Answer the following question using the basic Solow growth model, with neither population growth nor technological progress.

(a) Using the standard diagram (c, i, and y against k), illustrate the situation where the economy is in the golden rule steady state. What makes the golden-rule steady state special? (How does it differ from any other steady state?) What can be said about the marginal product of capital at the golden-rule capital stock?

(b) Suppose that the economy is in a steady state where the capital stock per worker is above the golden-rule level. Illustrate this situation (you may use your diagram from part (a)). To obtain the golden rule steady state, how should households change their rate of savings? Suppose that the saving rate changes 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.