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Unformatted text preview: Intermediate Microeconomics, 2008 Problem Set No 3: Solutions Problems 1) Consider three people, A,B,C and the relation at least as old as. Is this relation transitive? Is it complete? Each person has an age which can be represented as a number. at least as old as is equiva- lent to the sign on these numbers. on a set of numbers is both transitive and complete. 2) For the same group of three people, consider the relation strictly older than. Is this relation transitive? Is it complete? This relation is the usual > applied to ages. > on a set of numbers is transitive: if person A is older than person B and person B is older than person C , then it must be the case that person A is older than person C . However, this relation is not complete: two distinct people of the same age cannot be compared using this relation. 3) Suppose a trainer wants to pick among a group of players and suppose he always weakly prefers someone who is bigger and faster. Is his preference relation complete? Is it transitive? His preference relation is not complete: Suppose player A is strictly bigger than player B but B is strictly faster than A . Then the trainer cannot compare players A and B . His preference relation is transitive: Suppose player C is both bigger and faster than D and D is bigger and faster than E . Then C is necessarily at least as big as E and C is at least as fast as E . Therefore, C is both bigger and faster than E and transitivity is satisfied. 4) What is your marginal rate of substitution between $ 10 Bills and $ 1 Bills? Each $10 bill is worth exactly 10 $1 bills (they are perfect substitutes) so the MRS =- 1 10 . 5) What is the marginal rate of transformation between a $ 10 Bill and a 10Euro Bill? Dollars can be transformed into Euros according to the exchange rate, so the MRT is equal to the exchange rate between dollars and Euros. 6) What are some goods for which you might have concave (or at least not weakly convex) prefer- ences? Apple accessories and PC accessories: If the two products are not compatible, Id prefer to have all of my computer accessories made by one company to having a mixture. 1 7) We learned in class that utility is all about ordering. Suppose someone has preferences repre- sented by the utility function U ( q 1 ,q 2 ) = aq 1 + bq 2 . Suppose someone else has preferences given by the utility function U ( q 1 ,q 2 ) = aq 1 + bq 2 + 5 . 1 . If you choose some parameters, a and b , can you draw their indifference curves? How would they rank the bundles A = (1 , 1) and B = ( 1 2 , 2 ) depending on a and b ? Do they rank A and B differently?...
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- Winter '08