concfinal2002new2

# concfinal2002new2 - Final Exam Econ 413/513 18 April 2002...

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Final Exam — Econ 413/513 18 April 2002 Department of Economics Concordia University Section A: do all three problems 1. The Ramsey model [10 marks] Consider a Ramsey Model with no population growth or technological progress ( n = g =0). Thetime-0 utility function of an agent (or household) can be written as U = Z t =0 e ρ t [ c ( t )] 1 θ 1 θ dt where c ( t ) is his/her consumption at time t . The budget constraint says that the present value of the agent’s income streams must equal the present value of his/her consumption. We can then set up the Lagrangian as L = Z t =0 e ρ t [ c ( t )] 1 θ 1 θ dt + λ k (0) + Z t =0 e R ( t ) w ( t ) dt Z t =0 e R ( t ) c ( t ) dt , where w ( t ) is the wage income at time t , R ( t )= t R τ =0 r ( τ ) d τ and r ( τ ) is the real interest rate at time τ . (a) Take the f rst-order condition of the above Lagrangian with respect to c ( t ). Your answer should be an equation containing c ( t ), θ , ρ , R ( t ), and λ .[5ma rk s ] (b) Derive the so-called Euler equation from the f rst-order condition derived in (a). [If you could not

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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.

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concfinal2002new2 - Final Exam Econ 413/513 18 April 2002...

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