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so moving on to the proofs so to prove sufficiency uh we start with the spans Mery condition so by a standard static mechanism design argument we can show that The Spence mer condition with imply Q being implementable and and by some small amount of algebra we can show that the single Crossing condition the PST condition implies that the the Z or the marginal incentive functions are increasing and the marginal incentive being increasing implying the difference between the value function and utility function being increasing in turn implies that the QT is implementable this part is given in in KS so what I did here is very small so all I did is a small amount of algebra that proves that the single claing condition is equ to the set being increasing so for the conver the ne necessity part so itamp;#39;s itamp;#39;s similar so implementable go back to inite Spence Merle is could be done by a standard static mechanisms and design argument as well uh so so in the Cru and strike paper and
