Question

Question 3 : Solow model with long-run TFP growth [20 marks] Suppose output is given by Y = K}(AN) As in the basic model, the workforce grows at rate n, capital depreciates at rate d and the savings rate is s. In addition, suppose that TFP grows at a constant rate g. That is: ΔΑ A9 We will refer to the product AN as the "effective workforce". It follows that the effective workforce grows at rate n+g. a. Express the production in per "effective worker" terms by letting ye b. The growth in capital per effective worker can be written as k, ΔΚ ΔΑ ΔΝ ke KAN Using the same steps as described in class, derive the dynamics of capital per effective worker. c. Illustrate the steady-state for this economy on a diagram and derive an expression for the steady-state capital stock per effective worker, k*. How does it depend on g? d. Derive an expression for the steady-state output per effective worker, y*. In this steady-state, at what rate must output per worker, y e growing?

Answer 1

) Y (AN) 2 0 a) Doviding the both his owne by (AN), AN Taking logarithun an both siden log ke tog togalogn ANIN dhe drav dt dria d or, Ake ke AK - DA - AN K A N (stnig) ke Al the Bloody - alte Are =0 or, 81 (19) - (sintg ke b or, c. Rel2 (&tntg ke ow, the - (otning joy a lotnia) Dividing by N'; yech X War orly- / k121 Por his steady arte, y A2 (stinto)

Taking logantana logy = I logA + logo - log 8 - logn - logg Differentiating wat 'ti n . dyka 4 249 **