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Unformatted text preview: 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 ( 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 ( k ) > and f 00 ( k ) < . (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 ) = s¢ & A ( t ) K ( t ) ¡ 1 ¢ & . where £ is the capital share of output, A ( t ) the level of technology, s the rate of saving, and ¢ 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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This note was uploaded on 01/07/2012 for the course ECON 4020 taught by Professor Zafarkayani during the Spring '09 term at York University.
- Spring '09