Dear Professor Pfeifer,
The model I am coding includes patient household and impatient one , and I want to figure out the household’s welfare variation. I can calculate the welfare variation of patient and impatient household separately. Does this make any sense? How should I get the aggregate welfare variation of all the types of household?
Any reply will be appreciated. Thank you!
That is up to you. You need to define a social welfare function by giving weights to the different agents. Those weights do not follow from the model but are your choice. Of course, people quite often use equal weights.
One possibility, as in Mendicino and Pescatori (2011), is to weigh each agent’s welfare in the social welfare function by their respective discount factor. This convex combination allows each agent type to receive the same level of utility from a constant consumption stream . This approach is quite popular in the literature, by now. What I am referring to is something along the lines of
where in your case S indexes savers and B indexes borrowers
Many thanks, Professor Pfeifer, I really appreciate that .
Mr Marchesini, thank you very much for your detailed answer. I really appreciate that .