Unformatted text preview:  f (a) 2. A function f is said to be strictly concave if for all x y, f (x + (1  )y) > f (x) + (1  )f (y) for all (0, 1). > 0 and for all x > 0, 6. The contrapositive of P R is R P . 7. A set is said to be compact if it is both closed and bounded. 8. The diameter of a set X is diam(X) = sup{d(x, y) x, y X}. Section B: Proofs Choose 6 of the following 8 questions. This section of the exam is worth 40%. For each of the following, answer true or false. If true, prove. If false, derive a counterexample 1. If f C 1 is homogeneous of degree k then f is homogeneous of degree k  1. Solution: True. If f is homogeneous of degree k then: f ( x) =
k Taking the derivative of the above identity with respect to x yields: f ( x) =
k f (x) 2. The function f (x) = 20 + x is weakly concave and weakly convex over R. and hence f is homogeneous of degree k  1. f (x) f ( x) = k1 f (x) 3. Let f be a continuous function...
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This document was uploaded on 03/20/2014 for the course ECON 2p30 at Brock University.
 Fall '12
 laster
 Economics

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