# Euler equation of consumption in RCK model

(...) usually called the Euler equation for consumption (in effective units of labor) or the Keynes-Ramsey Rule (after those first deriving it): $$\frac{\dot{c}(t)}{c(t)} = \frac{r(t) - \rho -\theta g}{\theta}. \tag{18}$$

The Euler equation of consumption is derived from the maximization problem for the household in Ramsey Cass Koopman model using control theory, but what does it tells us?

• If you add the utility function and the budget constraint, you should see that this describes the path of consumption that allows the consumer to equalize the marginal utility and marginal cost (that is to max her utility under constraint). – Bertrand Jan 22 at 7:46