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ECON4020 - Final Exam Econ 4020 11 December 2009 Department...

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Final Exam °Econ 4020 11 December 2009 Department of Economics York University Part A: do all three problems below 1. The Solow model [10 marks] Consider a Solow model, where output ( Y ) is produced with a neoclassical production function, Y = F ( K; AL ) , which exhibits constant returns to scale, meaning that °F ( K; AL ) = F ( °K; °AL ) for all ° > 0 . The notation is standard and as usual we let lower-case variables denote per-e¢ cient-worker units, so that y = Y= ( AL ) , k = K= ( AL ) , etc. (a) Show that there exists an intensive-form production function. That is, show that there exists a function, f , such that y = f ( k ) = F ( k; 1) . [4 marks] (b) Firms choose K and L to maximize pro±ts, ± , given by ± = F ( K; AL ) ° rK ° wAL , where w is the wage rate and r is the real interest rate. Use the pro±t maximization problem to ±nd an expression for r in terms of (some or all of) f ( k ) , f 0 ( k ) , and k . [3 marks] (c) Use the pro±t maximization problem described under (b) to ±nd an expression for w in terms of (some or all of) f ( k ) , f 0 ( k ) , and k . [3 marks] 2. The Ramsey model [10 marks] Consider a Ramsey model with a general neoclassical production function. We saw in class that the dynamics of consumption per e¢ cient worker, c , are given by the so-called Euler equation: ° c c = r ° ² ° ³g ³ , where r is the real interest rate, and ² , ³
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