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This paper provides a theoretical framework for explaining counterintuitive behaviors of a university choosing an unfavorable consequence in the long term while attempting to optimally allocate its resources in the short term. Our analysis demonstrates the process through which conflicting in terests among different departments within an institution may lead to an internal allocation arrangement, which would not necessarily yield the highest possible outcome for the whole.

Regardless of profit or non-profit nature of productive activities, every organization faces the challenge of achieving objectives through internally allocating limited resources. An institution of higher education, for instance, is recognized as a prestige-seeking entity allocating limited resources among academic units, while providing multiple products and services for their stakeholders, which include students, parents, communities, and governments [

This paper lays out a simple theoretical framework for understanding a counterintuitive outcome of such conflicting behaviors leading to an unfavorable consequence while an institution attempts to optimally allocate resources into multiple activities. The analysis is carried out particularly with not-for-profit organizations such as higher education institutions and hospitals in mind, whose aims are considered to be serving the public need under financial constraints, yet seeking to improve social reputation or prestige [

Assume that an institution of higher education provides N distinguishable fields of study as well as functionally differentiated outputs such as student teaching, research, community services, or a mixture of these services, from which it gains separately independent prestige

and thus

for

The basic setup formulated as above enables us to explore the optimizing allocation arrangement, which maximizes the overall prestige of an institution.^{1} Considering that the institutional activities are bound by the

resource constraint

with the required first-order condition

The second-order condition for maximization

must also be satisfied for an arbitrary vector of

Proposition 1. For a sufficiently small amount of available resources, a university never finds the optimal allocation set, which yields the highest possible institutional prestige.

Proof: See Appendix.

For intuitive validity of Proposition 1, assume a university with N = 2 and an allocation arrangement^{2}

In this section, we assume that the total financial resources granted to a university (by the state or other stakeholders) in one period is proportionate with the institutional prestige established in the previous period. The university strives for the highest possible overall prestige, as exemplified in global university rankings, through optimally allocating the available resources as much as the internal “adjustability” permits, which of course is confined by the internal rigidity existing due to conflicting interests among competing departments [

Assume that the total budget granted to a university in period

period

Suppose now that a university begins its operations at ^{3} Given the initial resources and allocation, the university earns the total prestige ^{4} The adjustment made from the preliminary allocations

In practice, however, there might be internal rigidity in altering the allocation ratio assigned to each department, which makes it difficult for an institution to change the allocation composites drastically from the previously assigned ratios, as noted by Johnson and Turner [

In order to accommodate such internal rigidity, the adjustment made from the initial allocation set

where

and (4) are defined for all the departments for which the resource allocated in the previous period was not equal to 0. The inequality in (3) means that a large modification in the allocations does not occur unless a large increase in the total prestige can be expected as a result of the modified arrangement. The inequality in (4) simply describes the condition whereby even if a large increment would be obtained in the total prestige, the modification of the arrangement is limited by a certain ceiling. Both

late the organizational adjustability to internally shift the allocations from the initial

Proposition 2. Given any initial conditions, a university reaches the optimal allocation arrangement at which the maximal prestige is achieved: 1) with all

Proof: See Appendix.

What is stated in Proposition 2 appears a sterile result at first, but an important implication drawn from Proposition 2 is that the point of convergence may represent an inferior state for a university in terms of achieving the highest potential objective. In the following subsection, it is demonstrated for a heuristic example with

Suppose that a sufficiently funded university with

severe budget cut, then the optimizing position shifts from the local maximum (point A) to the global minimum (point B) as depicted in

Then, whether the new allocation set moves to the right or left from the prestige minimizing point B depends on the highest overall prestige found “within the mobility range”. In the graph, the new allocation set is reached

at point C, where the level of gained institutional prestige is the highest within the “ticked range”. If the institutional budget in period

As described so far, the process would typically repeat over the courses of modified allocations and corresponding overall prestige, ultimately reach the leftmost “corner solution” where the total budget

This paper examines an important scenario, which a standalone institution of higher education is predicted to follow in order to achieve its potential maximal performance when the available resources are severely limited. Our result clearly indicates that a collection of multiple departmental performances does not necessarily yield the highest level of institutional prestige; that is, diversification of functional specialties is not necessarily the prudent approach to attaining the highest potential recognition when a university faces a scarcity in its financial resources. We also find that the limited internal adjustability caused by conflicting interests within a university impedes the goal of attaining the best outcome in the long term although the university “optimally” allocates its resources in the short term.

This paper was completed while S.P.W. was a visiting scholar at the University of California, Berkeley. We are grateful to colleagues at UC Berkeley for valuable comments and discussions on earlier drafts of the paper and would like to express sincere gratitude for all the encouragement and general resources provided by the Center for Studies in Higher Education and UC Berkeley.

YasumiAbe,Satoshi P.Watanabe, (2015) Implications of University Resource Allocation under Limited Internal Adjustability. Theoretical Economics Letters,05,637-646. doi: 10.4236/tel.2015.55074

Proof of Proposition 1

For all the

Suppose the resource allocated to the Nth field is

More explicitly,

and the individually allocated resources sum to

It is obvious that

For the uniqueness of the (global) minimum in the interior, suppose the total resources available for the institution is reduced further to an extremity such that

Suppose there exists, other than

The result in (A2) clearly indicates

Suppose further that optimization is sought with the closures of

Proof of Proposition 2

Let

Scenario 1.

Since

The equality

Scenario 2.

If the total resources granted in period

To summarize both scenarios, other than the clearly convergent cases, the total resources

・ Strictly increasing

・ Strictly decreasing up to a certain point, then strictly increasing thereafter

・ Strictly decreasing

The common feature for all three paths is that they eventually turn to monotone sequences (either strictly increasing or decreasing). Since the sequence ^{5} If

We first note that convergence of

two separate movements from the set

with corresponding changes in the total prestige

Substituting the definition

Therefore, the convergence of sequence

has a positive sign, which affirms that the right-hand side of the inequality in (A8) converges to 0. This means that

If the point of convergence does not yield any of 1), 2), and 3) stated in Proposition 2, the value of prestige added by the modification process from