the probability that the economy is good given that the government is low ability is 1/4.

In this case, the incumbent government can manipulate the economy and the electorate will learn (update) their beliefs about the ability of the incumbent government based on the observed state of the economy.

Use Bayes Theorem to find the answer to all the following questions.

a) What is the probability that the government is high ability given that the economy is good?

b) What is the probability that the government is high ability given that the economy is bad?

Suppose that the opposition is a high type with probability 1/2. Voters vote for the government with the highest probability of being of a high type.

c) What is the probability that the incumbent government will win an election against the opposition if the economy is good?

d) What is the probability the incumbent government will win if the economy is bad?