 The Hamiltonian becomes

The optimality conditions are

in addition to the transversality condition formula_109.If we let formula_110, then log-differentiating the first optimality condition with respect to formula_54 yields

Inserting this equation into the second optimality condition yields

which is known as the Keynes–Ramsey rule, which gives a condition for consumption in every period which, if followed, ensures maximum lifetime utility.A Large Attendance in the Antechamber

A Large Attendance In The Antechamber is a one-man play by Brian Lipson about Francis Galton the English scientist, statistician and founder of the eugenics movement.