# How to determine a corner solution? Growth Model

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

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

• 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.
– 1muflon1
Jul 8 '20 at 23:49

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.