Suppose that the production function is Y = 40K1/4(EL)3/4and capital lasts for an average of 10 years so that 10% of capital wears out every year (depreciate rate = 1/10 = 0.1 or 10%). Assume that the rate of growth of population is 4 percent, the rate of technological growth is 2 percent and the saving rate is s = 0.128.
a) Derive the equation for output per effective worker y = Y/ (EL) = f(k), where k equals the amount of capital per effective worker.
b) Calculate the steady-state levels for each of the following: capital per effective worker, output per effective worker, consumption per effective worker, saving and investment per effective worker, and depreciation per effective worker.
c) Now calculate the steady-state growth rates of capital per worker, output per worker, saving and investment per worker, and consumption per worker.
d) Finally, calculate the steady-state growth rates of capital, output, saving and investment, and consumption.