whichever comes first. When the highest ERR in the ranking does not exceed the social cutoff rate, no
R&D projects should be implemented at all.
In a situation of abundant funding (i.e., where every project with an ERR equal to or higher
than the social cutoff rate will be financed), the peak or mode of the ranked project distribution can be
expected to be at the social cutoff rate. In a tight funding situation, however, the cutoff point of
research proposals takes place before the social cutoff rate is reached.
The postulated distribution of R&D projects on an ERR scale can be thought of as taking the
following semi-log form:
[2] Y = eβ0 eβ1X
where Y stands for the number of R&D projects and X for the ERR. The coefficient β1 has to be
negative in order to get an asymptotic curve, as shown in figure 1. The closer the slope coefficient is
to zero, the flatter the ranked distribution.
The accumulated number of R&D projects can be approximated by the following integral:
[3] Yr = ∞ ββ ββ Xdx
r
where Yr stands for the number of R&D projects with a rate of return of r and higher.
The relative under- or overinvestment in (agricultural) R&D as a percentage of the original
investment level can be estimated as follows:
|
Γ∞ 1 p ββ Xdx |
^∞ „ ∫ββ1 Xdix | |||
|
[4] |
■s--1 ∞ |
× 100 = |
s∙--1 ∞ |
×100 = (ββ1∆X -1)×100 |
|
∫ββo ββ X dix |
∫ββ1 Xdix | |||
|
Lr J |
Lr J |
where s is the social cutoff rate and r the implicit cutoff rate and where X represents the difference
between r and s.
Based on this simple stylized model, underinvestment in R&D can be captured in the
following two postulations:
(1) Assuming full information and a strict economic selection of R&D projects, under-investment
in R&D manifests itself in a cutoff rate that is higher than the social cutoff rate.