We denote by αl ()and αu() the level of ability where households with given other characteristics switch from rent out land to autarky or fromautarky to renting in land, respectively. In other words, households with αi < αl will rent out land, those with αi > αu rent in, and those with αu>αi< αl stay autarky. We can solve for αu, and αl jointly with a i l from the FOCs
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