119Sols1

119Sols1 - Economics 119 Midterm, Spring 2007 - Suggested...

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Economics 119 Midterm, Spring 2007 - Suggested Solutions Please see David Owens for questions on grading and the solutions for this midterm. Question 1. A decisionmaker has reference-dependent preferences over mugs and money. Specif- ically, if her consumption in mugs and money is c 1 and c 2 , respectively, and here reference point in mugs and money is r 1 and r 2 , respectively, her utility is v (4 c 1 - 4 r 1 ) + v ( c 2 - r 2 ), where the value function v satisﬁes v ( x ) = x for x 0 and v ( x ) = 2 x for x 0. Normalize the decisionmaker’s current wealth to zero, and suppose she starts oﬀ with zero mugs. Part a: [8 Points]. Suppose the decisionmaker receives no mugs or money, and this is her reference point. Calculate her buying price (the maximum amount she is willing to pay for a mug). u (0 , 0 | 0 , 0) = u (1 , - p b | 0 , 0) v (4 × 0 - 4 × 0) + v (0 - 0) = v (4 - 4 × 0) + v (0 - p b ) v (0) + v (0) = v (4) + v ( - p b ) 0 + 0 =4 + 2 × ( - p b ) p b =2 The decisionmaker’s buying price is \$2. Part b: [8 Points]. Suppose the decisionmaker receives a mug and no money, and this be- comes her reference point. Calculate her selling price (the minimum amount for which she is willing to sell the mug). u (1 , 0 | 1 , 0) = u (0 ,p s | 1 , 0) v (4 × 1 - 4 × 1) + v (0 - 0) = v (4 × 0 - 4 × 1) + v ( p s - 0) v (0) + v (0) = v ( - 4) + v ( p s ) 0 + 0 =2 × ( - 4) + p s p s =8 The decisionmaker’s selling price is \$8 . Part c: [8 Points]. What is the amount the decisionmaker from Part (b) would be willing to pay to buy another mug? u (1 , 0 | 1 , 0) = u (2 , - p 2 b | 1 , 0) v (4 × 1 - 4 × 1) + v (0 - 0) = v (4 × 2 - 4 × 1) + v (0 - p 2 b ) v (0) + v (0) = v (4) + v ( - p 2 b ) 0 + 0 = 4 + 2 × ( - p 2 b ) p 2 b =2 1

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The decisionmaker would be willing to pay \$2 for a second mug. Part d [8 Points]. Now suppose that the decisionmaker from Part (b) makes two decisions that will be carried out at the exact same time. One decision is whether to sell the mug for \$6. The other decision is whether to buy another mug for \$3. She knows in advance that she will be making both decisions. But suppose that when she makes each of these decisions, she does not take into account that she is also making the other one, acting as if there was no other decision. (i: [2 Points]) What concept you have learned in the class describes this type of decisionmaking? narrow bracketing (ii: [6 Points]) What decisions will the person make? Is there something weird about them? As p 2 b < 3 from part c, and p s > 6 from part b, the decision-maker would reject both choices if she brackets narrowly. This is weird, as if she brackets broadly, she would wind up with the same amount of mugs (1) and 3 additional dollars, which would clearly be to her beneﬁt. Part e: [18 Points].
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This homework help was uploaded on 04/20/2008 for the course ECON 119 taught by Professor K during the Spring '08 term at Berkeley.

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119Sols1 - Economics 119 Midterm, Spring 2007 - Suggested...

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