Microeconomics 20th Edition by McConnell, Sean Flynn, Stanley Brue

Exercise 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-of-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.
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