Econ501aMidansW07

Econ501aMidansW07 - The Ohio State University Department of...

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Department of Economics Econ 501.02 Winter 2007 Prof. James Peck Midterm Questions and Answers Part I: Short Answer. 1. (10 points) True or False, and explain. If a consumer’s preferences for goods x and y can be represented by the utility function, u ( x, y )= xy ,then the preferences can also be represented by the utility function, u ( x, y )=10 xy . Answer: There are many ways to see that the answer is True. The coe - cient of 10 does not a f ect the underlying preferences, because the indi f erence curves are the same, only the labelling is di f erent. For example, the indi f er- ence curve corresponding to utility of 2 with the f rst utility function is the indi f erence curve corresponding to utility of 20 with the second utility func- tion. Another way to see that the preferences are the same is to notice that the marginal rate of substitution at any point ( x, y ) is y/x with either utility function. Finally, whenever ( x A ,y A ) is preferred to ( x B ,y B ) with the f rst utility func- tion, so x A y A >x B y B holds, then ( x A ,y A ) is preferred to ( x B ,y B ) with the second utility function, because 10 x A y A > 10 x B y B holds, and vice versa. 2. (10 points) True or False, and explain. If the price elasticity of demand for Honda Accords in the eastern half of the U.S. is 2 ,andifthepr ice elasticity of demand for Honda Accords in the western half of the U.S. is also 2 , then the price elasticity of demand for the entire U.S. market must be 2 . Answer: The answer I had in mind was True. Intuitively, if a 1% increase in price causes demand to fall by 2% in the East and 2% in the West, then overall demand must fall by exactly 2%. To show this formally, we know dX E dp x p x X E = 2= dX W dp x p x X W , so we can write dX E dp x = 2 X E p x (1) dX W dp x = 2 X W p x .
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This note was uploaded on 07/17/2008 for the course ECON 501.02 taught by Professor Yang during the Spring '08 term at Ohio State.

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Econ501aMidansW07 - The Ohio State University Department of...

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