[Question to Hand-In] Output Y is produced by firms according to the production function Y = Kª(BN)'-ª, where K is the capital stock, N is the workforce (equal to the population), B is the level of...

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Extracted text: [Question to Hand-In] Output Y is produced by firms according to the production function Y = Kª(BN)'-ª, where K is the capital stock, N is the workforce (equal to the population), B is the level of labour-augmenting technology, and a is a parameter that lies between 0 and 1. The population N is constant over time (n = 0). Capital depreciates at rate d, so the evolution of the capital stock is K' – K = I – dK, where K' is next year's capital stock and I is the level of investment. Investment is equal to saving sY, which is a constant fraction s of income. Assume that technology B is constant. (a) Show that output per person y =Y/N is given by y = B'-ªkª, where k = K|N is capital per person, and that capital per person evolves over time according to k' – k = sy – dk. Sketch the saving line sy and the depreciation line dk in a diagram, and explain why the economy has a steady state for both k and y.