Hi I'm a Sophomore in economics attempting to read published economics papers. I often encounter models such as the one below:
I've taken several lower-level mathematics courses but have difficulty with fully comprehending models such as the one shown above.
How does one generally improve understanding of such models, with respect to changes in the parameters and variables and the general behaviour of the model?
If you have an engineering background you could also read: $$q_t \approx \sum_{i=0}^{100} (bd)^i u'(b^î k_t)= u(k_t) + bd u'(bk_t)+(bd)^2u'(b^2 k_t) \dots (bd)^{100}u'(b^{100} k_t) $$ And if that does not approximate real life closely enough, we add more terms - or make a different model. The skills you would need to read this come from sequences and convergent and divergent series from calculus. If you want to really know the background you can study analysis, but I wouldn't advise it. There are some nice MOOCs out there that treat the material very intuitively, for instance:
https://odee.osu.edu/odee-moocs/calculus-two-sequences-and-series