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Unformatted text preview: Final Exam &Econ 4010 2 March 2009 Department of Economics York University Part A: do any three of the six problems below 1. The Solow model [10 marks] Consider the Solow model, with Cobb-Douglas production. The capital stock per e/ective worker evolves over time according to & k = sf ( k ) & ( n + g + & ) k , where f ( k ) > and f 00 ( k ) < . The steady-state level of k (where & k = 0 ) is denoted k , and the interest rate is given by r = f ( k ) & & . Consider a poor economy, where k lies below k . In this economy, will r be increasing or decreasing over time? (In other words, what is the sign of & r when k < k ?) [10 marks] 2. The Ramsey model [10 marks] Consider a Ramsey model with a general neoclassical production function. It can be shown that the dynamics of consumption, c , are given by the so-called Euler equation: & c c = f ( k ) & & g , where f ( k ) is the real interest rate (assuming that capital depreciation is zero). The dy- namics of k are given by & k = f ( k ) & c & ( n + g ) k . We assume that f ( k ) > and f 00 ( k ) < . It can be shown that there exists a steady-state level of k , denoted k , such that & c > for k < k and & c < for k > k . How does k change when increases (agents become less patient)? That is, nd the sign of @k =@ . [10 marks] 3. Endogenous growth [10 marks] Consider an endogenous growth model. Total output, Y , is produced using Y = A " [1 & a L ] L & , where and " are strictly positive exogenous parameters, A is the level of technology (the number of ideas), L is the total labor force, and 1 & a L is the fraction of workers employed in goods production. Note that Y , L , and A depend on time (although we suppress the t ), but a L , , and " do not depend on time. New ideas, & A , are produced using &...
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- Spring '09