Systematic shifts in scaling behavior based on organizational strategy in universities
Ryan C. Taylor, Xiaofan Liang, Manfred D. Laubichler, Geoffrey B. West, Christopher P. Kempes, Marion Dumas
Abstract
To build better theories of cities, companies, and other social institutions such as universities, requires that we understand the tradeoffs and complementarities that exist between their core functions, and that we understand bounds to their growth. Scaling theory has been a powerful tool for addressing such questions in diverse physical, biological and urban systems, revealing systematic quantitative regularities between size and function. Here we apply scaling theory to the social sciences, taking a synoptic view of an entire class of institutions. The United States higher education system serves as an ideal case study, since it includes over 5,800 institutions with shared broad objectives, but ranges in strategy from vocational training to the production of novel research, contains public, nonprofit and for-profit models, and spans sizes from 10 to roughly 100,000 enrolled students. We show that, like organisms, ecosystems and cities, universities and colleges scale in a surprisingly systematic fashion following simple power-law behavior. Comparing seven commonly accepted sectors of higher education organizations, we find distinct regimes of scaling between a school’s total enrollment and its expenditures, revenues, graduation rates and economic added value. Our results quantify how each sector leverages specific economies of scale to address distinct priorities. Taken together, the scaling of features within a sector along with the shifts in scaling across sectors implies that there are generic mechanisms and constraints shared by all sectors, which lead to tradeoffs between their different societal functions and roles. We highlight the strong complementarity between public and private research universities, and community and state colleges, that all display superlinear returns to scale. In contrast to the scaling of biological systems, our results highlight that much of the observed scaling behavior is modulated by the particular strategies of organizations rather than an immutable set of constraints.
Highlights
Revenue and expenses at universities and colleges follow power law behavior with respect to enrollment
“We show that, like organisms, ecosystems and cities, universities and colleges scale in a surprisingly systematic fashion following simple power-law behavior.”
Most socioeconomic metrics scale with population as a power law with exponent 1.15
“from total wages and GDP to the number of social interactions and number of patents produced, scale with population size as a power law with an exponent of 1.15.” … “Consequently, on a per capita basis, socio-economic metrics increase proportionally to X0.15, implying that on a per capita basis, larger cities promote more social interactions and greater production of patents, and therefore more innovation”
On average, universities and colleges scale revenue and expenses linearly with student enrollment
“financial throughput scales linearly with size, suggesting that, on average, there is no advantage to being larger at least as far as these economic indicators are concerned”
Research universities scale revenue and expenses superlinearly with respect to enrollment
“research universities (both public and non-profit private) scale superlinearly: as they enroll more students, their revenues and expenditures increase faster than linearly” … “Research universities (public and private) scale superlinearly in all activities and sources of revenue, but sacrifice affordability. As they grow larger, they seek to attract increasingly prestigious faculty (as indicated by the superlinear scaling in faculty pay, especially in private universities) and charge higher tuition, also attracting better-resourced students, who later on enjoy higher earnings. The fact that both research and educational outcomes scale superlinearly suggest that these activities are synergistic.”
Community colleges demonstrated sublinear scaling with respect to enrollment, leading to declining per capita spending as they scale:
“community colleges and state colleges display remarkably sublinear scaling, that is, financial throughput per student decreases with size, representing strong overall economies of scale”
“non-profit private colleges and professional schools scale roughly linearly with size, indicating little advantage in being larger”
For profit colleges demonstrate linear revenue scaling and sublinear expenditure scaling, implying rising profit margins as they scale:
“for-profit colleges display linear scaling in revenue but sublinear scaling in expenditure, which implies that they are able to make aprofit by exploiting economies of scale in their costs.”
“Maintenance and administrative costs scale slightly superlinearly, but do not systematically outpace production processes (teaching, research and student completions). This indicates that there are no apparent diseconomies of scale in maintenance function. On the contrary, efficiency in maintenance seems to support the diversification of activities”
“average mid-career earnings increase with a school’s mean test scores and its out-of-state tuition costs”