Bit of an overcomplicated proof that DMU implies that gains add less utility than an equivalent loss removes. A simpler proof goes as follows:<p>Let U be a concave utility function, and let &#x27;w&#x27; and &#x27;e&#x27; be some amount of &#x27;wealth&#x27;. Concavity implies:<p>U(w+e)&#x2F;2 + U(w-e)&#x2F;2 &lt;= U(w)<p>hence<p>U(w+e) + U(w-e) &lt;= 2*U(w)<p>rearranging the terms we find<p>(U(w+e) - U(w)) + (U(w-e) - U(w)) &lt;= 0<p>and therefore<p>U(w+e) - U(w) &lt;= U(w) - U(w-e).<p>So gains add less utility than losses remove.