Answer:

Part A:

1) No mutual benefit in this transaction.

2) Mutual benefit in this transaction.

3) Mutual benefit in this transaction

4) Mutual benefit in this transaction

5) No mutual benefit in this transaction.

6) No mutual benefit in this transaction.

Part B: The government will enter in the market to control the monopoly firm by keeping their price under control, to control the negative externality by taxing their production, by creating a mechanism of providing relevant information to both trading parties to avoid the problem of asymmetric information, and to provide public goods which are important for society but expensive to produce for private sector.

Step-by-step explanation

Part A

1) A complicated medical procedure has been discovered that cures a rare form of cancer in patients who would otherwise certainly die. Staff shortages make it impossible to treat all those who would benefit, and the hospital has established a policy of first come, first served. Ben, a wealthy patient who is at the bottom of the list, offers to pay Alex, a poor person on the top of the list, $1 million to exchange places. If Alex dies (which is very likely), then her children will inherit the money. Alex agrees.

I don't approve this transaction.

It is given that if Alex exchange its position with Ben and went at the bottom of the list, then he is very likely to die. The exchange price offered by Ben is $1 million cannot be compared to a person's life. If Alex does not accept my proposal and stays at the top of the list, then he will be treated soon and can save his life, which will enable him to work and earn for his family.

2) Dylan is 18. He has been admitted to a good university but does not have any financial aid, and cannot get any. He signs a four-year contract to be a stripper on the Internet and will begin work when he is 19. The company will pay his tuition fees.

The transaction will lead to the mutual benefit because both Dylan and company will find it profitable. Dylan will get his tuition fees paid and company will get an employee.

3) You are waiting in line to buy tickets for a movie that is almost sold out. Someone from the back of the line approaches the woman in front of you and offers her $25 to exchange positions in the line (he takes her position in front of you and she takes his at the back of the line).

The transaction can take place with the mutual benefit to both the woman and the man.

It is because tickets are almost sold out so the woman knows that her chances of getting tickets are low, thus she will be fine by exchanging her position for $25. On the other hand, a person standing back of the line also knows that he won't be able to buy the tickets if he stays there and thus, he will try to come closure to the ticket counter to increase his chances of getting tickets.

4) A politically apathetic person, who never votes, agrees to vote in an election for the candidate who pays him the highest amount.

The transaction will lead to the mutual benefit to both parties.

It is because voter will get the money and politician will get an extra vote.

5) William and Elizabeth are a wealthy couple who give birth to a baby with a minor birth defect. They sell this baby to their (equally wealthy) neighbours and buy a child without any birth defects from a family who needs the money.

The transaction won't lead to mutual benefit to both parties.

It is because the given proposal may benefit William and Elizabeth but it is not beneficial for their neighbors to buy a minor birth defect kid. They won't be willing to buy. Since having a baby involves many emotions and sentiments, thus a minor birth defect might not result in selling the baby because wealthy parents can treat their baby.

6) An individual with an adequate income, decides that he would like to sell himself to become the slave of another person. He finds a buyer willing to pay his asking price. The aspiring slave will use the money to further his children's education.

I don't approve this transaction for mutual benefit.

It is because if an individual has adequate income then selling himself to be the slave of another person for his children's future education is an irrational behavior.

Part B

What should be the role of government in providing public goods, limiting firms' power, addressing externalities or alleviating information problems? Use Naked Economics chapter 3 ,  Core Unit 12 or Sandel's Ted Talk to answer this question.  

The government intervention in the market economy arise in the case when market failure. It means that when the market fails and leads to market inefficiency, then the government intervention is required to operate the market effectively. The examples of market failure are: presence of externality, monopoly power, asymmetric information, and provision of public goods.

In these cases, the government enter in the market to control the monopoly firm by keeping their price under control, to control the negative externality by taxing their production, by creating a mechanism of providing relevant information to both trading parties to avoid the problem of asymmetric information, and to provide public goods which are important for society but expensive to produce for private sector.