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Unformatted text preview: over the domain D R. If D is not compact, a maximum may not necessarily exist. 4. If f (x) is a homogeneous function of degree k and g(x) is a homogeneous function of degree s then h(x) = f (x)g(x) is a homogeneous function. Solution: True. If f is homogeneous of degree k then f ( x) = homogeneous of degree s then g( x) = s g(x). Naturally: and so h is homogeneous of degree k - s. h( x) = f ( x) = g( x)
k s g(x) k Solution: True. f (x) = 0 and so f 0 and f 0 for all x R. Hence, f is weakly concave and weakly convex over R. Solution: True. Consider, for example, f (x) = x over the domain D = (0, 1). No maximum exists over this domain. f (x). Similarly, if g is f (x) = k-s f (x) g(x) = k-s h(x) 5. The function f (x) = x is not dierentiable at x = 0.
0 Solution: True. The derivative of a function at x exists if: lim + f (x + ) - f (x) f (x + ) - f (x) = lim - 0 2 For the function f (x) = x, at x = 0, we have:
0 since > 0. Conversely: since < 0. Since: lim + 0 + - 0 = lim = 1 + 0 0- lim 6. If X and Y are...
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This document was uploaded on 03/20/2014 for the course ECON 2p30 at Brock University, Canada.
- Fall '12