<P> x _̄ + (x _̄ − y _̄) d p d t = ∑ d I h d t + (∑ π z f d z f d t − ∑ E z h d z h d t) (\ displaystyle (\ bar (x)) + \ left ((\ bar (x)) - (\ bar (y)) \ right) (\ frac (dp) (dt)) = \ sum (\ frac (dI ^ (h)) (dt)) + \ left (\ sum \ pi _ (z) ^ (f) (\ frac (dz ^ (f)) (dt)) - \ sum E_ (z) ^ (h) (\ frac (dz ^ (h)) (dt)) \ right)) </P> <P> Since x _̄ = y _̄ (\ displaystyle (\ bar (x)) = (\ bar (y))): </P> <P> ∑ d I h d t = x _̄ − (∑ π z f d z f d t − ∑ E z h d z h d t) (\ displaystyle \ sum (\ frac (dI ^ (h)) (dt)) = (\ bar (x)) - \ left (\ sum \ pi _ (z) ^ (f) (\ frac (dz ^ (f)) (dt)) - \ sum E_ (z) ^ (h) (\ frac (dz ^ (h)) (dt)) \ right)) </P> <P> Differentiating the objective function of the maximization problem gives: </P>

The idea of the invisible hand operating in the competitive market system means that