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YorkFinal2007+solutions

YorkFinal2007+solutions - Final Exam Econ 4010 17 December...

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Final Exam °Econ 4010 17 December 2007 Department of Economics York University Section A: do all three problems 1. The Ramsey model [10 marks] Consider the Ramsey model. It can be shown that the dynamics of consumption, c , are given by the so-called Euler equation: ° c c = r ° ° ° ±g ± , where r = f 0 ( k ) is the real interest rate. (We assume that depreciation is zero.) The dynamics of k are given by ° k = f ( k ) ° c ° ( n + g ) k . We assume that f 0 ( k ) > 0 and f 00 ( k ) < 0 . (a) Draw the ( ° k = 0 )-locus in a phase diagram with c on the vertical axis and k on the horizontal. Explain why it is shaped the way it is. [5 marks] (b) Find an expression for the steady-state level of r , denoted r ± , in terms of exogenous parameters. [5 marks] 2. Endogenous growth [10 marks] Consider an endogenous growth model. We can write the growth rate of capital, K ( t ) , as g K ( t ) ± ° K ( t ) K ( t ) = ° A ( t ) K ( t ) ± 1 ² ° . where ³ is the capital share of output, A ( t ) the level of technology, s the rate of saving, and ² a constant which depends on exogenous parameters. (The labor force is also constant and set to 1 .) The growth rate of technology can be written as g A ( t ) ± ° A ( t ) A ( t ) = ! ° K ( t ) A ( t ) ± ± , where ´ is a parameter in the production function for technology (i.e., new ideas), and ! is constant and depends on exogenous parameters. The growth rates of A ( t ) and K ( t ) are constant on the balanced growth path. We denote these by g ± A and g ± K , respectively.
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