Chapter 05 - Government's Role and Government Failure
5-7
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PROBLEMS
1. Suppose that there are 1 million federal workers at the lowest level of the federal bureaucracy
and that above them there are multiple layers of supervisors and supervisors-of-supervisors.
Assume that each higher level is one-tenth the size of the one below it because the government is
using a 10:1 ratio of supervisees to supervisors. That is, for every 10 workers at the bottom, there
is 1 supervisor; for every 10 of those supervisors, there is 1 supervisor-or-supervisors; for every
one of those supervisors-of-supervisors, there is a supervisor-of-supervisors-of-supervisors; and
so on, all the way up the bureaucratic pyramid to the president. LO1
a. How many supervisors will there be in each supervisory layer of the federal bureaucracy? Start
with the layer of supervisors directly above the 1 million workers at the bottom.
b. How many supervisors are there in total at all levels of the federal bureaucratic pyramid,
including the president?
c. If you count the 1 million workers at the bottom as the first layer of the federal bureaucracy,
how many total layers are there, including the president?
d. How many federal employees are there in total at all layers, including the president?
e. What fraction of all federal employees are supervisory, including the president?
Answer:
a.100,000; 10,000; 1,000; 100; 10; 1.
b.111,111 = (100,000+10,000+1,000+100+10+1).
c.7 total layers corresponding to the 1 million workers at the bottom and then six layers
of supervisors above them (the 100,000, then the 10,000, then the 1,000, then the
100, then the 10, then the president.)
d.There are 1,111,111 total federal employees (=1 million workers at the bottom +
111,111 supervisors, including the president).
e.9.999 percent (which can be rounded up to 10 percent) of all federal employees,
including the president, are supervisory.
2. Consider a specific example of the special-interest effect and the collective-action problem. In
2012, it was estimated that the total value of all corn‐production subsidies in the United States
totaled about $3 billion. The population of the United States was approximately 300 million
people that year. LO2
a. On average, how much did corn subsides cost per person in the United States in
2012? (Hint: A billion is a 1 followed by nine zeros. A million is a 1 followed by six zeros.)
b. If each person in the United States is only willing to spend $.50 to support efforts to overturn
the corn subsidy, and if anti‐subsidy advocates can only raise funds from 10 percent of the
population, how much money will they be able to raise for their lobbying efforts?
c. If the recipients of corn subsidies donate just one percent of the total amount that they receive
in subsidies, how much could they raise to support lobbying efforts to continue the corn subsidy?
d.By how many dollars does the amount raised by the recipients of the corn subsidy exceed the
amount raised by the opponents of the corn subsidy?
Answers: (a) $10 (b) $15 million (c) $30 million (d) $15 million