5) Suppose that Fred has preferences over two goods (x1 and x2). Unlike the examples we've studied so far in class, Fred has a "satiation point". In other words, there exists a bundle X= (x1 *, x2 *) such that, for any other bundle A, X* > A. a) Suppose Fred's indifference curves look like circles around the point X*. Make a sketch in two- dimensional good space showing two or three indifference curves and the point X*. For any bundle A, let rA be the radius of ICA, i.e., the length of a line segment connecting X and A in two-dimensional space. Fred's preferences are such that A B if and only if rA <rB. b) Do Fred's preferences satisfy our three axioms? c) Do Fred's preferences satisfy monotonicity? Explain why or why not. (Use of graphs is highly encouraged!) d) Do Fred's preferences satisfy convexity? Explain why or why not. (Again, graph recommended!)/ne) If you answered "no" to one or more of parts b) - d), is there a region in good space where Fred's preferences are well-behaved? Problem 5. Suppose that Marsha, Jan, and Cindy each have transitive preferences over oranges, apples, and pears. (Ignore quantities, all we're talking about is who likes what fruit better; so, for example, Marsha's preferences could be apples oranges, oranges pears, and thus by transitivity, apples pears.) Suppose we define "group preference", ZG, by simple majority vote: for example, "apples ZG oranges" means that at least two of Marsha, Jan, and Cindy have preferences where apples oranges. Show by example (i.e., specify each consumer's preferences over the 3 fruits) that it is possible that G is not transitive even if Marsha, Jan, and Cindy's preferences all satisfy transitivity. (Hint: The solution here is often referred to as the "Condorcet Paradox", or paradox of voting. The Wiki for this is actually pretty informative and is a decent place to nerd out if you're interested.)

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5) Suppose that Fred has preferences over two goods (x1 and x2). Unlike the examples we've studied so far in class, Fred has a "satiation point". In other words, there exists

a bundle X= (x1 *, x2 *) such that, for any other bundle A, X* > A. a) Suppose Fred's indifference curves look like circles around the point X*. Make a sketch in two- dimensional good space showing two or three indifference curves and the point X*. For any bundle A, let rA be the radius of ICA, i.e., the length of a line segment connecting X and A in two-dimensional space. Fred's preferences are such that A B if and only if rA