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I'm working on a paper called "Fertility clubs and economic growth" of Ahituv and MOav (linked below) and arrived at this point:

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enter image description here The paper shows three optimal conditions respect to consumption (ct), intergenerational transfers (st+1), solved in the images and the educational level (et+1). Following the paper, I shall use the rt+1 equation derived on the images to get the et+1 optimal level, but, there is a note that says the following:

enter image description here According to the corner solution showed in the note and replacing the value of rt+1 that I get in the first two images I get the result, but is not a good answer, because I need to know how to get that condition.

I tried to solve the general model detailed on Moav (2001), and I get the result showed, but in this case it doesn't includes the intergenerational transfers and the interest rate. In the next image you could see the general model solution respect to et+1

enter image description here

As Moav (2001) says, the extended model is just a case where Teta is =1, but I can't just justify the development of the model with that answer, I need to solve it.

Am I doing something wrong? If I have to compute the corner solution in the note, how should I do it? THANKS A LOT!!

Ahituv Moav Paper: http://scholar.google.com.ar/scholar_url?url=https://www.cesifo-group.de/dms/ifodoc/docs/Akad_Conf/CFP_CONF/SC_CONF_1999-2006/GRI_2001X2002/PAPERS2/gri02-moav__221461_en.pdf&hl=es&sa=X&scisig=AAGBfm0HqRpnafuT244j5-Exa5QjPYhtbA&nossl=1&oi=scholarr

Moav (2001) Cheap Children an persistence of poverty (sorry, I couldn't find the link)

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    $\begingroup$ Please do not post pictures of equations typeset them. In this site you can write equations in the same easy and convenient way as in LaTex. See the site’s help page on how to ask good questions. $\endgroup$ – 1muflon1♦ Jul 8 '20 at 23:49
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What the authors seem to be doing in the footnote is imposing a condition stating that if intergenerational transfers tend to infinity (say for the case of children of billionaires) there will be no growth in wealth from human capital investment.

This condition is here to just communicate that the parent views allocation between human capital of the child and physical capital as substitutes.

This is communacated by the fact that we have $w_{t+1}h_{t+1}+r_{t+1}s_{t+1}$ being concidered in the same logarithm together.

Hope this helps

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  • $\begingroup$ Thanks for your help, don`t you think is necessary to find the euler equation to arrive to arrive to that condition? $\endgroup$ – RLF Jul 10 '20 at 21:33

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