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spring2008_midterm1_soln

# spring2008_midterm1_soln - First Midterm Exam Econ 150b...

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First Midterm Exam Econ 150b. Intermediate Microeconomics February 6, 2008 Please put your discussion-section time and TA’s name on the blue books. 1. True or False? Explain. (a) The optimal solution of the consumer’s problem depends not only on the con- sumer’s preferences but also on the particular utility function that the consumer has. That is, two consumers with different utility functions but same preferences, may choose different bundles optimally. This is because the marginal rate of substi- tution is not fully determined by the preference relation, but depends on the utility function. Soln.: False. The optimal solution depends only on the preference relation, not on the particular utility function chosen to represent it. This is because two utility functions represent the same preference if and only if one is a monotone transfor- mation of the other. Another way of seeing this is by noticing that two utility fcns. that represent the same preferences give rise to the same MRS and the optimal is determined by MRS D p 1 =p 2 . (b) Every consumer whose preferences are represented by a utility function has transi- tive preferences. Soln.: True. Suppose X Y and Y Z , where X , Y and Z are bundles. Let u be a utility fcn. that represents the consumer’s preference relation . Since u represents we have u.X/ u.Y / and u.Y / u.Z/ , which implies u.X/ u.Z/ . In turn, since u represents , we can conclude that X Z . Hence, is transitive. (c) The marginal rate of substitution between two goods equals (minus) the ratio be- tween the marginal utilities. Soln.: True. The MRS is the slope of the indifference curve at a point. Along an indifference curve, we have u.x 1 ; x 2 / D constant for all .x 1 ; x 2 / . Hence, MU 1 dx 1 C MU 2 dx 2 D 0; which implies MRS D dx 2 =dx 1 D MU 1 =MU 2 . 1

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(d) The slope of the budget line has a kink whenever the two goods are perfect com- plements. Soln.: False. Whether the budget set has a kink or not does not depend on the consumer’s preferences at all. Rather that depends on whether there are nonlinear taxes or subsidies. One example of kinked budget set is the food stamps subsidy example from Homework #2. (e) Every inferior good is a Giffen good. Soln.: False. Whether an inferior good is a Giffen good or not depends on the relative magnitudes of the income and substitution effects. If for a certain inferior
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