Read from book

• sections 5.1 to 5.7 and the lecture

Institutions and power

• Institutions: Both written and unwritten rules that governs
  • interaction among people in a joint setting
  • the distribution of products in a joint setting
  • for example: when doing a group work, a document (contract) saying how people should interact in different scenarios with one another serves as an institution.

• Power: The ability to do and get things we want as opposed to intentions of others.

• Bargaining power: This can be understood using an ultimatum game between the proposer or responder. Recall that the power to construct a take-it-or-leave-it offer gives more bargaining power to the proposer compared to the responder, leaving proposer with more than half of the pie.
  • Note that the proposer’s power is still restricted as the responder can reject the offer (from previous lecture).
  • In cases where there are two responders, the proposer’s bargaining power will increase as the responders are more likely to accpet the offer because of increasing uncertaintly regarding what the other responder might do.

• Although games like ultimatum games are made up, the principles of the ultimatum game can be seen being unfolded in real events.

• Example 1: When an instructor assigns a homework.
  • Students can decide whether to do the homework or not. However, they will be penalized if they do not do the homework. However, power of instructor is restricted as well; she/he cannot penalize unreasonably.
• Example 2: Labor market: An employer can offer a wage.
  • Sure, the employee has a right to refuse the wage, but the employer might get another replacement. Hence, the employer usually has the higher bargaining power.

The Dictator Game

• Are there situations when the proposer of the ultimatum game hold all of the bargaining power and the responder holds none?

• Certainly. Some examples of the Dictator Game are:
  • Political dictatorship: The Democratic People’s Republic of Korea (North Korea)
  • Slavery: existing in the US prior to the Civil War in 1865

The Pareto Criterion to evaluate institutions and outcomes

• Vilfredo Pareto (1848-1923): Came up with a concept of pareto’s law to show income inequality. According to his 80-20 rule, 20 percent of people held 80 percent of wealth. It’s 90-10 in America.

• What’s Pareto efficiency?
  • A way of considering which allocation is more efficient.
• Let’s take Anil’s and Bala’s example from Lecture 4. Recall that each is deciding whether to use an insecticide called terminator (T) or Integrated Pest Control (I).
  

  Figure 1.

  

  Figure 2.

• (I, I) lies to the north-east of (T, T), so when both Anil and Bala use IPC, it dominates the outcome of using the terminator. The comparison tells us that allocation (I, I) is better than (T, T).

• However, three of the outcomes (I, I), (I, T), and (T, I) are not dominated by any outcome. Hence, these outcomes are Pareto efficient, meaning that there isn’t a better outcome that makes atleast one party better off and no party worse off.

Limitation of Pareto efficient allocation

1. There are often more than one Pareto efficient allocation. Don’t know which one is the most efficient in Pest control game.

2. What is Pareto efficient might not be what is fair. For example, Anil using IPC and Bala using Terminator is pareto efficient. But this is the case that Bala is free riding off of Anil.

Question

Which of the following statements about the outcome of an economic interaction is correct?

1. If the allocation is Pareto efficient, then you cannot make anyone better off without making someone else worse off.
2. All participants are happy with what they get if the allocation is Pareto efficient.
3. There cannot be more than one Pareto-efficient outcome.
4. According to the Pareto criterion, a Pareto-efficient outcome is always better than an inefficient one.

A Model of Choice and Conflict

• We will make use of Angela and Bruno to develop a model of choice and conflict, and evaluate allocation of resources. Let’s consider the following case:

• Angela is a farmer, who produce a crop. There are these scenarios that we’ll consider:

1. Angela works on her own, and gets everything that she produces.

2. Bruno then comes along. He is a person who at first forces Angela to work for him. In this case, Bruno is ethically worse than a dictator. Angela needs to do what Bruno says.

3. Then rule of law replaces the rule of force. Think of its Bruno’s land, but Bruno can no longer force Angela to work. Bruno can put forth an offer (part of the harvest) needs to come to him. But Angela gets to decide whether she wants to work for him.

Note that there are other cases in book, but we’ll only evaluate these two for the class.

Case 1. Angela works on her own.

Figure 3.

Note: The orange curve represents Angela’s production possibility frontier. The indifference curves are given by the blue curves. The optimal allocation is when the marginal rate of substitution (MRS) (slope of the indifference curve) is equal to the marginal rate of transformation (MRT, the slope of the frontier). - This happens at the tangential point C. At this optimal point, Angela would have 16 hours of free time and get 9 bushels of grain.

