ECON 2 Midterm: Economics 210A UCSB Midterm13
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ECON 2 Full Course Notes
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Answer question 1 and any 4 of the other 6 questions. Good luck: let f be a real-valued concave function whose domain is a convex subset of. Let g be a function from the reals to the reals and de ne the composite function h(x) = g (f (x)). State whether each of the following claims about the function h is true or false. If true, give a proof, justifying each claim made in your proof. If false, give a counterexample and prove that your counterexample is a counterexample: if g is a strictly increasing function, then h is a concave function. Let f be a function of a single variable, f (x) = x. But h is not a concave function, as you can verify by taking the second derivative of h: if g is an increasing, concave function, then h is a concave function. True: take any x and y in the domain of f .
