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Unformatted text preview: University of California, Davis Date: June 27, 2005 Department of Economics Time: 4 hours Microeconomics Reading Time: 20 minutes PRELIMINARY EXAMINATION FOR THE Ph.D. DEGREE ================================================================================== Please answer four of the following five questions 1. Choice with statusquo bias. A consumer’s consumption set is X . Her choice depends on both her attainable (or budget) set B ⊂ X and on her statusquo point s ∈ B . She is endowed with both a utility function u : X → ℜ and a movingcost function c : X → ℜ ++ , where c ( s ) is interpreted as the cost of leaving the status quo s . We restrict our attention to attainable sets B with the property that u has a unique maximizer on B , denoted x *( B ). At ( B , s ) (i. e., when facing the attainable set B from the statusquo point s ), she chooses (1) the statusquo point s if u ( s ) > u ( x *( B )) − c ( s ), (2) point x *( B ) if u ( s ) < u ( x *( B )) − c ( s ) , (3) either the statusquo point s or point x *( B ) if u ( s ) = u ( x *( B )) − c ( s ) . (Note that in this case her choice is not unique.) (a) Show that her choices satisfy the following property: if x ∈ B 1 ⊂ B is chosen at ( B , s ), then x is also chosen at ( B 1 , s ). Interpret this property in terms of revealed preference. (b) Show that there exists a function f that has both the consumption point x and the statusquo point s as vector arguments such that solving the problem max x f ( x , s ) subject to x ∈ B is equivalent to applying the choice rules (1) and (2). Interpret f . Is f continuous when X = ℜ N + and both u and c are continuous? (c) Let X = ℜ 2 + , u ( x 1 , x 2 ) = ( x 1 ) 0.5 ( x 2 ) 0.5 , and ( ω 1 , ω 2 ) = (2, 2). Consider budget sets of the form B [ p ] = {( x 1 , x 2 ) ∈ ℜ 2 + : x 1 + p x 2 < ω 1 + p ω 2 }, parameterized by the positive number p (understood as the normalized price of good 2). In this section, graphs can be approximate, but they should clearly indicate the ranges over which the curves are increasing or decreasing. (c.1) Assume that the consumer maximizes u in the usual manner, without statusquo bias, i.e., given p > 0, the consumer chooses ( x 1 , x 2 ) in order to maximize u ( x 1 , x 2 ) subject to ( x 1 , x 2 ) ∈ B [ p ]. Compute the solution function ( x 1 *( p ), x 2 *( p )) and the value function v ( p ) of this maximization problem. What is ( x 1 *(1), x 2 *(1))? What is v (1)? Separately graph x 2 *( p ) and v ( p ), with p on the horizontal axis. (c.2) Assume now that the consumer has a statusquo bias, as defined above, with statusquo point s = ( ω 1 , ω 2 ) = (2, 2), and with movingcost function c ( x ) = 0.2. Obtain and graph the relationship between p and her choice of x 2 (again, with p on the horizontal axis)....
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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.
 Winter '06
 PONTUSRENDAHL
 Microeconomics

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