Exam 2 Note Sheet edited - Chapter 4: UtilityUtility- way...

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Chapter 4: Utility Utility- way to describe consumer preferences- doesn’t matter how much higher doesn’t matter. Utility function- assigning numbers to cons. bundles, more preferred= higher number. Ordinal utility- ranking cons bundles. Monotonic transformation- transform one set of numbers into another set of numbers, preserves order of numbers (e.g. multiplying all numbers by 2). Rate of change of f(u) as u changes- f/ u= (f(u 2 )-f(u 1 ))/(u 2 -u 1 ). Monotonic function- always pos. rate of change (pos slope) f(u 2 )- f(u 1 ) always has same sign as u 2 -u 1 . If f(u) is a mon trans of a utility func that reps some partic pref, then f(u(x 1 ,x 2 )) reps same pref. Utility func= way of assigning # to the diff indiff curves so higher curves get larger #s. Cardinal utility- size of utility difference between 2 bundles supposed to have significance (really no way to determine, almost useless). Level set- set of all (x 1 ,x 2 ) such that u(x 1 ,x 2 )= a constant. UTILITY FUNCTION= CONSTANT ALONG INDIFF CURVES and ASSIGN HIGHER LABEL TO MORE PREFERRED BUNDLES . Perfect substitutes- u(x 1 ,x 2 )= ax 1 +bx 2 (a and b are positive # that measure value of goods 1 and 2 to customer, slope= -a/b perfect complements (left and right shoes)- u(x 1 ,x 2 )= min{x 1 ,x 2 } in proportions other than one-to-one: (e.g 2:1) min{x 1 ,1/2x 2 } can multiply to get rid of fraction: min{2x 1 ,x 2 }. Basically: u(x 1 ,x 2 )= min{ax 1 ,bx 2 }. Qusilinear “partly linear” preferences: indiff curves vertical translates of one another (vertically shifted) x 2 =k-v(x 1 ) k= diff constant for each indiff curve height of each indiff curve is some function of x 1 , -v(x 1 )+constant k: higher value k give higher indiff curves . u(x 1 ,x 2 )=k=v(x 1 )+x 2 . (e.g.: sqrt(x 1 )+x 2 or lnx 1 +x 2 ). Cobb-Douglas utility function: u(x 1 ,x 2 )= (x 1 c x 2 d ) c and d are positive # that describe pref of consumer cobb-douglas indifference curves look just like the convex, monotonic indiff curves- referred to as “well behaved indiff curves” examples of mon transformation of cobb-doug util func: u(x 1 ,x 2 )=ln(x 1 c x 2 d )=clnx 1 +dlnx 2 and: u(x 1 ,x 2 )= x 1 c x 2 d then raise utility to 1/(c+d) power we get: x 1 c/c+d x 2 d/c+d then define a number a=c/(c+d) rewrite as: u(x 1 ,x 2 )= x 1 a x 2 1-a . We can always take a monotonic transformation of the cobb-douglas utility function that make the exponents sum to 1. Marginal utility- rate of change of consumer’s utility as we give him more of good 1: MU 1 = U/ x 1 =(u(x 1 + x 1 ,x 2 )-u(x 1 ,x 2 ))/ x 1 U= rate of change in utility, x 1 = change in amount of good 1 . to calculate change in utility associated with a small change in consump of good 1- multiply change in cons by marg utility of the good: U=MU 1 x 1 , marginal utility for good 2: MU 2 = U/ x 2 = (u(x 1 ,x 2 + x 2 )-u(x 1 ,x 2 ))/ x 2 to calc change in utility associated with change in consump of good 2: U=MU
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This note was uploaded on 09/23/2010 for the course BMGT 381 taught by Professor Dawson during the Spring '10 term at University of Maryland Baltimore.

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