Convergence Towards the Steady State
We examine how the capital stock changes over time. In the current time period, the 1.00 units of capital per worker produce 1.00 units of output per worker .
Because 55 percent of output is saved and invested and 45 percent is consumed, investment per worker is 0.55 and consumption per worker is 0.45.
Because 25 percent of the capital stock depreciates, is 0.250. With investment of 0.550 and depreciation of 0.250, the change in the capital stock is 0.300.
Thus, capital per worker will be 1.30 in the next period. Because investment exceeds depreciation, new capital is added and output grows.
Over many periods, the economy converges to a steady state with 4.80 units of capital per worker. In this steady state, investment of 0.75 exactly offsets depreciation of 1.20, so (i.e. the capital stock and hence output are constant).
Changing the savings rate will lead the economy to converge to a different steady state: