YorkMidt2007_3+solutions

# YorkMidt2007_3+solutions - Midterm Exam Econ 4010 24...

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24 October 2007 Department of Economics York University 1. The Solow Model [10 marks] Consider a Solow model with Cobb-Douglas production, where capital per e/ective worker evolves according to: k = s ( k ) k ( n + g + ) k , where 0 < ± < 1 . The novelty is that the saving rate, s ( k ) , is a function of k , which we let take this form: s ( k ) = b sk k + k where 0 < b s < 1 . (a) Draw the graph of s ( k ) in a diagram with k on the horizontal axis. [5 marks] (b) Find an expression for the steady state level of k in terms of n , g , , b s , and ± . (We assume that b s > n + g + , which must hold for a steady state with positive k to exist.) [5 marks] 2. The Diamond Model [10 marks] Consider the Diamond model. We set the productivity factor A t to unity ( 1 ) in all periods. The size of the young population in period t , denoted L t , grows at rate n , i.e., L t +1 = (1 + n ) L t . Lower-case letters denote per-worker terms, e.g. k t = K t =L t . We assume Cobb-Douglas production and full depreciation (

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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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YorkMidt2007_3+solutions - Midterm Exam Econ 4010 24...

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