400ps2-11-soln

# 400ps2-11-soln - ECON 400 Winter 2011 SOLUTIONS FOR PROBLEM...

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ECON 400 Hartman Winter 2011 SOLUTIONS FOR PROBLEM SET II 1(a) Since 2 3 2 1 2 1 2 ( )( ) tx tx t x x , the function is homogeneous of degree 3. Euler's theorem holds because 2 1 2 f x and 2 1 2 2 f x x so that 2 2 2 1 1 2 2 1 2 1 2 1 2 2 3 3 x f x f x x x x x x f . 1(b) Since 2 2 2 1 2 2 1 2 2 ( )( ) ( ) ( ) tx tx tx t x x x , the function is homogeneous of degree 2. Euler's theorem holds because 1 2 f x and 2 1 2 2 f x x so that 2 1 1 2 2 1 2 2 1 2 1 2 2 ( 2 ) 2( ) 2 x f x f x x x x x x x x f . 1(c) Since 1 1 2 1 2 1 2 2 2 2 2 2 2 2 1 2 1 2 1 2 ( ) ( ) 2( ) ( 2 ) 2 tx tx t x x x x t tx tx t x x x x , the function is homogeneous of degree 1 . Euler's theorem holds because 2 2 1 2 1 1 2 1 2 2 2 1 2 2 2 ( ) ( 2 ) x x x x x f x x and 2 2 1 2 2 1 2 2 2 2 2 1 2 2 4 ( ) ( 2 ) x x x x x f x x so that 2 2 2 2 1 1 2 1 1 2 2 1 2 2 1 2 1 1 2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 1 2 1 2 1 2 1 2 1 2 2
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