Unformatted text preview: Econ 121.
Intermediate Microeconomics. Eduardo Faingold
Yale University Lecture 5 Outline of the course
I. Introduction
II. Individual choice
III. Competitive markets
IV. Market failure Outline of the course
I. Introduction
II. Individual choice
Budget constraint (Ch. 2)
Preferences (Ch. 3)
Utility (Ch. 4)
Consumer problem (Ch. 5)
Revealed Preference (Ch. 7)
Slutsky Equation (Ch. 8) III. Competitive markets
IV. Market failure Slutsky Equation
We want a way to decompose the effect of a price change into “simpler”
pieces Break up price change into a rotation and a shift
These are hypothetical changes
We can examine each change in isolation and look at the sum of two
changes Substitution Effect
Change in demand due to rotation is the substitution effect
This measures how demand changes when we change prices, keeping
the original optimal bundle affordable this isolates the pure effect of change in relative prices
substitution effect must be negative, by revealed preference
the other effect is called income effect
the total effect is the sum of these two effects Income Effect
Change in demand due to shift is the income effect
Increase income, keep prices ﬁxed
Income effect can increase or decrease demand depending on whether
we have a normal or inferior good
Let x1 .p1; p2; m/ be the optimal consumption of good 1 at prices
.p1; p2/ and income m
Normal good: @x1 [email protected] > 0; Inferior good: @x1 [email protected] < 0. Total Effect
Total change in demand is substitution effect plus the income effect
if good is a normal good, the substitution effect and the income effect
reinforce each other if good is an inferior good, the substitution effect and the income effect
go in opposite directions; total effect is ambiguous when total effect is positive, good is called a Giffen good x2 EFFECT OF A PRICE
INCREASE
Initial budget line
Final budget line x1 x2 EFFECT OF A PRICE
INCREASE
Initial
Final x1 x2 EFFECT OF A PRICE
INCREASE
Initial
Final x1 x2 EFFECT OF A PRICE
INCREASE
Initial
Final
Incomeadjusted
(hypothetical) x1 x2
WHERE MUST BE LOCATED? Initial
Final
Incomeadjusted
(hypothetical) x1 x2
WHERE MUST BE LOCATED? Initial
Final
Incomeadjusted
(hypothetical) IS THIS COMPATIBLE
WITH REVEALED
PREFERENCE? x1 x2
WHERE MUST BE LOCATED? Initial
Final
Incomeadjusted
(hypothetical) IS THIS COMPATIBLE
WITH REVEALED
PREFERENCE? NO!!! x1 x2
WHERE MUST BE LOCATED? Initial
Final
Incomeadjusted SOMEWHERE OVER
HERE (hypothetical) x1 x2 INFERIOR GOOD:
IE < 0
TWO POSSIBLE CASES
Initial
Final
Incomeadjusted NORMAL GOOD:
IE > 0 (hypothetical) x1 x2 CONSIDER INDIFFERENCE
CURVES NOW
INCOMPATIBLE
WITH R.P. Initial
Final OK Incomeadjusted
(hypothetical) x1 x2 EFFECT OF A PRICE INCREASE
(NORMAL GOOD)
Initial
Final
Incomeadjusted
(hypothetical) I.E. S.E. x1 x2 EFFECT OF A PRICE INCREASE
(INFERIOR GOOD)
Initial
Final
Incomeadjusted
(hypothetical) I.E.
S.E. x1 Law of Demand
For a normal good, a price increase always results in a decreased demand.
That is, normal goods have a downward sloping demand. Examples
perfect complements: no substitution effect
perfect substitutes: no income effect
quasilinear: no income effect Rates of change
can also express Slutsky effect in terms of rates of change
takes the form:
s
@x1
@x1
@x1
.p1; p2; m/ D
.p1; p2; x1 .p1; p2; m//
.p1; p2; m/x1 .p1; p2; m/
@p1
@p1
@m where the function x s .p1; p2; x/ is such that for each vector of prices
.p1; p2/ and each bundle x ,
s
x1 .p1; p2; x/ D x1 .p1; p2; p1x1 C p2x2/;
s
i.e. x1 .p1; p2; x/ is the optimal consumption bundle given the budget line
that has slope p1=p2 and passes through bundle x . can interpret each part as before x2 SLUTSKY EQUATION:
NORMAL GOOD
Initial Price increase Final x1 x2 SLUTSKY EQUATION:
NORMAL GOOD
Initial
Final x1 x2 SLUTSKY EQUATION:
NORMAL GOOD
Initial
Final
Incomeadjusted
(hypothetical) x1 SLUTSKY EQUATION: x2 NORMAL GOOD
Initial
Final
Incomeadjusted
(hypothetical) x1
S.E
. I.E. ...
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 Spring '09
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 Microeconomics, X1, Slutsky, Eduardo Faingold

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