PS1 - Econ 100B Winter 2010

PS1 - Econ 100B Winter 2010 - q = L 1 4 K 3 4 When K = 1...

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ECO 100B Problem Set 1 Answers will be posted on January 19, 2010 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 (b) f ( L, K ) = LK (c) f ( L, K ) = ( LK ) 2 (d) f ( L, K ) = LK 1 2 . (e) f ( L, K ) = 10 KL K + L 2. Suppose that two firms, Firms 1 and 2, use the same technology but Firm 2 is only 75% as productive as Firm 1: for Firm 1, q 1 = f ( L, K ) and for firm 2, q 2 = 3 4 f ( L, K ). At a particular level of inputs, L and K , how does the Marginal Product of Labor differ across the firms? How does the Marginal Rate of Technical Substitution differ? 3. Suppose that the production function
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Unformatted text preview: q = L 1 4 K 3 4 . When K = 1 and q = 2, what are the MP L and the MRTS ? 4. Suppose that a production function, f , is homogenous of degree γ , i.e., f ( λL,λK ) = λ γ f ( L,K ). Under what conditions does such a production function have constant returns to scale? Prove the following statements about such a production function: (a) MP L is homogenous of degree γ-1. (b) L df dL + K df dK = γf ( L,K ). 5. For what values of a and b will the production function f ( L,K ) = ( L a + K a ) 1 b for a , b > exhibit increasing, constant, or decreasing returns to scale? 1...
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