(Population growth and technology growth) Consider an economy that is described by the production function Y= K^1/2 (LE)^1/ 2. Moreover the depreciation rate of capital is (delta) o = 0.15, the population growth rate is n = 0.05 and the technology growth rate is g = 0.1
(a) What is the per effective worker production function, that is y = Y/LE ? What is the marginal product of capital, that is dy/dk?
(b) If the saving rate is s = 0.3, find the steady state level of capital per effective worker k*. What is the steady state level of consumption per effective worker c*? What is the steady state level of investment per effective worker i*? What is the steady state level of output per effective worker y*?
(c) Find the golden rule level of capital per effective worker k*g, i.e. the steady state level of capital per effective worker that yields the highest steady state consumption per effective worker. Find also the golden rule consumption per effective worker level c*g that corresponds to this capital per effective worker and compare it to the one in question b. Is cg higher than c*?
(d) Find the savings rate sg that guarantees that we will reach the golden rule capital per effective worker k*g.
(e) What is the growth rate of GDP per effective worker in the long run? The growth rate of GDP per worker in the long run? The growth rate of aggregate GDP?