Case 2. Bruno comes along, uses force (e.g. guns), and claims some of Angela’s harvest

Figure 4.

• At point E, Angela gets 5.25 bushels of grain, but the other 5.25 bushels is taken by Bruno.
• The frontier is a combined frontier for both Bruno and Angela. Both outcomes G and F are feasible for Angela (note that Bruno decides these points). However, at point H, Angela gets nothing and can’t survive. Bruno does not like this outcome, as if this happens, Angela can’t work for him. So outcome H will not be feasible.
• Which allocation would Bruno pick?

Bruno’s pick

Figure 5.

• Bruno considers Angela’s survival condition when deciding how much of harvest to give Angela (or how many bushels to keep). Note that it is not benefecial to Bruno if Angela starves.
• So Bruno figures out Angela’s survival constraint. This describes the bundle of hours spent working and bushels required for Angela to survive. For example if Angela is working a lot, then she’d need a heafty bushels of wheat to replenish the lost calories, and survive. This describes the shape of the survival constraint in the figure (more hours worked, more bushels needed to replenish lost calories).
• The figure in the next slide shows the figure in more detail and points out the feasible set.

Bruno’s pick

Figure 6.

Bruno’s pick

Figure 7.

• The figure shows that providing 13 hours of free time and 4 bushels of grain to Angela is optimal for Bruno, where he takes 6 bushels of grain.
• The optimal is the bundle of which the distance between the frontier and survival cost is the maximum (A-B).
• Here, the slopes are equal to one another as well. Slope at point A (given by the tangent line) is equal to slople at point B.
  • We can think about this in terms of Marginal Rate of Transformation (MRT, slope of the frontier) and Marginal Rate of Substitution (MRS, slope of biological constraint). To the left of 13 hours of work the biological constraint is steeper than the frontier \((|MRS|>|MRT|)\), so by working an hour less Angela will be producing less but will also be requiring less grain to survive. The magnitude of grain that is left over due to working an hour less is more that what she will be able to produce when \(|MRS|>|MRT|\). So, Bruno will make her work to the point when \(MRS=MRT\).

Question

Figure 7 shows Angela and Bruno’s feasible frontier, and Angela’s biological survival constraint.

If Bruno can impose the allocation:

1. He will choose the technically feasible allocation where Angela produces the most grain.
2. His preferred choice will be where the marginal rate of transformation (MRT) on the feasible frontier equals the marginal rate of substitution (MRS) on the biological survival constraint.
3. He will not choose 8 hours of work, because the MRS between Angela’s work hours and subsistence requ

Case 3.

• Bruno is no longer using force as in Case 2. Bruno now owns the land and Angela must acquire permission to use his land for harvest. He no longer needs to use a gun because law is administered by the government and there are police to enforce the laws. Bruno can offer Angela a contract to use the land for farming, and in return agree to give her part of the harvest. Angela can decide whether to take up the offer from Bruno.
  • This is case with property rights: Bruno has rights for his land, and Angela owns labor.
  • However, note that Bruno is like the proposer of the ultimatum game. If Angela does not take up his offer, she goes hungry.
• We are interested in finding the economically feasible allocation when the exchange is voluntary. This is a set of points for which Angela would accept Bruno’s offer.

Case 3. Finding feasible set

Figure 8a.

• First find amount of grain that is required for Angela to survive without working. This is given by point Z, also the reservation option.

Figure 8b.

• Then use Angela’s indifference curve that passes through point Z (the reservation indifference curve). All the points on the IC yield similar value to Angela as to point Z. However, reservation IC is steeper than the biological constraint, as working x number of hours she needs to get more bushels as traced by the biological constraint. Otherwise she would not work.

Figure 8c.

• The area in between the Angela’s reservation indifference curve and the feasible constraint is the feasible set. And offer made in the feasible set, Angela will accept.
• If Bruno is profit oriented (objective to maximize profit), he chooses a point in the feasible set that gives him the most value.

Case 3

• Both Angela and Bruno can benefit if the offer is made in the feasible allocation set as shown in Figure 8c.
  • Bruno benefits if he gets anything (meaning if Angela accepts his offer), similar to the proposer of the ultimatum game.
  • Angela would take the offer as long as the offer makes her better off that the reservation option (any point on the feasible set).
• In other words, allocation that represent mutual gains (given by the feasible set) Pareto dominates the allocation that would not lead to a deal.
• However, Bruno has higher power.
  

  Figure 9.

• He chooses his optimal as in Case 2, but this time Angela’s reservation IC works as a constraint rather that her biological constraint.
  • MRS = MRT again.