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Unformatted text preview: ould be a rational choice.
D You are indifferent between the MacBook and the Dell. Gazzale (University of Toronto) ECO100: Consumer Choice I 10 / 21 Indifference Curves Building Preference “Maps”
A ﬁrst thought experiment Start with bundle a = {X a , Y a } I take “one unit” of X out of the bundle.
Marginal Rate of Substitution (MRSX ,Y ) at a: How many more
units of Y do I have to give you to exactly compensate you for this
oneunit X reduction? (∆1 )
New bundle b = {X a − 1, Y a + ∆1 } = {X b , Y b } Gazzale (University of Toronto) ECO100: Consumer Choice I 11 / 21 Indifference Curves Building Preference “Maps”
By construction U (a) = U (b) Gazzale (University of Toronto) ECO100: Consumer Choice I 12 / 21 Indifference Curves Reinterpreting Marginal Rate of Substitution
if MUx(x=6) = 10
MUy(y=20) = 5 Example
You tell me: A = {X = 6, Y = 20} gives you the same utility as
B = {X = 5, Y = 22}
What did you give up? MU (X = 6)
What did you get in return? Approximately 2 × MU (Y = 20)
“Exactly” 2 × MU (Y = 20) for really small decreases in X . . . Translation: At A = {X = 6, Y = 20} the last unit of X made you 2×
as happy as the last unit of Y
General Result
MRSx ,y at Gazzale (University of Toronto) ˆˆ
X, Y =
MUx
ˆˆ
at X , Y
MUy ECO100: Consumer Choice I 13 / 21 Indifference Curves Building Preference “Maps”
Repeating the thought experiment Start with bundle b = {X b , Y b } Again, I take “one unit” of X out of the bundle.
Marginal Rate of Substitution (MRSX ,Y ) at b: How many more
units of Y do I have to give you to exactly compensate you for this
oneunit X reduction? (∆2 )
New bundle c = {X b − 1, Y b + ∆2 } = {X c , Y c } Gazzale (University of Toronto) ECO100: Consumer Choice I 14 / 21 Indifference Curves Building Preference “Maps”
By construction U (a) = U (b) = U (c ) e I [x,y]
f Gazzale (University of Toronto) ECO100: Consumer Choice I 1. All points on I have same
Utility
2. Must slope down if x,y are
goods
3. Slope o...
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This note was uploaded on 06/10/2013 for the course AST 201 taught by Professor Abraham during the Fall '08 term at University of Toronto.
 Fall '08
 Abraham

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