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Econ 104 PS4 Solutions(3)

# Econ 104 PS4 Solutions(3) - Economics 104 Problem Set 4...

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Unformatted text preview: Economics 104 Problem Set 4 Solutions Molin Zhong October 18, 2011 1 Problem 1 1.1 Part A ˜ β 1 = n ∑ i =1 ( c 2 x i- c 2 x )( c 1 y i- c 1 y ) n ∑ i =1 ( c 2 x i- c 2 x ) 2 = c 1 c 2 c 2 2 n ∑ i =1 ( x i- x )( y i- y ) n ∑ i =1 ( x i- x ) 2 = c 1 c 2 c β 1 ˜ β = c 1 y- ˜ β 1 c 2 x = c 1 y- c 1 c β 1 x = c 1 c β 1.2 Part B ˜ β 1 = n ∑ i =1 ( c 2 + x i- c 2- x )( c 1 + y i- c 1- y ) n ∑ i =1 ( c 2 + x i- c 2- x ) 2 = n ∑ i =1 ( x i- x )( y i- y ) n ∑ i =1 ( x i- x ) 2 = c β 1 ˜ β = c 1 + y- ˜ β 1 ( c 2 + x ) = c 1- c β 1 c 2 + y- c β 1 x = c 1- c β 1 c 2 + c β 1.3 Part C ˜ β 1 = n ∑ i =1 ( x i- x )(log( c 1 y i )- log( c 1 y )) n ∑ i =1 ( x i- x ) 2 = n ∑ i =1 ( x i- x )(log( c 1 ) + log( y i )- log( c 1 )- log( y )) n ∑ i =1 ( x i- x ) 2 = n ∑ i =1 ( x i- x )(log( y i )- log( y )) n ∑ i =1 ( x i- x ) 2 = c β 1 ˜ β = log( c 1 y )- ˜ β 1 x = log c 1 + log( y )- c β 1 x = log c 1 + c β 1 1.4 Part D ˜ β 1 = n ∑ i =1 (log( c 2 x i )- log( c 2 x ))( y i- y ) n ∑ i =1 (log( c 2 x i )- log( c 2 x )) 2 = n ∑ i =1 (log( c 2 ) + log( x i )- log( c 2 )- log( x ))( y i- y ) n ∑ i =1 (log( c 2 ) + log( x i )- log( c 2 )- log( x )) 2 = n ∑ i =1 (log( x i )- log( x ))( y i- y ) n ∑ i =1 (log( x i )...
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Econ 104 PS4 Solutions(3) - Economics 104 Problem Set 4...

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