In macroeconomics, the Keynes–Ramsey rule is a necessary condition for the optimality of intertemporal consumption choice.
[1] Usually it is expressed as a differential equation relating the rate of change of consumption with interest rates, time preference, and (intertemporal) elasticity of substitution.
its change over time (in Newton notation),
[2] The Keynes–Ramsey rule is named after Frank P. Ramsey, who derived it in 1928,[3] and his mentor John Maynard Keynes, who provided an economic interpretation.
[4] Mathematically, the Keynes–Ramsey rule is a necessary first-order condition for an optimal control problem, also known as an Euler–Lagrange equation.