Unformatted text preview: f indiff curve @[x,y] =
M RS(i.e: tangent/[x,y] at point
[x,y] => MUx/MUy
4. Convex Shape due to
diminishing marginial utility
5.e > lots of y and little x
6. f > lots of x and little y 15 / 21 Indifference Curves Indifference Curve “Results”
Indifference Curve: All {X , Y } combinations giving same utility level
Northeast Rule
any point on i1 better than any point on i2
indiff curve for every [x,y] combination
cannot bend backwards
connot cross Gazzale (University of Toronto) ECO100: Consumer Choice I i1
i2 16 / 21 Indifference Curves Marginal Rate of Substitution: Summary
Deﬁnition MRSX ,Y
Given {X , Y , . . . , Z }, how many units of Y must you give me to
exactly compensate me for taking away one unit of X ?
We Can Show
MRSX ,Y X , Y , . . . , Z = MUX
MUY 2Good Case
With x on the horizontal and y on the vertical, the slope of the
MUx
indifference curve at {x , y } equals MRSx ,y (x , y ) = MUy
Interpretation: Trades I am willing to make
I am willing to give up MRS  units of Y in order to get 1
more unit of X .
Example Gazzale (University of Toronto) ECO100: Consumer Choice I 17 / 21 $1Bill MRS
steep io $1 bills vs. $5
bills EX. Left and Right
shoes
Computer and
keyboard MRS small/ ie
ﬂat ' Standard' indifference curve
general willingness to substitute
diminishing MRS io $5 Bill
Perfect Substitues Constant
M RS io Perfect complements
inability to substitute
M RS undeﬁned at kink The Budget Constraint Now: What can I buy?
A Consumer’s TwoGood Budget Constraint Goods X and Y with prices PX and PY
Assume consumer spends all income, denoted I
Consumption choice must satisfy PX X + PY Y = I
More generally, saving/borrow as good “Z ” Gazzale (University of Toronto) ECO100: Consumer Choice I 18 / 21 The Budget Constraint TwoGood Budget Line (Constraint), Graphically
I = 90, Px = 3; Py = 9 income Quantity Y Intercept!:
buy only Y>90/9 = 10
buy only X>90/3 = 30
Slope of budget
line
abs(rise/run)=
(income/py)/
(income/px)
=px/py 25 UNAFFORDABLE 20 15 10 Budget line
Spend all of
your income 5 AFFORDABLE
5 Gazzale (University of Toronto) 10 15 20 ECO100: Consumer Choice I 25 30 Quantity X 19 / 21 The Budget Constraint Budget Line, Interpreted
P
Slope of the budget constraint (budget line): − PX
Y Interpretation I: Trades I can make with the market
I must give up slope units of Y (the vertical one) in order to get 1
more unit of X (the horizontal one).
Our example: I must give up 1 units of Y (the $9 one) in order to
3
get 1 more unit X (the $3 one)
Alternatively: I must give up
more unit of Y . 1
slope = 3 units of X in order to get 1 Interpretation II: X ’s Opportunity Cost (in terms of Y ) Gazzale (University of Toronto) ECO100: Consumer Choice I 20 / 21 Optimal Choice Optimal Choice
1. Northeast Rule
A > Optimum
Slope Budget line = MRS
px/py = MUx/MUy
MUx/px = MUy/py(i.e Last
Dollar Rule)
B cannot be optimum
At B
MRS = 3/2 != slope of BL
= 1/3
MUx/MUy!=Px/Py => MUx/
Px > MUy/Py(need to spend
m ore on x) Gazzale (University of Toronto) ECO100: Consumer Choice I 21 / 21...
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 Fall '08
 Abraham
 Utility

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