Microeconomics, Module 18, “Externalities” (Chapter 13)

Homework

(The attached PDF file has better formatting.)

The Coase Theorem applies to many social activities. We illustrate with study time for actuarial exams.

An insurer provides its actuarial students with 120 hours of study time for each exam. The insurer presumes that candidates study six months for each exam, so study time is 20 hours a month. Each month has 20 work days, so study time is one hour a day. This is the official schedule, but trading among candidates and managers change the schedule.

The study program allows both managers and candidates to exchange study time among days, as long as they both agree with the exchange. The exchange rate may be 1 hour for 1 hour or any other rate, such as 1 hour for 2 hours; see below.

We use several assumptions to highlight the effect of transaction costs:

●    Candidates value study time more than managers do; managers value work more than candidates do.
●    Candidates prefer study time closer to the exam date. If the exam date is November 15, candidates prefer an hour of study time on Nov 10 to an hour on June 10. Preferences vary: some candidates prefer to study an hour each day and some candidates prefer to study heavily the month before the exam and enjoy leisure time the month or two after the exam.
●    Work pressure is heaviest in mid-May and mid-Nov. Work pressure increases steadily from December through mid-May and from June through mid-November. Work pressure varies: sometimes it is heavy during the off-peak summer months and light during the peak months of April, May, October, and November. (This is not realistic, but it is useful to illustrate the effects of transaction costs.)
●    Candidates can trade study hours with their managers. A candidate may offer to trade two hours in February for one hour in early May, since the early May hours are more valuable to candidates than the January hours. A manager may offer to trade one hour in early May for two hours in February, since work pressures are greater in early May. (These trades are in the opposite directions; each party prefers the May hours.)

We consider two scenarios.

●    Scenario YY: Transaction costs are zero. Each actuarial candidate trades with his or her manager; no other approvals are needed.
●    Scenario ZZ: Transaction costs are high. Each trade must be approved by all the Fellows in the Actuarial Department and by all candidates in the department. Fellows are reluctant to approve trades that seem too favorable to candidates and candidates are reluctant to approve trades that seem too favorable to managers. (We use Fellows interchangeably with managers.)

Homework #1: Which scenario generates greater social welfare? Use the following logic:

●    Each trade is done only if it creates benefits for both sides. If a candidate trades two study hours in February for one study hour in early May, the manager gains one hour of work and the candidate gains study time that is more valuable.
●    Transaction costs impede trade and create less social welfare.

Homework #2: To reduce the transaction costs but retain department control over trades, two options are considered:

●    Option #1: Trades must be approved by a committee of Fellows, but not by candidates.
●    Option #2: Trades must be approved by a committee of candidates, but not by Fellows.

Assume that salaries for candidates and study time are negotiated with no transaction costs. More study time makes the jobs more desirable and causes lower salaries; less study time reduces candidates’ desire for these jobs and requires higher salaries.

Assume that candidates are much concerned with the distribution of study hours during the year; they much prefer study hours right before the exam dates. Managers are not much concerned with the distribution of study hours during the year.

●    The Fellows say that study time is a privilege, not a right, so Fellows should approve all trades, not candidates.
●    The candidates say that study time is a right, not a privilege (just like salary); since candidates have the greater concern about the distribution of study time during the year, they should approve the trades.

Which perspective would Landsburg agree with? Explain how the proper choice creates greater social welfare gain for both candidates and Fellows. (The better choice allows the Fellows to negotiate lower salaries.)

I think that Option #1 is a proper choice. The reason is as follows. If a trading initiated by a candidate is proved, then there are more work hours but less study hours. Therefore, the job become less desirable to those candidates. Now if the fellows were to make the decision, the candidate who filed the case would wish to bribe the follows by offering not to get a pay-raise in the future. Therefore, the follows are happy to make thoses candidates happy. Does this make any sense?

In the beginning part of the homework, it states that work pressure increases as the time to exams increases - in other words, that BOTH managers and candidates value hours in early May more than those in February. However, in Part 2, it says we are to assume that managers are not much concerned with the distribution of study hours during the year - which is it?

