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Econ501aMidans04 - The Ohio State University Department of...

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The Ohio State University Department of Economics Econ 501a Spring 2004 Prof. James Peck Midterm Answers Part I: Short Answer. 1. (10 points) Suppose that a consumer°s preferences over bundles of goods x and y are represented by the utility function, u ( x; y ) = xy . That is, one bundle is preferred over a second bundle if and only if the amount of good x multiplied by the amount of good y is greater in the ±rst bundle than in the second bundle. Brie°y show that these preferences satisfy the ±rst three axioms of consumer rationality. That is, show that these preferences are complete, re²exive, and transitive (see the equation sheet). Answer: For any two bundles, ( x 1 ; y 1 ) and ( x 2 ; y 2 ) , exactly one of the following con- ditions will be true: x 1 y 1 > x 2 y 2 ; x 1 y 1 = x 2 y 2 ; or x 1 y 1 < x 2 y 2 : Therefore, preferences are complete. Preferences are re²exive, because x 1 y 1 = x 1 y 1 . Finally, if we have x 1 y 1 > x 2 y 2 and x 2 y 2 > x 3 y 3 , then it follows that we have x 1 y 1 > x 3 y 3 . Therefore, preferences are transitive. 2. (10 points) From January 1979 to January 1980, the price of gold more than doubled. As the price of gold rose, the quantity of gold demanded increased as well. Brie²y explain why it is not reasonable to say that this is an example of the income e/ect swamping the substitution e/ect. Answer: The substitution e/ect of the price increase would be for the demand for gold to decrease. The income e/ect is the change in the demand for gold, due to the resulting reduction in purchasing power, holding relative prices constant. For normal goods, the income e/ect will reinforce the substitution e/ect, so that demand for gold should fall further. Unless you believe that gold is an inferior good, where poor people have more gold than rich people, the explanation cannot be due to the income e/ect swamping the substitution e/ect.
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