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Chap3&4 Sol - Chapter 3 NAME Preferences...

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Chapter 3 NAME Preferences Introduction. In the previous section you learned how to use graphs to show the set of commodity bundles that a consumer can a ff ord. In this section, you learn to put information about the consumer’s preferences on the same kind of graph. Most of the problems ask you to draw indi ff erence curves. Sometimes we give you a formula for the indi ff erence curve. Then all you have to do is graph a known equation. But in some problems, we give you only “qualitative” information about the consumer’s preferences and ask you to sketch indi ff erence curves that are consistent with this information. This requires a little more thought. Don’t be surprised or disappointed if you cannot immediately see the answer when you look at a problem, and don’t expect that you will find the answers hiding somewhere in your textbook. The best way we know to find answers is to “think and doodle.” Draw some axes on scratch paper and label them, then mark a point on your graph and ask yourself, “What other points on the graph would the consumer find indi ff erent to this point?” If possible, draw a curve connecting such points, making sure that the shape of the line you draw reflects the features required by the problem. This gives you one indi ff erence curve. Now pick another point that is preferred to the first one you drew and draw an indi ff erence curve through it. Example: Jocasta loves to dance and hates housecleaning. She has strictly convex preferences. She prefers dancing to any other activity and never gets tired of dancing, but the more time she spends cleaning house, the less happy she is. Let us try to draw an indi ff erence curve that is consistent with her preferences. There is not enough information here to tell us exactly where her indi ff erence curves go, but there is enough information to determine some things about their shape. Take a piece of scratch paper and draw a pair of axes. Label the horizontal axis “Hours per day of housecleaning.” Label the vertical axis “Hours per day of dancing.” Mark a point a little ways up the vertical axis and write a 4 next to it. At this point, she spends 4 hours a day dancing and no time housecleaning. Other points that would be indi ff erent to this point would have to be points where she did more dancing and more housecleaning. The pain of the extra housekeeping should just compensate for the pleasure of the extra dancing. So an indi ff erence curve for Jocasta must be upward sloping. Because she loves dancing and hates housecleaning, it must be that she prefers all the points above this indi ff erence curve to all of the points on or below it. If Jocasta has strictly convex preferences, then it must be that if you draw a line between any two points on the same indi ff erence curve, all the points on the line (except the endpoints) are preferred to the endpoints. For this to be the case, it must be that the indi ff erence curve slopes upward ever more steeply as you move to the right along it.
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