Suppose the output per effective worker is production function is y=10k1/2, where k equals the amount of capital per effective worker and the capital lasts an average of 10 years. Assume that the saving rate is 32 percent, the rate of growth of population is 4 percent and the rate of technological growth is 2 percent.
a) Solve for the steady state levels of capital per effective worker, output per effective worker, investment per effective worker and consumption per effective worker.
b) Calculate the growth rate of total capital income and the growth rate of total labor income at the steady state. (Hint: Capital and labor each earn a constant share of the economy's income ).
c) Prove, at the steady state, (i) the capital-output ratio is constant; (ii) the real wage grows at the rate of 2 percent.
d) Calculate all of the following at their Golden Rule levels: Capital per effective worker, output per effective worker, saving and investment per effective worker, and the consumption per effective worker.
e) Whether the saving rate is too high or too low?