Should the subsidization of RJVs be made public knowledge?
396 M.P. Gos´albez, J.S. D´ıez J. of Economic Behavior Org. 42 2000 385–404
substitutes’. As we already know, with strategic substitutes, if firm 1 discloses the subsidy, firm 2 reacts by decreasing effort, which hurts firm 1. This effect should obviously reduce the
region of separating equilibria, relative to the strategic complements case. Fig. 3 confirms our intuitions.
9
On the other hand, observe that as the subsidy increases, the interval of separating equilibria is enlarged and the interval of pooling equilibria is reduced. Finally,
notice that for λ values lying between each pair λ
S
, λ
P
for a given subsidy s, both a pooling and a separating equilibria simultaneously exist.
7. Should the subsidization of RJVs be made public knowledge?
In the previous sections, we have shown that depending on the way in which the partners ex ante share the total expected profits of the project and on the strategic relationship between
the efforts, pooling equilibria exist in which the subsidized firm prefers not to reveal the existence of the subsidy to its partner.
An interesting normative question arising from the previous analysis is whether from a social point of view it might be desirable to impose more strict rules requiring the public
disclosure of any subsidy granted in European cooperative RD programs such as Eureka. In order to answer that question we first need to calculate the optimal efforts from a social
point of view the efforts a supranational institution such as the EU would like to implement and, second, we have to evaluate and compare welfare with and without information release
regulation and check whether the proposed technology policy would be able to increase total welfare. Notice that the proposed policy would affect the equilibrium efforts and welfare
only when, in absence of the proposed policy rule, we would have a pooling equilibrium. We shall proceed to compare both regimes, taking as given the cost subsidy granted to
firm 1. At the end of this section, however, we will discuss the possibility that the active country could react to the establishment of a rule that enforces information releasing by not
subsidizing its firm any longer. Regarding welfare, we obtain that for the case of strategic complements, the proposed policy rule is welfare improving. The line of the arguments is
as follows: let us consider the following welfare function:
10
W = E5
1
+ E5
2
− S, 7.1
where S denotes the total amount subsidized and let us denote by e
C 1
, e
C 2
the efforts that maximize function W . In Appendix B, we calculate the efforts that solve 19 and compare
these efforts with the equilibrium efforts for the case of strategic complements. We obtain that if the subsidy is not too high in particular not higher than 0.646 the equilibrium efforts
are suboptimal. Therefore, if we assume that the subsidy s is below that level and given that the welfare function is concave in both efforts, all we have to do is to check whether the
proposed policy increases the equilibrium efforts. However, these efforts coincide with the equilibrium efforts we obtained for the case of disclosure, that is, e
R 1
, e
R 2
, and we know
9
We have simulations for different patent values but the results are qualitatively identical.
10
Given that we do not model explicitly the innovation market, consumer surplus is not included in the welfare function. We only consider the sum of the firms’ expected profits minus the cost of the subsidy for the social
planner.
M.P. Gos´albez, J.S. D´ıez J. of Economic Behavior Org. 42 2000 385–404 397
Fig. 4. Total welfare.
by Proposition 3.1 that, with strategic complements, the disclosure of the subsidy leads to higher efforts in equilibrium, that closes the argument. Finally, notice that regarding firms’
relative performance the public disclosure of subsidies would hurt firm 1 and benefit firm 2. On the other hand, if the efforts are strategic substitutes, the public disclosure of the
subsidy leads firm 1 to exert a higher effort and firm 2 to exert a lower one. Therefore, in this case we cannot predict in general what the net effect of the proposed policy on welfare
would be. In order to illustrate this case, Fig. 4 represents in the W, s space the results of a numerical simulation comparing welfare in three different situations, namely, the first
best W C, a situation with information release regulation W R and a situation with no information release regulation W SN.
11
The comparison is made for V = 0.5 and for the case of a pooling equilibrium in which ˜
q = q = 0.5 and t = 0. Fig. 4 shows
that, for those particular values of the parameters, under strategic substitutes the proposed technology policy would, in fact, decrease total welfare.
So far, we have taken as given the subsidizing policy of the active country. However, an interesting question to consider would be the following. Would the imposition of a
technology policy that enforces the public disclosure of subsidies lead the active government to cease to subsidize its firm?
In order to answer that question, we would have to compare total welfare for the subsiding country, that is, W
1
= E ¯ 5
1
− S, resulting from both a situation in which the government
11
Due to the complexity of the expressions obtained for efforts, transfers and welfare in the case of strategic substitutes, Fig. 4 has been obtained by evaluating the welfare functions for many particular values of the subsidy.
Therefore, we can take those functions as an approximation to the real welfare functions.
398 M.P. Gos´albez, J.S. D´ıez J. of Economic Behavior Org. 42 2000 385–404
does not grant a subsidy to firm 1 and firm 2 knows it because, under information release regulation, no announcement is interpreted by firm 2 as no existence of a subsidy for firm
1, and a situation in which the government grants a subsidy to firm 1 and that information is publicly announced by the supranational institution. For the case of strategic complements
the result of the comparison is unambiguous: a cost subsidy cannot hurt the domestic firm because both the direct as well as the strategic effect of the subsidy are positive. For the case
of strategic substitutes however, things are not so clear because, in this case, the strategic effect of the subsidy is negative. Fig. 5a and b display, in the W
1
, s space, a numerical
simulation comparing welfare of the active country in the two situations, for V = 0.5, for two values of λ λ = 0.8 and 0.6 and for q = 0.5. W
NR 1
represents welfare of the active country in the case in which there is no subsidy for the firm and that information is public
knowledge and W
R 1
when the government grants a subsidy to firm 1 under information release regulation.
The figures show that for those values of λ the subsiding country prefers to grant a subsidy to its firm even under information release regulation whenever the subsidy is low
enough.
12
However, it can be shown that, for λ ≤ 0.5, it would not be optimal for the government to subsidize its firm any longer under information release regulation. This
result suggests that supranational institutions should be cautious when designing policies that enforce the public disclosure of subsidies, not only because that policy could reduce
the effectiveness of the subsidy, reducing welfare but also because in some cases it could even lead the active government not to subsidize its firm any longer.