Econ100B PS1 Solutions

Econ100B PS1 Solutions - ECO 100B Problem Set 1 Answers...

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ECO 100B Problem Set 1 Answers will be posted on April 11, 2008 MRTS, (ii) Diminishing Marginal Product in each input, and (iii) Constant Returns to Scale (assume throughout that L;K > 1 ): (a) f ( L;K ) = L + K Solution : MP L = df dL = 1 = df dk = MP K , and MRTS = MP L MP K = 1 . Hence, the product does not satisfy (i) or (ii). The technology does satisfy CRS. (b) f ( L;K ) = p LK Solution : MP L = df dL = 1 2 K L ± 1 2 , MP K = 1 2 K L ± 1 2 . MRTS = K L . By observation, j MRTS j is strictly decreasing in L . The technology also d dL MP L = 1 4 K 1 2 L 3 2 < 0 , and d dK MP K = 1 4 K 3 2 L 1 2 < 0 . Finally, f ( &L; ) = p ( ) ( ) = p LK , and hence, the technology does satisfy CRS. (c) f ( L;K ) = ( LK ) 2 Solution : MP L = 2 LK 2 , and MP K = 2 KL 2 . So, MRTS = K L . So, the technology
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Econ100B PS1 Solutions - ECO 100B Problem Set 1 Answers...

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