In earlier papers (McKibbin and Nguyen (2001, (2002)) we introduced demographic features into the MSG3 model of the world economy, following the approach of Bryant and McKibbin (2001). In this paper we use the same theoretical technique to develop a series of models based on a consistent database from a simple two country symmetric theoretical model to the complete 4 country MSG3 model, which represents the empirical characteristics of Japan, United States, Rest of OECD and Rest of World. We explore a stylized decline in fertility similar to that experienced by Japan since the 1950 (exactly the same shock as the stylized shock used in Bryant (2004)). We first explore the properties of the theoretical model with both a global and a single country shock. This gives similar results to that found in the basic framework underlying the Bryant (2004) approach. We then move from the simplest fully optimizing framework to increasing add complexity to the model until we build a model of Japan. We explore the same shock across the models of increasing complexity in this paper and compare our results to the Bryant approach. We find that although the basic insights from the sequences of theoretical papers in the Brooking-ANU project continue to hold, the quantitative results change significantly as the model is adapted to have more characteristics of Japan. In a final section, we use the complete model to explore the likely impacts on Japan of the demographic change already experienced from 1970 and look to the likely changes to be experienced out to 2040.