Question

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?

Answer 1

Answer:

The answers are:

A) 100,000 layer 1 supervisors; 10,000 layer 2 supervisors; 1,000 layer 3 supervisors; 100 layer 4 supervisors; 10 layer 5 supervisors; and 1 President

B) Including the President there are 111,111 supervisors

C) Including the federal workers at the bottom, there are 7 layers of federal employees

D) Including the President, the total amount of federal employees is 1,111,111 people

E)Almost 10%, the actual number is 9.999991%

Explanation:

The federal bureaucratic pyramid would be like this:

Layer 6 supervisor:                                                   1 president

Layer 5 supervisors:                                               10 people

Layer 4 supervisors:                                             100 people

Layer 3 supervisors:                                          1,000 people

Layer 2 supervisors:                                       10,000 people

Layer 1 supervisors:                                      100,000 people

The base of the pyramid (only workers): 1,000,000 people