Economic impacts of a declining population In the article “Japan’s population problem” in The Japan Time, Hugh Cortazzi write: 


  Japanese leaders and Japanese people generally are well aware of their
  nation’s demographic challenges. The population has begun to decline
  […] The implications for the Japanese economy and for Japan’s position
  in the world should be obvious.


I can see some “intuitive” reason why a decline in population would be an issue for a country, mostly if it comes with a decline in the workforce (roughly decreased labor supply, decreased international competitveness and problems with funding pension system?). But I am interested in more careful and more general analysis.   

My questions are:


What are (if any) the economic challenges of a declining population, in the case of Japan (or in general,if not too broad)?
Does there exist modern macroeconomic models (say open economy DSGE) including demographics and studying declining populations ?
Have some paper tried to compare the welfare costs of a declining population with the potential welfare benefits of a declining population (e.g. for a dense country like Japan, decreasing housing prices)?
ad 2. 
This phenomenon has been studied a lot. Broadly it is referred to as the demographic transition. A good overview is given by the respective Wikipedia article.

In the field of Long-term macro there are several publications. One of the latest top-journal publications is:
Cervellati M.; Sunde U., Life Expectancy and Economic Growth: The Role of The Demographic Transition, «JOURNAL OF ECONOMIC GROWTH», 2011, 16(2), pp. 99 - 133.

Demographic elements can for sure be endogenised into every macro model. But I doubt that it would be very useful for short run DSGE things, since all demographic changes take place with huge time lags. If you want to study those interesting phenomena, you probably have to go more into Long-run Macro / Economic Growth (Unified Growth Theories put emphasis on demographic elements for instance)