MAT 2322 Final: MAT 2322 University of Ottawa 20051 mat2322 Final Exam +Solutions
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Provide an intuitive explanation with the help of a simple graphic: (20 points) a consumption bundle is represented by a vector x n. We represent a consumer"s pref- erences by a binary relation %, i. e. , if x1 % x2, we say that x1 is at least as good as x2. Assume that % can be represented by a real-valued function u : n. +, u(x0) u(x1) x0 % x1. u : n. + , i. e. , for all x0, x1 n. Show that u(x) is quasiconcave if and only if % is convex. (hint: proceed by contradiction. : (30 points) suppose that a consumer"s welfare depends on the quantities of agricultural goods x1 and manufactured goods x2 that she consumes. Suppose more precisely that her utility level can be represented by the following utility function: u(x1, x2) = (x1 1)1 (x2 2) , where i are positive parameter values and (0, 1). The respective prices of the goods are p1 and p2.
