prelims_Micro Prelim August 2007

prelims_Micro Prelim August 2007 - University of...

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University of California, Davis Date: August 30, 2007 Department of Agricultural and Resource Economics Department of Economics Time: 5 hours Microeconomics Reading Time: 20 minutes PRELIMINARY EXAMINATION FOR THE Ph.D. DEGREE Please answer four of the following five parts Part 1. The present and the future Let there be two goods: Good 1 is interpreted as present consumption and good 2 as future consumption . We assume that the utility function of the consumer is differentiable, strictly quasiconcave and locally nonsatiated, and that her Walrasian demand function, denoted 112 212 ((, ,) , (, ,) ) xppwxppw %% , is well-defined and differentiable, and we restrict our attention to domains for which ) is strictly positive. The consumer is endowed with ω 1 units of present consumption and ω 2 units of future consumption, but has no other sources of wealth (no nonendowment wealth, or profit income). The market allows the consumer to exchange the two goods, in any direction and at any scale, at the constant rate of 1 + r units of future consumption for each unit of present consumption. The real number r is called the market interest rate , which the consumer takes as given. If, given r , the consumer chooses x 1 < ω 1 (resp. x 1 > ω 1 , resp. x 1 = ω 1 ), then we say that she is a saver (resp. a borrower , resp. autarkic ) at r . We refer to the difference s ω 1 - x 1 as the savings of the consumer, which can be positive, negative or zero. 1.1. Write the consumer optimization problem in terms of the parameters p 1 and p 2 , interpreted as the prices of present and future consumption, respectively. Assume that the solution function, denoted 112 212 ˆˆ ((,) ,(,) ) xpp xpp , is well defined and differentiable. What is the relationship between p 1 , p 2 and r ? Graphically represent the consumer optimization problem in consumption space. 1 . 2 . Write the Slutsky equation for 12 ˆ (, ) ,, 1 , 2 k j xpp kj p = .
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1.3. Assume that both goods are normal, i. e., 12 (, ,) 0, 1,2 k x ppw k w >= % . 1 . 3(a) Without further information, what can we say about the sign of 112 1 ˆ (, ) xpp p when the consumer is a borrower? A saver? Autarkic? Argue your answer, and provide an intuitive explanation. 1 . 3(b) Without further information, what can we say about the direction of the change in present consumption as the interest rate r rises when the consumer is a borrower? A saver? Autarkic? Argue your answer and provide an intuitive explanation. 1.3(c) Without further information, what can we say about the sign of 212 2 ˆ p when the consumer is a borrower? A saver? Autarkic? Argue your answer, and provide an intuitive explanation. 1.3(d) Without further information, what can we say about the direction of the change in future consumption as the interest rate r rises when the consumer is a borrower? A saver? Autarkic? Argue your answer and provide an intuitive explanation.
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This note was uploaded on 02/09/2010 for the course ECON 200D taught by Professor Pontusrendahl during the Winter '06 term at UC Davis.

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prelims_Micro Prelim August 2007 - University of...

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