Problem Set 8 - Solution

# Problem Set 8 - Solution - Econ 313-1 TA Tian Liang...

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Econ 313-1 TA: Tian Liang Solutions to Problem Set 8 1. (a) i. A = 1 ;a = 1 ;b = 2 f (4 ; 6) = 1 4 6 2 = 144 2 f (2 ; 3) = 2 1 2 3 2 = 36 f (4 ; 6) > 2 f (2 ; 3) ii. A = 1 ;a = 1 3 ;b = 2 3 f (4 ; 6) = 2 f (2 ; 3) = 5 : 24 iii. A = 1 ;a = 1 6 ;b = 2 6 f (4 ; 6) = 2 : 29 ; 2 f (2 ; 3) = 3 : 24 ;f (4 ; 6) < 2 f (2 ; 3) (b) f ( tK;tL ) = A ( tL ) a ( tK ) b = t a + b AL a K b = t a + b f ( K;L ) i. a + b > 1 ) f ( tK;tL ) > tf ( K;L ) ) IRS ii. a + b = 1 ) f ( tK;tL ) = tf ( K;L ) ) CRS iii. a + b < 1 ) f ( tK;tL ) < tf ( K;L ) ) DRS (c) i. A = 1 ;a = 1 ;b = 2 ;f ( L;K ) = LK 2 Isoquant: LK 2 = y a + b > 1 ) IRS ii. A = 1 ;a = 1 3 ;b = 2 3 ;f ( L;K ) = L 1 3 K 2 3 Isoquant: L 1 3 K 2 3 = y 1

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a + b = 1 ) CRS iii. A = 1 ;a = 1 6 ;b = 2 6 ;f ( L;K ) = L 1 6 K 2 6 Isoquant: L 1 6 K 2 6 = y a + b < 1 ) DRS (d) MP L = @f @L = aAL a 1 K b > 0 @MP L @L = a ( a 1) AL a 2 K b ; so MP L is decreasing as L increases if a < 1 . TRS
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Problem Set 8 - Solution - Econ 313-1 TA Tian Liang...

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