Modern Applied Science; Vol. 7, No. 5; 2013 ISSN 1913-1844 E-ISSN 1913-1852 Published by Canadian Center of Science and Education 39 Why Is It So Difficult to Optimally Choose Innovation? Lest We Forget the Real World Partha Gangopadhyay 1 , Takemi Fujikawa 2 & Yohei Kobayashi 3 1 School of Economics and Finance, University of Western Sydney, Sydney, Australia 2 Faculty of Economics, Otemon Gakuin University, Ibaraki, Japan and Graduate School of Business, Universiti Sains Malaysia, Penang, Malaysia 3 Brain Functions Laboratory, Yokohama, Japan Correspondence: Partha Gangopadhyay, School of Economics and Finance, University of Western Sydney, Locked Bag 1797, Penrith South DC, NSW 2751, Australia. Tel: 61-2-9685-9347. E-mail: P.Gangopadhyay@uws.edu.au Received: October 8, 2012 Accepted: April 5, 2013 Online Published: April 19, 2013 doi:10.5539/mas.v7n5p39 URL: http://dx.doi.org/10.5539/mas.v7n5p39 Abstract In order highlight the non-steady state and real world dynamics associated with competitive innovation we develop a model involving choice of product quality in a simple duopoly characterised by two key departures from the dominant framework of quality ladder: first, we consider firms who refrain from maximising short-run profits. Instead, firms are started their function or action by their long-run goal of survival and growth. Secondly, we introduce the full-cost pricing model as opposed to market clearing prices. Based on these two key features we are able to derive the dynamics that can characterise the evolution of product quality in the non-steady state. We establish that the presence of an unstable equilibrium creates a threshold effect, which can also give rise to either a virtuous or vicious, path of quality choices. We further show that the quality dynamics can exhibit chaotic behaviour. As a consequence, firms become unsuccessful to see systematic errors. Firms also become unsuccessful to make long-run predictions with certainty even though they act in a deterministic world. The corollary is that time profiles will separate exponentially and these time profiles begin very close together. We offer interesting simulations to support the theoretical findings. Keywords: regions of instability, full-cost pricing models, Chaotic dynamics 1. Introduction High-tech products have, in recent years, assumed paramount significance in the prosperity of nations. These products seriously impinge on the quality of life for millions. Autos, health merchandise, the internet and PCs are among a wide array of products that have long gone high-tech. The quality of these products is ever-changing as new products regularly replace old products. The quality of a product also poses serious challenges to a firm as its long-run survival and growth are intrinsically predicated on its ability to compete with rivals in quality. We examine the quality competition in a novel framework: in our framework a typical firm is assumed to be a duopolist (can be easily extended to an oligopolist) with a particular internal structure and group of investment necessities that are hinged upon their long-run goals of survival and growth (Arestis & Milberg, 1994). Our proto-type firm is therefore different from the postulated firms of the steady state framework of quality choice that assumes firms to be solely driven by their short-term goals of profit-maximization along the steady state path. In the existing literature the standard model of innovation assumes that the product development, or progress, takes place along a pre-existing quality ladder. An innovator is actuated by ex ante excess, or monopoly, profits that the innovator expects to acquire at each rung of the quality ladder. There is a fixed cost of innovation and an innovator, hence, jumps from one rung to the next only when the ex ante excess profits can outweigh the exogenous fixed costs. For more than seven decades, since it was first advanced in Schumpeter (1942), the standard model has been the primary tool in order to explain the dependence of technology progresses on economic fundamentals such as patience and cost (Boldrin & Levin, 2009). This model of innovation has been used as the propelling force behind economic growth in the models of Romer (1990), Grossman and Helpman (1991), and Aghion and Howitt (1992), among other. The important issue of technological diffusion across space