Problem 3. Show that the Cobb-Douglas production function, F(K; L) = KaL¹-a (for K; L> 0 and 0 < a < 1) satisfies the following properties. Hint: The derivative of rª with respect to x is axª-¹. a) is increasing in each input. [Hint: Show that the partial derivative regarding each input is positive]; b) has constant returns to scale; for every > 0. c) Has diminishing returns to L holding K constant. [Hint: take the second partial derivative of F respect to L and check that is negative.]

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