ECON 345: Research Problem

Posted: August 25th, 2021

ECON 345: Research Problem

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ECON 345: Research Problem

Question 1. Setting the Research Question

      The study targets to establish the relationship between the cost of information and the change in the supportive rate of people for the government. Drawing on this background, the following will be the research question for the study:

• How does the supportive rate of the people in the country change as the cost of information increases?

Question 2.The Mathematical Model of the Setting

The variables of the research include Country A, the people of Country A, third party Country B, and a source of correct information. By activity, the sender is Country A while the receiver is the people in Country A.Country B provides information to the people in country A.The people in Country A acquire information from Country B at a cost.The people in country A receive information about the state of the country from the government.

Depending on the relevance and the sensitivity of the information, they can decide to support the government or seek to verify the information from Country B.The cost of verifying the information from Country B varies depending on the state of the economy.If the state of the economy is good, the government has no reason to lie to the people. Therefore, if the government is not lying, people have no reason to verify the information. If the state of the economy is bad, the government has a reason to lie, hence necessitating the people to verify the information from country B.

Moreover, there are two-states of the economy, that is,  H and L.H denotes when the state is good, and L donates when the state is bad.The equilibrium point occurs at the point where the cost of acquiring information from Country B is equivalent to the value of the information that the people in Country A attach. Thus, at the equilibrium point, the people in Country A are indifferent between acquiring the information from country B and believing what the government provides.

Question 3.The Sender’s Strategy

The sender in this scenario is the government in Country A.The sender knows the actual state of the economy and it conveys the message to the people. If the state of the economy is good, or H, the government has no reason to lie to the people. However, if the state of the economy is low, denoted by L, then the government must choose between lying to the people and telling the truth. Hence, the sender’s function can be represented by the function below, where the aim is to find the probability that the government will lie if the economy is bad.

, indicating the probability that the government will lie if the state of the economy is good. Thereis no reason for Country A to lie if the economy is good;hence, the probability of lying is zero. Accordingly,

, implying that Country A is forced to lie if the economy is poor. Thereby, the probability of lying if the economy is poor is 0.7. However, the probability of not lying would be hence, the people are indifferent between acquiring information and not acquiring information from Country A.The country is also indifferent. Given αis strategy of the people. The payoff when people believe economy is given as;

Question 4. The Receiver’s Strategy

The receivers in this scenario refer to the people. The People in Country A receive information about the state of the economy from the government. They can decide to confirm the information with Country B or support the government. C denotes the cost of acquiring the information from Country B.If the information is H,people go to country B to check the validity of the information.If the information is L, there is no reason for the people to confirm the validity of the information in Country B.The people choose whether to confirm information when it is H depending on the cost of verifying the information.The receiver’s strategy, in this case, is to confirm the information in Country B, given that the information issued by the government in Country A is H.If the government issues the information that the economy is bad, the people have no reason to verify the information. However, if the government issued the information that the economy is good, then the people are forced to seek and verify the information. If the cost of getting the information from country B is high, then the people choose to believe the government’s word and support the government. However, if the cost of information were low, then the people in country A would be indifferent between going to confirm the information offered by Country A in Country B. Their probability of confirming the information would make the government indifferent between telling the truth and lying.

Question 5. What Is The Equilibrium Point Basing on The Analysis From Above Scenario?

The equilibrium point occurs at the point where the people are indifferent between verifying the information from Country A in Country B and supporting the government in Country A.Assume that the probability of the economyis good (H) is 0.6.Note that if the economy is L, the people have no reason to verify the information from country B.If the economy is H, the probability of the government in Country A lying is 0.5.If the economy is L, the people have no reason to verify the information.At the same time, the probability of the people in Country A verifying the information about the state of the economy in Country A is 0.4.Further, if the people do not acquire information from Country A, they may not necessarily support the government. If the authorities in country A claim that the economy is H, the people are forced to verify the information from Country B.The cost of acquiring the information from country B about the state of the economy in Country A is $ 0.35.  Similarly, people in Country A may not acquire information to verify the truth of information given by Country A about the state of the economy because of the high cost of information in Country B. Assume the high cost of information is $0.45.The equilibrium point, according to Bayes’ theorem is given by the formula;

Where;

P(A) is the probability that the economy in Country A is H or bad. In this scenario, 0.6 gives the probability that the economy in Country A is L.

P (B) is the probability that the authorities in country A will lie. In this scenario, the probability of the authorities lying is 0.5

P(A/B) is the probability that the people in Country A will verify the information if the government states that the economy is good.

P {(A/B*(H/l)} is the probability that the people in Country A will verify information when the cost are low. In this scenario, the probability is 0.7

Pr {(A/B)*(L/h)} is the probability that the people in Country A will not verify the information. In this scenario, the probability is 0.3

P(B/A) is the probability that the people will support the authorities in Country A after verifying the information. Therefore, using the figures given above, the equilibrium point is given by;

Hence, the probability that the people of country A will support the authorities in country A after verifying information about the economy of country A in country B is 0.357 or 35.7%

Interpretation

The above scenario indicates that there is a 35.7% chance that the people in Country A will support the authorities in Country A after verifying the information about the economy in Country B.At this equilibrium point,the receivers of the information who are the people in Country A are indifferent about the cost of verifying information in Country B and the payoff of the information. At this point, the government in Country A can lie whatever it wants since the people no longer care about the state of the economy.

Assumptions of Bayes theory

Bayes theory makes the following assumption based on the conclusions about the study;

1. The conditional probability that the probability of event A occurring given the occurrence of event B is known and true. In the above scenario, the probability of the authorities in Country A lying given the economy is good is known, and it is true.
2. The marginal probability of both events occurring is derived by observing the two events independently.In the above scenario, the state of the economy in Country A and the probability of the people verifying the information are observed independently.

Question6.Were You Able To Answer The Research Question?

The research question is,‘how does the supportive rate of the people change as the cost of information increases?’ This analysis provided conclusive evidence to prove that the supportive rate of the people in Country A increases as the cost of information increases. Atthe high cost of information, the people cannot afford to verify the information given by the authorities, hence is forced to support the authorities. However, when the cost of information is low, people can afford to verify the information, hence reducing their supportive rate.