ECON 200 Problem Set 1 Solutions Fall 2007

ECON 200 Problem Set 1 Solutions Fall 2007 - Economics 200...

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Economics 200 Macroeconomic Theory Solutions to Problem Set 1 1. (a) Let and calculate , ] œ +O  ,P ] œ +Ð O Ñ  ,Ð P Ñ œ Ð+O  ,P Ñ œ ] !! ! " ! ! ! ! ! -- - - showing that this production function exhibits constant returns to scale. (b) Let and calculate , ] œ Ö+O ß,P × Ö+ O ß, P ל Ö+O ß,P ל ] ! " ! ! ! ! ! min min min - - showing that this (Leontief) production function exhibits constant returns to scale. (c) Let and calculate ] œE +Ð,O Ñ Ð"+ÑÒÐ",ÑP Ó ! " ˜™ )) " ) E +Ð, O Ñ  Ð"  +ÑÒÐ"  ,Ñ P Ó œ E + Ð,O Ñ  Ð"  +Ñ ÒÐ"  ,Ñ P Ó ˜ - - - ! ! ) ) ) ) " " ) ) œE Ò+Ð,O Ñ Ð"+ÑÒÐ",Ñ P Ó Ó œ E +Ð,O Ñ Ð"+ÑÒÐ",Ñ P Ó ˜ - - ) ) ) " " ) ) œ] - ! , showing that this (constant elasticity of substitution or CES) production function exhibits constant returns to scale. 2. (a) The original level of output is and the new level is ]œEOP 0 αα " ] œ EO ÒÐ"Þ!#ÑPÓ œ œ Ð"Þ!#Ñ œ "Þ!" œ 1 3 α " " ] ]E O P EO ÒÐ"Þ!#ÑPÓ " . Thus, 3 for . That is, " !
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This note was uploaded on 04/26/2010 for the course ECON 101 taught by Professor Staff during the Spring '08 term at Vassar.

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ECON 200 Problem Set 1 Solutions Fall 2007 - Economics 200...

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