Academic Crossover and Functional Differentiation of Universities

This study is motivated by a theoretical deficiency in the research on internal resource allocation and functional differentiation of higher education institutions in relation with their prestige maximizing behaviors. Our finding, despite its purely theoretical nature, suggests that a prestige-maximizing college or university achieves the highest potential prestige by optimally allocating its limited resources and equalizing the prestige of the closely associated academic departments or disciplines. The result certainly indicates that the interdisciplinary activities and functional differentiation, which represent two major efforts found in the recent higher education community, have indeed counteractive effects on their separate objectives.


Introduction
Academic crossover as typified by interdisciplinary research and learning have contributed tremendously to the creation of new knowledge in nearly every aspect of today's multifaceted human activities.At large research universities in the US, internal resources are strategically allocated to encourage such cross-disciplinary activities to further enhance collaborative research and development.Yet, another noteworthy trend found in an increasingly diverse higher education environment is the rising importance of differentiating institutions with regard to their missions or functions (Gumport and Bastedo [1]).For instance, state-funded colleges and universities with multiple campuses in the US are often concerned about the cost-effectiveness of their regional system in funding redundant academic instruction and research activities (Nelms et al. [2]).A vital question from the perspectives of public finance and higher education policy, then, is whether or not these two forces, i.e., academic crossover and mission differentiation, produce synergetic effects that enhance, or counteractive effects to impede, the attainment of their separate objectives.
A theoretical foundation laid by Abe and Watanabe [3,4] provides a mechanism which helps us understand optimizing behaviors of colleges and universities with regard to internal resource allocation and maximization of institutional prestige.Abe and Watanabe [5], using the same analytic apparatuses further show that different institutional funding schemes could cause different impacts on the extent to which functional differentiation is achieved by colleges and universities.However, the theoretical model developed by Abe and Watanabe hinges on an additively separable form of prestige functions, for which each institution of higher education is considered to simply maximize the sum total of prestige, earned independently in separate academic disciplines and/or functional activities offered by the institution.The additive separability is an unattractive feature for the analysis, particularly if different academic disciplines, e.g., economics, physics, and psychology, contribute non-negligibly through combined efforts to new knowledge production, which in turn leads to enhancement of academic strengths and eventually of overall institutional prestige.
This study is motivated by the theoretical deficiency in the relevant research and addresses the issue by explicitly incorporating the correlation potentially existing between different academic disciplines.Our main finding suggests that academic overlapping across multiple disciplines within an institution yield a neutralizing effect on the focus of the involved fields.That is, the result indicates that collaborative efforts involving multiple departments could impede functional differentiation of higher education institutions.

Basic Framework
Preceding studies exist in the literature, which perceive the industry of higher education as a marketplace where individual colleges and universities, acting as prestige or reputation maximizers, offer multiple products and services such as student instruction, research output, and community services, for their stakeholders which include students, alumni, communities, and governments (Baumol et al. [6], Breneman [7], Brewer et al. [8], Cyrenne and Grant [9], Del Rey [10]).Abe and Watanabe [3,4], in particular, demonstrate a mechanism through which optimal allocation arrangement of resources is sought by an institution of higher education in pursuit of the highest institutional prestige.The proposed model conceives the total prestige of an institution as the sum of the partial prestige collected from each field where represents partial prestige independently earned esource i in disciplines 1, , i N   , with x i being the corresponding financial r nput.We assume d d 0 i i p x  and that an institution allocates its limited reso so as to maximize its overall prestige.


Although the f hat a university attempts to maximize a indings by Abe and Watanabe contribute to a fundamental understanding with regard to internal resource allocation and attainable prestige for colleges and universities, the additive separability of the prestige function certainly limits its full applicability, particularly when collaborative work by multiple departments jointly produce synergizing effects on the enhancement of institutional strengths.
Assume instead t more generalized form of prestige function   i P p , which is not necessarily an additive separable func f and satisfies 0 with the required optimality conditions is captured by the possible prestige hypersurf as the effect of the change in the functional form of the prestige function ace, where   i P p is captured by the iso-prestige hypersurface.Thus ffects of these two changes on the optimization may be analyzed and discussed separately.
, the e

Analysis
the following id tru .
Using the identity (4), we derive from which we obtain . Similarly, g both s iden with respect to 1 p gives differentiatin ides of the tity (5) which also yields sought where the tw tangent,   d  d , The new maximum is attained on the identical possible pr Expanding the Equation ( 9) to the first-order approxi m δp , and δP , and using the result (10) gives The slope of the iso-prestige c rve at δp may be rewritten as


The last term  1 2 π , p p represents the between the two disciplines and is assumed to satisfy 1 correlation ) ; and 4) Using th esult in Equation ( 7), e r are satisfied, 2 a university with two associated academic fields s an incentive to allocate its i ternal o es so as to gain an equal level of prestige in both fields.Thus, the result suggests that the functional differentiation among universities becomes more difficult when they manage the identical set of correlated disciplines and/or institutional activities than otherwise.This study predicts tion cross-disciplinary disciplines/activities with regard to the extent to which functional differentiation is achieved.Our finding, despite its purely theoretical nature, demonstrates that there exists a compelling force for a prestige-maximizing institution to make an internal allocation arrangement so as to gain the equal level of prestige for separate but correlated disciplines/departments.The result certainly indicates that the academic crossover and functional differentiation, which represent two major trends observed in the recent higher education industry, have counteractive effects on the attainment of their separate objectives.The analysis is also readily applicable to other scenarios, such as an institution attempting to differentiate its mission by undergraduate student instruction (e.g., as a liberal arts college) versus placing heavier weights on graduate teaching and faculty research (as a research university).The future agenda certainly involves empirical research with existing data and testing the validity of the proposed model as well as the predicted outcomes.

Figure 1 .
Figure 1.Shift in the optimizing point as a result of change in the functional form of prestige function.

2 ,
p p , the sign of ined by whether the the iso-prestig urve at smaller than -1 after the change in tional form P. the func We know with certainty that nd

ollege omics 2 s
For a heuristic analysis with N = 2, consider a c with only two academic departments, e.g., econ and physics, maximizing the objective function ,