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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 × ] œ Ö+ O ß , P × œ Ö+O ß ,P × œ ] ! ! ! " ! ! ! ! ! min min min - - - - showing that this (Leontief) production function exhibits constant returns to scale. (c) Let and calculate ] œ E +Ð,O Ñ  Ð"  +ÑÒÐ"  ,ÑP Ó ] œ ! ! ! " ˜ ) ) " ) E +Ð, O Ñ  Ð"  +ÑÒÐ"  ,Ñ P Ó œ E + Ð,O Ñ  Ð"  +Ñ ÒÐ"  ,Ñ P Ó ˜ ˜ - - - - - ! ! ! ! ) ) ) ) ) ) " " ) ) œ E 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 ] œ EO P 0 α α " ] œ EO ÒÐ"Þ!#ÑPÓ œ œ Ð"Þ!#Ñ œ "Þ!" œ 1 3 α α α " " ] ] EO P EO ÒÐ"Þ!#ÑPÓ " . Thus, 3 for . That is, " !
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