Keynes–Ramsey rule
In macroeconomics, the Keynes–Ramsey rule is a necessary condition for the optimality of intertemporal consumption choice. Usually it is a differential equation relating the rate of change of consumption with interest rates, time preference, and elasticity of substitution. If derived from a basic Ramsey–Cass–Koopmans model, the Keynes–Ramsey rule may look like
where is consumption, is the discount rate, is the real interest rate, and is the elasticity of substitution.
The Keynes–Ramsey rule is named after Frank P. Ramsey, who derived it in 1928, and his mentor John Maynard Keynes, who provided an economic interpretation.
Mathematically, the Keynes–Ramsey rule is a necessary condition for an optimal control problem, also known as an Euler–Lagrange equation.
