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Problem set 5 Buan 6340 Linear algebra 1. Real business cycles: Consider the macroeconomic model for real business cycles taken from Dejong and Dave (2011) Chapter 3. In your last problem set you derived the nonlinear system: 1-Oct = (1-a) Y nt ulq-1,-1) E-1 [pulceale ) (+1-o)] Ct-1 1-a y = zkont 1= net +12 yt = a +it ky = it-1 + (1 - 8)kt-1 -1 (cll-*):-* u(cl) = 1-0 In z = (1-P) In + pln 2-1 +et Your job is to log-linearize the above system around the steady state using first-order taylor series approxima- tions to find a model in the form: Art = Ba2+-1 + Cet Programming 2. Hierarchical clustering Implement a hierarchical clustering procedure from scratch (without using sklearn or a similar package) in python. Problem set 5 Buan 6340 Linear algebra 1. Real business cycles: Consider the macroeconomic model for real business cycles taken from Dejong and Dave (2011) Chapter 3. In your last problem set you derived the nonlinear system: 1-Oct = (1-a) Y nt ulq-1,-1) E-1 [pulceale ) (+1-o)] Ct-1 1-a y = zkont 1= net +12 yt = a +it ky = it-1 + (1 - 8)kt-1 -1 (cll-*):-* u(cl) = 1-0 In z = (1-P) In + pln 2-1 +et Your job is to log-linearize the above system around the steady state using first-order taylor series approxima- tions to find a model in the form: Art = Ba2+-1 + Cet Programming 2. Hierarchical clustering Implement a hierarchical clustering procedure from scratch (without using sklearn or a similar package) in python