COU 9: Calculating Probabilities Using a Marginal-Conditional Diagram

Infrastructure investments are not only made by governments, of course. Firms and wealthy individuals use their own cash and take out loans to build buildings, purchase long-lived machinary, and even to build roads, power generation facilities, ports, and other structures you might assume are only built by government. Politics, however, is just as important in private as in public infrastructure investments. Government policy can and does change over time, and thus private investors in an infrastructure project must consider how the future course of politics will affect their returns.

One especially dramatic (but rare) political risk that investors in a private infrastructure project face is nationalization. Governments sometimes decide that a privately-owned factory, road, or other facility ought to instead by owned and operated by the government, and will thus “nationalize” it – i.e. take it forcibly from its owners without compensation. Such “nationalizations” of foreign-owned facilities sometimes occurred, for instance, in the mid-twentieth century when nationalist rebels seized power from European colonizers in Africa, Asia, and the Middle East.

Imagine an investor who is considering funding the construction of a factory in a country in which three political parties – labeled Party A, Party B, and Party C – are vying for power. Suppose the investor can recoup the costs of building the factory so long as she is permitted a share in the profits earned by the factory during its operation over the next five years. Suppose, however, she is uncertain about two things:

Here is a marginal-conditional diagram of a model of this uncertainty:

Political risks of an investment

Prompt 1

Explain how to use the diagram above to calculate the marginal probability that the factory will be nationalized. Write your explanation as a series of steps (e.g. “Step 1…”, “Step 2…”, “Step 3…”, etc.), articulated in complete and coherent sentences, in your own words.

Prompt 2

Write the marginal probability that the factory will be nationalized.

Prompt 3

Explain how to use the diagram above to calculate the probability that Party B wins power conditional on the event that the factory is nationalized. Write your explanation as a series of steps (e.g. “Step 1…”, “Step 2…”, “Step 3…”, etc.), articulated in complete and coherent sentences, in your own words.

Prompt 4

Write the probability that Party B wins power conditional on the event that the factory is nationalized.

Rubric

Prompt 1

A completely correct answer to this prompt meets all the following criteria:

  1. It amounts to a list of instructions, with the items in the list clearly marked off from one another by (for instance) bullets, or headings such as “Step 1”, “Step 2”, etc.
  2. Each instruction in the list is composed of complete, coherent and easily understandable sentences.
  3. As a whole, the list of instructions correctly states how to use the diagram to compute the marginal probability that the factory will be nationalized.

You get four points if what you write meets all of criteria (A), (B), and (C). You earn three points if what you write fully meets criteria (A) and (C) but does not fully meet (B) only because of no more than three minor problems with spelling, grammar, or English usage that do not substantially hinder ease of understanding. You earn zero points otherwise.

Prompt 2

You earn one point if you write the correct answer and zero points otherwise.

Prompt 3

A completely correct answer to this prompt meets all the following criteria:

  1. It amounts to a list of instructions, with the items in the list clearly marked off from one another by (for instance) bullets, or headings such as “Step 1”, “Step 2”, etc.
  2. Each instruction in the list is composed of complete, coherent and easily understandable sentences.
  3. As a whole, the list of instructions correctly states how to use the diagram to compute the probability that Party B takes power conditional on the event that the factory is nationalized.

You get four points if what you write meets all of criteria (A), (B), and (C). You earn three points if what you write fully meets criteria (A) and (C) but does not fully meet (B) only because of no more than three minor problems with spelling, grammar, or English usage that do not substantially hinder ease of understanding. You earn zero points otherwise.

Prompt 4

You earn one point if you write the correct answer and zero points otherwise.