1.3 The Equilibrium
1.3.2 When resources and adaptative-skills are non-contractible
When de…ning the rules of the prizes, the Government may establish the monetary values gi; i = A; B; I; conditional on the production level, y~i: Given that there is no uncer-tainty in the production, these funding rules determine the level of the productive e¤orts.
Furthermore, since (gi;y~i)can di¤er between …elds, there is still su¢ ciently ‡exibility to choose the …rst-best option of the Government, namely in terms of the type of research.
However, it may be interesting to study how the decision variables of the University, ef-forts and acquisition of the adaptative-skills, depend on the funding rules. This section analyses it in detail.
The choice variables of the Government are now: …rst, the type of research, special-ization or interdisciplinarity; second, the funding rules for specialspecial-ization, (gA;y~A) and (gB;y~B); and for interdisciplinarity,(gI;y~I):
Once accepting the proposal of the Government, and facing a discrete-type of re-ward (getting or not the prize), the University decides on the resources spent, and on the investment in the adaptative-skills. Because there is no extra-bene…t of producing above the required standard, a pro…t maximizer institution seeks the most e¢ cient way of producing, at most, that level.5
Proposition 1.3.3 Given the funding policy for …eld i; (~yi; gi); i = A; B; I; the best
The investment in the adaptative-skills is increasing in both policy variables, y~I and gI :for smaller valuesgI andy~I;the University prefers not to acquire any adaptative-skills; for intermediate gI andy~I; it invests in the researcher that is closer to …eldI;
and for high values of gI andy~I;it acquires both adaptative-skills. When 2 0;12 ;
The outside option of no research is preferred: i) to specialization when the standard
5This conclusion is in line with Result 1 of Betts (1998).
~
yi is at least gi
i, i=A; B; ii) and to interdisciplinarity wheny~I is at least
~
yI11 = mA 1mB gI 1 1 .
As in the benchmark situation, the acquisition of the adaptative-skills depends posi-tively on the amount of funds available for the interdisciplinary project. Having to choose how to spend the funds, the priority is to remunerate the inputs necessary to produce and, only after, to invest in more e¢ cient ways of producing.
More interesting is to notice that, even if the prize gI allows to acquire adaptative-skills, the optimal decision is contingent on y~I: As the required production increases, it also increases the e¤ort the researchers must exert to accomplish it. But the higher the e¤ort, the higher the bene…ts of acquiring adaptative-skills. Thus, only when the pol-icy is su¢ ciently demanding, the investment is made. This result follows from Lemma 1.2.1 . Formally, I can derive the conditions for University’s best choice ( A; B)through the upper envelope-curve of the pro…t curves UI ( A; B), when considering the di¤erent possible combinations of( A; B): Figure 1.5 illustrates the reasoning, plotting the maxi-mum interdisciplinary pro…t of the University as a function of the standardy~I. The …gure stands for the case of a prize su¢ ciently high to allow the acquisition of skills for both researchers, i.e.,gI gI10.
Figure 1.5: Maximum interdisciplinary pro…t, for 2 0;12 :
From the solution of the interdisciplinary problem stated in Proposition 1.3.3, it is possible to derive some comparative statics results.
Corollary 1.3.3 At the optimal solution for the University, the e¤ort of researcher i in the interdisciplinary project, eUiI; increases when: i) his cost coe¢ cient i decreases, or the cost coe¢ cient of the other researcher j increases, ii) he acquires adaptative-skills ( i = 1), or the other expert does not ( j = 0), j 6=i. A negative relation betweeneUAI and
is guaranteed when (1 A)mA > 1 :
To produce the required y~I at the most e¢ cient way, whenever the productive mar-ginal cost of one expert decreases, the University should increase his contribution for the common project, so that @e@UiI
i <0. By a similar argument, and using the complementary characteristic of interdisciplinarity,i should work more whenj’s marginal cost increases,
@eUiI
@ j > 0. Since the productive marginal cost of the researchers depends negatively on the acquisition of the adaptative-skills, in the optimal solution @e@UiI
i > 0 and @e@UiI
j < 0:
Regarding the impact of the distance parameter on the level of e¤orts chosen by the University, opposite e¤ects emerge. Because determines not only the cost of producing the interdisciplinary output, but also the process of production itself, ambiguity is solved when the relative marginal cost of eAI is higher than the relative importance of eAI for the interdisciplinary production. Under such restriction, a negative relation betweeneUAI and stands out.
Corollary 1.3.4 Given the funding policy of the Government for interdisciplinarity (~yI; gI); the maximum pro…t that the University may obtain with this type of research, conditional on the acquisition or not of the adaptative-skills, is given by
U
which increases with: i) a higher value of the prize, gI; and ii) a smaller productive marginal cost for the researchers; i.
When 2 0;12 and A = B = ; a marginal increase in decreases UI ( A; B),
The achievement of a given standard, with higher productive marginal costs, necessar-ily leads to a smaller interdisciplinary pro…t, meaning that @@ UI
i ( A; B)<0:Considering the e¤ect of in the interdisciplinary pro…t, the conclusion is ambiguous for general values of the parameters. Nevertheless, when A= B = and the researcherB (the researcher furthest fromI) is su¢ ciently costly, I may conclude that @@M UI ( A; B)<0:
In the particular setting of our analysis, two characteristics have a signi…cative role for the results. First, the lack of incentive of the University to exceed the standard, o¤sets the potential asymmetric information problem. Second, since the funding rules may di¤er between …elds, the Government has enough ‡exibility to implement the …rst-best solution.
Corollary 1.3.5 Let (eA; eB) and ( A; B) be non-veri…able. Assuming that the Gov-ernment can choose di¤erent funding policies (~yi; gi) for each …eld i (i=A; B; I); it is still possible to achieve the …rst-best solution. Then, the funding rules for the specialized
projects must be y~A = yA; y~B = yB; gA = A yA; and gB = B yB; whereas for the interdisciplinary research y~I( A; B) =yI( A; B); and gI =G:6
The …nal decision on which type of research must be contracted, follows from the comparison of the maximum social welfare on both situations. Interdisciplinarity is the best choice for the society whenVI(~yI) VAB(~yA;y~B):