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Unformatted text preview: ECO 100B Problem Set 1 Solutions 1. For each of the following, say whether the production technology satisfies (i) Diminishing 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 ) = √ 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, the technology satisfies (i) since | MRTS | is strictly decreasing in L . The technology also satisfies (ii) since 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 ( λL,λK ) = p ( λL )( λK ) = λ √ 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 satisfies (i). However, the technology does not satisfy diminishing marginal product insatisfies (i)....
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This note was uploaded on 01/20/2010 for the course ECON 100 taught by Professor Hnewhous during the Spring '08 term at UCSD.
- Spring '08