Question 2 [50 Marks] 2.1 An economy follows a Harrod neutral production function. At time t-1, the share of labour into production is 2/3. The savings rate, the growth rate of population and the technological progress are respectively 5%, 3% and 2%. Capital loses its usefulness at a rate of 5% per year. Answer the following questions. (a) What will be the values of the per effective capital-labour ratio and the per capita income at the steady state? Show all your working. [10] (b) What will be the golden level of per effective capital to labour and per capita income?[6] (c) What will be the wage and return of capital at time t=2? [8] 2.2 A Harrod neutral production function with technological progress has a as the share of capital into production. Given capital depreciation and population growth, answer the following questions. (d) By how much the per effective capital to labour at the steady state will change following a one unit increase in population? Show all your working. 10] (e) Prove that at the golden level, the savings rate will be equal to the share of capital into production. [8] (f) Prove that, without technological progress and with a zero population growth, the rate of return of capital will be equal to the depreciation rate of capital [8]