Consider an economy that has the following production function:
Y = zF (K,N) = K1/3N2/з
where Y, Z, K and N denote output, total factor productivity, capital stock and labour employment respectively (z = 1 for simplicity). Assume the depreciation rate d = 0.18, saving rate s = 0.2, and population growth rate n = 0.02.
a) Write down the production function in per worker terms.
b) Calculate capital, income and consumption per capita in the steady state. Use a diagram to illustrate your answer.
c) The economy is initially in the steady state that you calculated in part (b). Now suppose that there is a surge in the saving rate such that s = 0.4.
i) Calculate capital, income and consumption per capital in the new steady state.