Consider a world with two different production technologies, High and Low. Technology Low is the one available in developing countries with low level of capital per worker and is described by the following production function: 1 Y AK N where 1 2 Technology High can be used only in developed countries where capital per worker is bigger than 50, and is described by the following production function: Y AK Suppose that the depreciation rate ( ) is 1% and the growth rate of population is 1% in all countries. Also assume that all countries save 10% of output and that A is constant at the level of 1. The capital accumulation equation in all countries follows +1 = where t t I sY . (25 points) a) Find the per capita production function for low and high technology (3 points) b) Find the capital per worker accumulation equation for all countries c) Find growth rate of GDP per capita as a function of capital stock per capita for low and high technology [hint: growth rate of GDP per capita is d(lny) or (1/y)dy] d) The Roughly draw a graph showing the evolution over time of the growth rate of GDP per capita (graph the growth rate of y against time), and graph the evolution over time of the natural log of GDP per capita (graph lny against time) in a country starting with a capital stock per capita of (10 points) i) 16 [hint: low technology country] ii) 64 [hint: high technology country] e) Will there be convergence in GDP per capita for these two economies? Explain