@

일반적증명


y=f(k)


dy/y=dk × dy/dk / y--------dy=dk ×dy/dk라서

        =dk×f'(k) / y----------dy/dk=f'(k)

        =(sf(k)-(델타+n)k)×f'(k)/f(k) --- (dk=sf(k)-(델타+n)k 


이때 f(k)가 1차 콥더글라스함수라면,

f(k)=k^a, f'(k)/f(k)= a/k(0<a<1)

dy/y= a×(sf(k)-(델타+n)k) / k

        = a×dk/k




균제상태일때의 증명


dk=(sf(k)-(델타+n)k)=0

dy/y=0