Unformatted text preview: 3. Suppose that the production function 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 ). (a) Under what conditions does such a production function have constant returns to scale? (b) Prove that MP L is homogenous of degree γ-1. (c) Prove that 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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- Spring '07
- Economics of production, Monotonic function