Question 5 An economy is described by the extended Solow model with technological progress and population growth, that is gA > 0 and go > 0. The production function is of the Cobb-Douglas type: Y = K"(AN)1-Q where o = 0.5. Suppose that the economy is initially in a steady state and due to a permanent change in weather patterns the depreciation rate in the economy rises from of to 6, at time to. A Using a graph showing the production function, investment function and depreciation-and-dilution function (all in per-effective workers) analyze how the economy is affected by this shock to the depreciation rate. Clearly label each axis, all functions and the old and new steady states in the economy before and after the shock. b. From the equation 4- = sf ( K K AN AN) - (8+ 94 + 9N) AN derive an expression for the growth rate of capital per effective worker g x - C. Note that output per worker can be written as Y AN X A = f (AN * A and recall the aggregate production function from the beginning of the question. Derive the growth rate of output per worker gr as a function of the growth rate of capital per effective worker g x