ECON 500 Quiz: ECON 500 UIUC quiz_1_2007_w
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All questions must be answered on this form. Use the back of this form and the last page as scratch paper do not use your own paper. Question 1 suppose preferences (cid:23) are rational and convex, but not necessarily continu- ous. Let x(p, w) be the walrasian demand at prices p and w. prove that x(p, w) is a convex set if x(p, w) , . Proof recall that the preferences are convex if {z rl y rl. Let x, x x(p, w) and [0, 1]. +|z (cid:23) y} is a convex set for all. That is, you must use the same notation. Also, you must specify the choice of y (in the de nition of convexity). Question 2 let x = {a, b, c} and b = {{a, b}, {a, c}, {b, c}}. Question 3 suppose a utility function is given by u(x1, x2) = max{2x1, x2}.
