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Hi I'm a Sophomore in economics attempting to read published economics papers. I often encounter models such as the one below:enter image description here

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?

Taylor Tam
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  • Have you tried applying the model and visualising it in some way? I feel the best way for someone whom is unfamiliar with certain conventions is to plug it into mathematica and expand some terms, change them around, see what the behaviour is. See if one can plot it in lower dimensionality, –  Oct 13 '18 at 09:56
  • Are you thrown off by the infinite summation over powers? –  Oct 13 '18 at 09:57
  • Apparently there is some function $u'$, dependent on $t$ in a specific way, that determines these $p_{t+i} $ is what I get from this. If that is indeed what is meant and $u'$ is not some constant. Sure, $t$ is the index, but are we supposed to consider $u'$ as a function, this should be in the text somewhere. –  Oct 13 '18 at 10:01
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    Hi @WesleyGroupshaveFeelingsToo, thanks for your reply. Yes, the infinite summation of powers is what's throwing me off the most. I remember learning about divergent and convergent series in my calculus classes. Would those concepts be relevant here? – Taylor Tam Oct 14 '18 at 17:19
  • Yes, so for instance the sum: $$ \frac12 +\frac14 +\frac18 ...$$ goes on forever, right? but so does $$ 2 +4 + 8 ...$$ For the above we say it converges, to a certain value, if you take enough terms you can see this computationally quite quickly. Some convergent series converge faster than others. Other series just diverge, they are pretty useless we thought, but physicists managed to even use those, but that's a completely different story altogether. –  Oct 15 '18 at 08:46
  • Bottom line: the infinity symbol means that you can never write down all the terms, but you can definitely approximate it by taking... welll... "quite a lot". This is another mathematical question, how quickly DOES a certain series converge? What you need to take home is: 1) can't write them all out. 2) I can approximate this or in some special cases there is a nice formula that gives a precise answer for infinite terms (but rarely in applied economics).. these are precisely the skills you acquired during calculus –  Oct 15 '18 at 08:51

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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