Rising marginal cost and concavity of the production function

Suppose a production function, f, is continuous, quasi-concave and weakly monotone on the non-negative orthant of Euclidean n-space. Let c(·, ·) be the associated cost function. Then it is shown that f is concave if and only if for each w, c(w, ·) is convex.     

Optimal Mortgage Refinancing with Regime Switches

A model of rational mortgage refinancing is developed where the drift and volatility of interest rate process switch between two regimes. Because of the possibility of a regime shift, the optimal refinancing policy is characterized by the different threshold of interest differential for each regime. Numerical simulation demonstrates that the optimal refinancing threshold in each regime can be smaller or larger than the threshold under single-regime models. Finally, we evaluate the predictions of the model, based on the estimated parameters for a two-regime model to capture the evolution of the mortgage rates in the US. Our model can produce both late and early refinancing, which is consistent with the observed refinancing behavior. The views expressed in this paper are solely those of the authors and do not necessarily reflect official positions of the Sumitomo Trust and Banking Co., Ltd.     

How an innovation is formed: A case study of Japanese word processors

An innovation is formed in the social system through the diffusion process, and artifacts that embody the innovation alter their aspects considerably. This study proposes an innovation-diffusion model on the assumption that an innovation interacts with a social system, which shows dynamic and self-organizing characteristics. That is, firstly, an innovation appears that overthrows the existing technological paradigm. Secondly, after the appearance of an innovation, engineers or relevant professionals witnessing the innovation conduct various kinds of trial and error to compete with each other. Thirdly, under passing through the turmoil period, the social system in which an innovation has been implemented becomes changing its structure. Fourthly, once an innovation has surpassed the irreversible phase, obtaining the dominant design, it becomes embedded into the social system. In order to verify the model, I refer to the diffusion process of the Japanese word processors into the Japanese society around 1980s. Following the result of this study, this paper points out that the diffusion theory should be reconsidered, especially about the meanings of the critical mass, the dichotomy of the innovator-imitator model, and so on. Besides, strategic planners or policy makers would do well to construct innovation strategies or technology policies to implement the innovation by affecting such factors as the internal and external influence factors and the population of the potential adopters.     

On China’s Exchange Rate Flexibility and Stability: The More Flexible against the U.S. Dollar, the More Stable in Effective Terms

I. IntroductionFor many years, the Chinese authorities have often expressed their appreciation for the merits of a flexible exchange rate regime for China and their willingness to make the exchange rate of the renminbi, China’s national currency, be determined by market forces. 1 In the same breath, however, they also stressed the importance of a “stable exchange rate” forChina, although it is not clear what the authorities meant by a “stable exchange rate.” (The People’s bank of Chin…