In a particular school system, a teacher's aide must report to her teacher, and the teacher must report to his assistant principal, who then must report to her principal, who then must report to the superintendent, who ultimately is responsible to the board of education. this illustrates which characteristic of a bureaucracy?

I believe the answer to this question is authority. This statement clearly explains how power and authority is executed in form of personnel relations from low to high. 

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The business cycle is the periodic but irregular up-and-down movement in economic activity, measured by fluctuations in real gross domestic product (gdp) and other macroeconomic variables. a business cycle is typically characterized by four phases—recession, recovery, growth, and decline—that repeat themselves over time. economists note, however, that complete business cycles vary in length. the duration of business cycles can be anywhere from about two to twelve years, with most cycles averaging six years in length. some business analysts use the business cycle model and terminology to study and explain fluctuations in business inventory and other individual elements of corporate operations. but the term "business cycle" is still primarily associated with larger (industry-wide, regional, national, or even international) business trends.