Question

Suppose that the the economy is in a steady state where the capital stock per worker is above the golden-rule level. Illustrate this situation. To obtain the golden rule steady state, how should house- holds change their rate of savings? Suppose that the saving rate decreases at time t0. On a graph plot c, k, and i against t and show how the economy adjusts between the original and the new steady-state. Briefly explain why each variable is changing in the way that you have drawn it in your diagram.

Answer 1

Suppose that the economy is in a steady state where the capital stock per worker is above the golden rule level . Then , to rech at golden rule steady state, policymakers must reduce the savings rate.

Initially, when savings rate (s) decreases , then consumption per worker (c) rises and investment per worker (i) falls.

Now, i<dk (Because investment and depreciation were equal in the initial steady state, and after fall in investment , now investment will now be less than depreciation), which means the economy is no longer in a steady state.

As a result, gradually the capital stock per worker, k falls, which leads to fall in investment (i) and fall in output (y) and also fall in consumption per worker (c) .

But this consumption per worker level is more than the old steady state c.

By reducing the savings rate , the economy obtains the golden rule steady state where consumption per worker is at higher level, output , capital and investment per worker is at low level.