Bit of an overcomplicated proof that DMU implies that gains add less utility than an equivalent loss removes. A simpler proof goes as follows: Let U be a conca

Bit of an overcomplicated proof that DMU implies that gains add less utility than an equivalent loss removes. A simpler proof goes as follows: Let U be a concave utility function, and let 'w' and 'e' be some amount of 'wealth'. Concavity implies: U(w+e)/2 + U(w-e)/2 <= U(w) hence U(w+e) + U(w-e) <= 2*U(w) rearranging the terms we find (U(w+e) - U(w)) + (U(w-e) - U(w)) <= 0 and therefore U(w+e) - U(w) <= U(w) - U(w-e). So gains add less utility than losses remove.