A. True, False, Uncertain and Explain: determine whether the statement is true,

Question

A. True, False, Uncertain and Explain: determine whether the statement is true, false or uncertain and explain your reasoning – you only earn points for your explanation. 1. If preferences are convex, the set of points at least as good as any given point is a convex set. 2. If preferences are strictly convex, the set of points “no better than” any given point is a convex set. 3. If a consumer has strictly convex preferences over two goods and she is indifferent between bundle A given by (4, 6) and bundle B given by (2, 8), then she prefers bundle C given by (3, 7) over either bundle A or bundle B. 4. If a consumer has preferences over two "bads" then these preferences cannot be convex. 5. If apples (a good) are on the horizontal axis and dirty socks (a bad) are on the vertical axis then the indifference curves that represent convex preferences over these two items is upward sloping and flattens out as moving from left to right. 6. If preferences are not monotonic then they cannot be transitive

Explanation / Answer

1. If preferences are convex, the set of points at least as good as any given point is a convex set.

False. Reason: Convex preferences are those where the consumer prefers the weighted average of two bundles than either bundle. Thus, the correct statement should have been, ‘If preferences are convex, the set of points are exactly as good as any given point is a convex set.’

2. If preferences are strictly convex, the set of points “no better than” any given point is a convex set.

True. Reason: Since the points are no better than, it means they are similar to any given point, which means all the set of points show average. Thus, it is correct.

3. If a consumer has strictly convex preferences over two goods and she is indifferent between bundle A given by (4, 6) and bundle B given by (2, 8), then she prefers bundle C given by (3, 7) over either bundle A or bundle B.

True. Reason: Since the consumer has a strict convex preference, the consumer prefers the weighted average of two bundles than either bundle. So if the consumer wants to compare and choose bundle C, it can choose and compare it over either bundle A or bundle B because both mean same to him.

4. If a consumer has preferences over two "bads" then these preferences cannot be convex.

False. Reason: Convex preferences are such when the consumer is indifferent between both the given bundles. These bundles can either be ‘bad’ type or ‘good’ type. It is the weight of the bundles that make the preference convex and not the type.

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