Question 3 {Solow Growth Model]. Suppose that the economyr is characterized by the standard assumptions of the Solos;r growth model, but that production is CobbDouglas in capital and reective labor. Specically, total output is given by e = min = smear- where K, is capital, L, is effective labor, Et is technology, or the productivity of a given worker, and N, is the total number of workers. Assume these grow at rates pg, 9E: and n. a} Does this production function exhibit constant returns to scale [CR3] in capital and workers? Prove your answer using the denition of CR3. b} Write down output per effective worker y, := th as a function of capital per effective R worker k: :2 EtN: in this economy. e} Let s E {l}, 1} denote the exogenous saving rate and (5 IE [I], 1} denote the depreciation rate of capital. Using the law of motion of the total capital stock Kg, derive the law of motion of capital per effective worker kt. d} Find the steady state It. and prove that it is increasing in the saving rate s. e} In the steady state, nd the growth rate of capital per effective worker it, from above, capital per individual worker it, where if, :2 %:, and total output H