Economic Growth and Development Professor Olivier de La Grandville Fall 2008 Problem Set 1 To be returned Friday, Oct 3 rd , 2008 * 1. In his classic paper, Robert Solow gives the solution of the diﬀerential equation for r , corre-sponding to the Walras-Leontief case, when n = n 1 > s a . Please determine his solution in the case n 3 < s a .(Hint: start with r0 < a b where r0 is chosen by yourself. When at time t 1 which you can determine, r reaches a b , this sets the ‘initial conditions’ for solving the second diﬀerential equation governing the movement of r ( t ); you will set r ( t 1 ) = a b .) Draw with precision the whole curve r ( t ), for t ∈ [0 , ∞ ). For this last part of the question, choose yourself values for s and n 3 . You can choose a b = 1. 2. Determine r ( t ) and y ( t ) in the Cobb-Douglas case Y = K α L 1-α , for two initial values, r0 < r * and r00 > r * . (Hint: make the change in variable x = r 1-α .) Draw the corresponding curves r ( t ) and
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