Reflections on the Relation Between Competition and Innovation

Abstract

In this paper some reflections are developed on the relation between the organization of markets and innovative activities. The IO (Industrial Organization) predictions often depend crucially on the structural and behavioral characteristics of markets (or industries). To some extent this is also the case for the relation between innovation and competition. But a synthesis of existing work provides nevertheless some robust tendencies, including the predictions that in many cases the aggregate R&D activity is positively or inverted-U related with competition intensity. Clearly this tendency may be useful for positive analysis and policy.

Appendix

In the KS model, the optimal introduction date T * is given by (see Eq. 20 in Kamien and Schwartz (1976)):

$$ {T^* } = - \left[ {{{\left( {m\left( {r + h} \right)} \right)}^{ - 1}}} \right] \times \ln \left[ {1 - z{{\left( {m\left( {r + h} \right)} \right)}^{1 - a}}} \right] $$

with

• $z{\left( {m\left( {r + h} \right)} \right)^{1 - a}} < 1\,,$

• $m = a/\left( {1 - a} \right),$

• $z = A{\left[ {r/\left( {P\left( {1 - {e^{-rL}}} \right)} \right)} \right]^a},$

• $A = \int_0^T {{y^a}dt}$ representing the cumulative effort to complete the project,

• 0 < a < 1,

• P representing the rewards of the innovation

• L the patent life, and

• r the interest rate.

Now, assume the following parameter values:

P = 1,000, L = 20, r = 0.05, a = 0.25 and A = 100.

Then, the optimal introduction time T* is an increasing function of the all possible values of the degree of rivalry h. Consequently, optimal R&D efforts, which are inversely related with the introduction time, are always decreasing in the hazard rate h, see Fig. 1

Fig. 1

Introduction time T* in function of competition intensity h

.

Assume the following parameter values:

P = 1,000, L = 20, r = 0.05, a = 0.4 and A = 10.

Then, the optimal introduction time T* is a U shaped related with the degree of rivalry h. Hence, the optimal R&D investments are inverted U function of the hazard rate h, see Fig. 2

Fig. 2

Introduction time T* in function of competition intensity h

.