I am totally lost on the second part. If only fellows approve trades, won't they tend to accept any trade that lowers the overall number of study hours, regardless of when those hours end up being used (since they are "not much concerned with the distribution")? The result would be that fellows could offer a greater number of study hours, and hence a lower salary, knowing that some of these study hours will be lost in bargaining to schedule them as the candidates prefer. The candidates benefit from a better study schedule, the fellows benefit from the lower negotiated salary.

But that seems counter-intuitive... shouldn't the candidates have to pay for the right to approve trades by accepting lower salaries too?

From a common sense perspective, it seems that since candidates have preferences not held by the fellows, a committee of candidates will only approve FEWER trades than a committee of fellows - hence Option #2 has a higher transaction cost and generates less social welfare.

OK, how does this reasoning sound...

Suppose we assume the company gives new employees 20 hours each in February and May.
* To a CANDIDATE, 2 February hours are worth 1 May hour
* To a FELLOW, 1.2 February hours are worth 1 May hour
That is, fellows have a preference for May over February, but it is not as strong as candidates preferences.

The only way a trade can occur is for a candidate to give up X February hours (where X is bigger than 1.2 but smaller than 2) for 1 May hour - no fellow will agree to the reverse trade, because it decreases the number of hours worked.
* The candidate gains 2 - X study hours (in units of February hours)
* The fellow gains X - 1.2 work hours (in units of February hours)

Now suppose we require approval by a committee.
* Candidates on the committee will not approve trades in which the fellow gains more than, say, 0.6 hours - that is, candidates will approve only exchange rates LOWER than 1.8 February to 1 May.
* Fellows on the committee will not approve trades in which the candidate gains more than, say, 0.6 hours - that is, fellows will approve only exchange rates HIGHER than 1.4 February to 1 May.

Suppose, on average, that candidates will have the following distribution of trades when there are no transaction costs:
I) 5 hours are traded at 1.9 to 1 (0.1 to candidate, 0.7 to fellow)
II) 5 hours are traded at 1.6 to 1 (0.4 to candidate, 0.4 to fellow)
III) 5 hours are traded at 1.3 to 1 (0.7 to candidate, 0.1 to fellow)
IV) 5 hours are not traded (remain in February)
As a result, the average candidate will end up with 29.6 May hours and 5 February hours, for a total of 34.6 hours. The candidate gains the equivalent of 4.2 hours of February study time while the fellows gain 3.5 hours of February work time.

Now if trades are approved by a committee of only fellows, III will not occur. The candidate ends up with 25.8 May hours and 10 February hours, for a total of 35.8 hours. The candidate gains 1.5 hours and the fellow gains 3.1 hours.

If trades are approved by a committee of only candidates, I will not occur. The candidate ends up with 27 May hours and 10 February hours, for a total of 37 hours. The candidate gains 3.9 hours and the fellow gains 1.6 hours.

If trades are approved by a committee of BOTH, I and III will not occur. The candidate ends up with 23.1 May hours and 15 February hours, for a total of 38.1 hours. The candidate gains 1.3 hours and the fellow gains 1.3 hours.

In this case, having a committee of CANDIDATES is:
* Good for the candidates because they have the biggest gain from trade (3.9 > 1.5 > 1.3)
* Good for the fellows because they can offer the highest number of total study hours and
with it negotiate a lower salary.

Of course, if the expected distribution of proposed trades is different, the result can be different too! If we now say that candidates wish to trade 2 hours at 1.9:1 and 8 hours at 1.6:1 (while still trading 5 hours at 1.3:1), then the results are:

Committee	May Hours	Feb Hours	Total Hours	Candidate Gain	Fellow Gain	Total Gain
Neither	29.9	5.0	34.9	4.8	3.1	7.9
Candidates	28.8	7.0	35.8	4.7	2.4	7.1
Fellows	26.1	10.0	36.1	2.1	2.7	4.8
Both	25.0	12.0	37.0	2.0	2.0	4.0

In this instance, a committee made up of candidates will increase the gain of the candidates, but will not produce as many total study hours (and hence as low of a salary) as a committee composed of fellows.