Answer the following questions using the basic Solow growth model, without population growth or technological progress.
(a) Draw a diagram with per worker output, y, consumption, c, saving, s and investment, i, on the vertical axis and capital per worker, k, on the horizontal condition. On this diagram, clearly indicate steady-state values for c, i, and y. Briefly outline the condition that holds in the steady-state (i.e. what is the relationship between investment and the depreciation of capital?).
(b) Suppose that society becomes less thrifty, resulting in a lower rate of savings, s. Using the above diagram, how does the new steady-state capital stock per worker, k, compare to the stock in part (a)? How does output per worker compare? How does consumption per worker compare? [Note: Even if output per worker decreases, consumption per worker need not decrease. Why not?]
(c) 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.