Suppose that we modify the Solow growth model by allowing long-run technological progress. That is, suppose that z = 1 for convenience, and that there is a labour-augmenting techno- logical progress, with a production function Y = =F(K, bN) = =K(bN)1-a where b denotes the number of units of "human capital" per worker, and bN is "efficiency units" of labour. Letting b' denote future human capital per worker, assume that b' = (1+ f)b, where f is the growth rate of human capital.1. Derive the evolution of the capital stock per effective worker. Describe your steps as you go along. [5 points] 2. Show that the long run equilibrium has the property that Ir\" = % is a constant.[5 points] 3. Using a diagram, show how to determine the steady state value of capital per worker [5 points] 4. At what rate dom aggregate output, aggregate consumption: aggregate investment... and per capita income grow in this steady state'ill Explain. [Ill]I points] 5. Mat is the effect of an increase in f on the growth of the per capita income? Discuss how this model behaves relative to the standard Solow growth Model. [5 points] ti. Assume that the economy starts on a balanced growth path. Suppose that the savings rate, s suddenly and unexpectedly increases. 1What- are the effects on capitalper worker? Explain using a diagram. [5 points] T. Following such a change in the savings rate, can you unambiguously say whether the consmnption c is higher or lower in the long run? Explain. [5 points] 3. Sketch the time paths of to Fr. In. 3;; and In. c, following such a change in the savings rate.[1|I points]