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Chapter 4: Utility
Utility
 a way to describe
consumer preferences. Utility function
 assigning numbers to consumers’ bundles
such that more preferred = higher number. Ordinal utility
 the ranking of consumer bundles. Monotonic
transformation
 transforms one set of numbers into another set of numbers while preserving the order (ex:
multiplying all numbers by 2). Rate of change of F(u) as u changes:
∆
f/
∆
u= (f(u2)(f(u1))/(u2u1). Monotonic
function:
always has a positive rate of change (positive slope), i.e. an increasing function, f(u2)f(u1) always has
same sign as u2u1. If f(u) us a monotonic transformation of a utility function that represents some preference,
then f(u(x1,x2)) represents the same preference. Utility function
 way of assigning numbers to the different
indifference curves so that higher curves get larger numbers. Cardinal utility
 size of the utility difference
between two bundles has significance. Level set:
set of all (x1, x2) such that u(x1,x2) is a constant. Utility
function:
is constant along indifference curves and assign a higher label to more preferred bundles.
Perfect
substitutes
u(x1,x2) = ax1 + bx2 (a and b are positive numbers that measure values of goods 1 and 2 to
customer, slope = a/b).
Perfect complements
(left and right shoes) u(x1,x2) = min{x1,x2} in proportions
other than one to one – (example: 2:1 – min{x1, ½ x2}, multiply out fraction, min{2x1, x2}, basically
u(x1,x2)= min{ax1, bx2}.
Quasilinear preferences
“partially linear” – indifference curves are vertical
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This note was uploaded on 12/01/2010 for the course ARTT 150 taught by Professor Staff during the Spring '10 term at Maryland.
 Spring '10
 staff

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