I am reading Chapter 20 (Insurance vs Incentive) in Sargent's Recursive Macroeconomics Theory.
I don't understand this part on his book (on page 809, 3rd version). Why we know that the optimal contract $c_s, w_s = g_1(.), l_1(.)$, not $g_2(.) l_2(.)$ for any state $s$? In particular, how can we make sure that the participation constraint is binding for all state?
If anyone has ever read this chapter and understand it. Plz kindly explain to me.
Thanks a lot!