Innovation Dynamics and Industry Structure Under Different Technological Spaces

Abstract

The paper presents an Agent-Based model to analyze the reciprocal influence between industry structure and industry innovation patterns. This topic was originally investigated through the seminal models of Schumpeterian competition developed by Nelson and Winter (Am Econ Rev 67:271–276, 1977, An Evolutionary Theory of Economic Change. Harvard University Press, Cambridge, 1982), Winter (J Econ Behav Organ 5:287–320, 1984), and Nelson (National innovation systems. A comparative analysis. Oxford University Press, Oxford, 1993). However, the knowledge accumulation process depicted in these models was extremely simplified. In particular, they did not provide any insight about the direction of firms’ technological advancement, within the range of possible alternative technological paths. This aspect is instead of topical importance for the generation of sectoral spillovers affecting the diffusion of innovations and the evolution of the industry structure. Our model aims at filling this gap by amending the framework proposed in Nelson and Winter (An Evolutionary Theory of Economic Change. Harvard University Press, Cambridge, 1982) so to to account for different characterizations of the ‘technology structure’ of the industry, and their possible influence on the process of Schumpeterian selection. More precisely, technology is represented as a directed network where each node constitutes a batch of technological skills to be learned by firms. The model shows that firms’ ability to imitate competitors generates spillover effects whose relevance depends upon the topological structure of Technology Network and firms’ specialization trajectories. In turn, by influencing the process of Schumpeterian competition, these spillovers exert a fundamental impact on both the industry innovative performance and the evolution of the industry structure.

Appendix

1.1 Investment

As explained in the text the function defining desired investment reflects the idea that firms are afraid of ‘spoiling’ their own market if they increase too much the scale of production, thereby reducing the market price and possibly their own profit margin. Assuming that the demand curve has a constant elasticity $\eta$ and firm’s market share is equal to s, the elasticity of the residual demand facing the firm, under the firm’s conjecture that other producers will maintain constant their output, is given by: $\frac{\eta }{s}$ Given that $\pi =(P(Q)-\frac{c}{A})sQ$, the firm maximizes her profit when it chooses a level of output such that:

$$\begin{aligned}&\frac{\partial \pi }{\partial Q}=\left( \left( \frac{\partial P}{\partial Q}\frac{Q}{P}P+P\right) -\frac{c}{A}\right) s=0 \Rightarrow \left( -\frac{1}{\eta /s}+1\right) P=\frac{c}{A}\Rightarrow \nonumber \\&\quad \Rightarrow \frac{\eta }{\eta -s}=\frac{PA}{c}=\rho \end{aligned}$$

(A.1)

If instead firm’s conjecture is that the rest of the industry consists of price-takers that respond along a supply curve with constant elasticity $\psi$ we obtain a more general results. The profit maximizing price-to-marginal-costs ratio is given by:

$$\begin{aligned} \rho =\frac{\eta +(1-s)\psi }{\eta +(1-s)\psi -s} \end{aligned}$$

(A.2)

Notice that, when $\psi =0$, we obtain the previous equilibrium condition. The right-hand side of the above equation can be interpreted as the target mark-up $\rho ^{T}(s)$ of the firm, expressed as a function of the firm’s market share.

Hence, desired investment can be expressed as:

$$\begin{aligned} I_{D}=\delta +1-\rho ^{T} \frac{c}{P_{t} A_{it}} \end{aligned}$$

(A.3)

When the realized mark-up $P_{t} A_{it}/c$ is exactly equal to the target mark-up $\rho ^{T}(s)$ the firm considers herself to be in a profit maximizing equilibrium at the current level of production and her desired investment is simply equal to the amount required to replace depreciated capital. Instead, when the realized mark-up is greater (smaller) than the target one, the desired net investment will be positive (negative). Equation (2.8) in Sect. 2 was obtained by setting $\eta =1$ and $\psi =1$.

1.2 A.2 Tables of Results

Table 2 Results of the simulations-5 networks generated with $P_{Split} = 25\%$ & Initial parents number = 10

Table 3 Results of the simulations-5 networks generated with $P_{Split} = 10\%$ & Initial parents number = 10

Table 4 Results of the simulations-5 networks generated with $P_{Split}=40\%$ & Initial parents number = 10