Given the Production Function Y = a K0

Essay

Given the production function Y = A K0.3L0.7 and fixed values for the saving rate and depreciation, if productivity is growing at an average rate of three percent, and the labor input grows at two percent, there is a unique growth rate of capital that is sustainable. That is, if the growth rate of capital is either higher or lower than this steady-state value, then it must eventually change, even if nothing else in the economy changes. Calculate this steady-state growth rate of capital, and explain why it alone is a sustainable rate. [Hint: Use the fact that the growth rates of output and capital per worker are 43% higher than the growth rate of productivity.]