Universities as partners in research joint ventures

Abstract

Sustainable economic growth depends on a continual flow of innovations that depends in turn on a continual flow of knowledge. While empirical evidence suggests that universities can play a significant role in the creation and dissemination of that knowledge, little is known of the characteristics of research joint ventures involving universities. One of the few studies to investigate this issue is Link and Scott (Research Policy 34:385–393, 2005), which found a positive relationship between university participation in RJVs and the size of RJVs which they attributed to universities providing higher marginal value and lower appropriability problems to larger RJVs. Boardman and Bozeman (Economics of Innovation and New Technology 15:51–69, 2006), however, suggests that the explanation might be more complex and not necessarily associated with profit maximization. The purpose of this paper is to present a theoretical model based on a profit-maximizing approach of the decision to invite a university to participate in an RJV that can serve as a foundation for future empirical work, an exploration of the relative explanatory power of a profit-maximizing approach, and a framework for evaluating empirically the policy implications of the Link and Scott’s (Research Policy 34:385–393, 2005) findings.

Appendix: proof that the revenue-cost ratio is downward sloping with respect to n*

The revenue-cost ratio R is defined as:

$${\text{R(}}n^{*} ,x )= \frac{{a(n^{*} ) \times p(n^{*} ,\sigma )}}{{c(n^{*} )}}$$

(7)

Dropping the functional notation for expositional clarity, greater σ results in greater n* and marginal revenue ($\partial p/\partial n^{*}$). Therefore, it must be that greater n* also results in greater marginal costs (dc/dn*) because in equilibrium, marginal cost must equal marginal cost at n*. Hence:

$$sgn\left( {\frac{\partial R}{{\partial n^{*} }}} \right) = sgn\left( {\frac{{\left( {\frac{\partial a}{{\partial n^{*} }}p + a\frac{\partial p}{{\partial n^{*} }}} \right)c - ap\frac{\partial c}{{\partial n^{*} }}}}{{c^{2} }}} \right)$$

(8)

$$= sgn\left( {\left( {\frac{\partial a}{{\partial n^{*} }}p + a\frac{\partial p}{{\partial n^{*} }}} \right)c - ap\frac{\partial c}{{\partial n^{*} }}} \right)$$

(9)

$$= sgn\left( {\frac{{\left( {\frac{\partial a}{{\partial n^{*} }}p + a\frac{\partial p}{{\partial n^{*} }}} \right)}}{{\frac{\partial c}{{\partial n^{*} }}}} - \frac{ap}{c}} \right)$$

(10)

But the first ratio in Eq. (10) is the ratio of marginal revenue and marginal cost. Under the assumption of profit maximization, this ratio equals 1. Given that, and given that the revenue-cost ratio [which is the second part of the Eq. (10)] is greater than 1 by assumption of market power, it must be that the revenue-cost function is downward sloping.