ajaz_eco_204_2012_2013_chapter_16_Market_Power

Are let of data points the 1st foc implies

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Unformatted text preview: ̅ )( ∑( (,) () ̅ ∑( ̅̅̅) ̅ )( ∑( ̅) ∑( ̅̅̅) ̅) __________________________________________________________________________________________________ Optional “ECO 220” Proof: The regression model: This is a special case of the general simple regression model: We now show how to compute , by regressing (the dependent variable) on a constant and variable) by minimizing the sum of squared errors (aka OLS or “Ordinary Least Squares”)5: , ∑ ∑( (the independent ) The FOCs are: ∑ ∑( ∑ Let ∑( ) # of data points. The 1st FOC implies that: ∑( 5 ) ) You will see this derivation in ECO 220 as well. 10 ECO 204 Chapter 16: Analysis of Firms with Market Power (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ∑ ∑( ) ∑ ∑ ∑ ̅ ∑ ̅ ̅ ̅ ̅ The 2nd FOC implies that: ∑( ̅ Substitute ) ̅ to get: {̅ ̅} ∑( ̅ ̅ ∑( ̅) ∑ ̅∑ ∑ ∑ ̅∑ ∑ ∑( ∑( ∑( ̅) ̅) ∑ ∑ ∑̅ ∑̅ ) ) ∑( ̅) ∑ ̅ ̅ ∑ (, ) () ̅̅̅ ̅̅...
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