Dynamics of Boundedly Rational Monopoly with Time Delay  Akio Matsumoto y Chuo University Ferenc Szidarovszky z University of Arizona Abstract The purpose of this paper is to study dynamics of a monopolistic rm in a continuous-time framework. The rm is assumed to be boundedly ra- tional implying that it can obtain only limited information and experience delay information on demand. A dynamic adjustment process is based on the gradient of the expected prot. It is analytically demonstrated that a monopoly equilibrium undergoes a Hopf bifurcation when it loses stability. Global dynamic behavior is conrmed by numerical simulations. 1 Introduction In the recent literature, it has been recognized in continuous-time economic dy- namics that a delay di/erential system is useful to describe the periodic and aperiodic behavior of economic variables. Time delays can be modeled in two di/erent ways: xed-time delays and continuously distributed time delays. Inv- ernizzi and Medio (1991) investigate various economic models with the latter and conrm analytically as well as numerically the conditions for chaotic solution. On the other hand Matsumoto (2009) reconstructs Goodwins accelerator model with the former as a delay neutral di/erential equation and examine the condi- tion under which multiple limit cycles coexist. More recently, Matsumoto and Szidarovszky (2011a) introduce a production delay of both types and a mound- shaped production function into the neoclassical one-sector growth model and show the birth of complex dynamics. With the innite dimensionality created  The authors highly appreciate nanical supports from Chuo University (Joint Research Grant 0981), the Japan Society for the Promotion of Science (Grant-in-Aid for Scientic Re- search (C) 21530172) and the Japan Economic Research Foundation. The research leading to this paper started when the rst author visited the Department of Systems and Industrial Engineering of the University of Arizona and nished when the second author visited the De- partment of Economics, Chuo University. They appreciated hospitalities of those universities over their stay. The usual disclaimer applies. y Department of Economics, Chuo University, 742-1, Higashi-Nakano, Hachioji, Tokyo, 192- 0393, Japan. akiom@tamacc.chuo-u.ac.jp z Department of Systems and Industrial Engineering, University of Arizona, Tucson, Ari- zona, 85721-0020, USA. szidar@sie.arizona.edu 1