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Unformatted text preview: Midterm Exam &Econ 4020 29 October 2009 Department of Economics York University 1. The Solow model [10 marks] Consider the Solow model, where k evolves according to & k = & ( k ) , where & ( k ) = sk & & ( n + g + ¡ ) k . The linearization of this equation around the steady-state level of k , denoted k ¡ , is given by & k = ( k ) , where ( k ) = & ( k ¡ ) + & ( k ¡ ) ( k & k ¡ ) . (a) Find an expression for ( k ) as the product of ( k & k ¡ ) and something involving ¢ , n , g , and ¡ . [5 marks] (b) Find an expression for the ¡gap¢at time t , given by k ( t ) & k ¡ . Your answer should be the product of two factors: (1) the initial gap, k (0) & k ¡ ; and (2) something that involves time, t , and the parameters ¢ , n , g , and ¡ . To get there you must solve the linear di/erential equation & k = ( k ) . Hint: if & x = ax , then x ( t ) = x (0) e at . [5 marks] 2. The Diamond model [10 marks] Consider a version of the Diamond model where the interest rate ( r ) and the wage rate ( w ) are constant, and there is no technological progress or population growth....
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- Spring '09
- Economics, Endogenous growth theory, Exogenous growth model, SID number, gY =L