The Saving Rate and the Golden Rule

Keep in mind that the economy does not automatically converge toward the Golden Rule steady state. To reach any particular steady state, including the Golden Rule, we need a particular saving rate. Assuming that the policymaker can control the saving rate, he/she can select a saving rate to support the Golden Rule level of capital:

Setting $s$ to 0.20 produces the Golden Rule level of capital. Hence, we call it the Golden Rule saving rate, which we denote $s_{gold}$ .

If the saving rate is higher than 0.20, the steady state capital stock will be too large. If the saving rate is lower, the steady state capital stock will be too low. In either case, steady state consumption will be lower than for the Golden rule level of 0.20.

In practice, policymakers don't directly control the saving rate but can implement policies to influence it.