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Unformatted text preview: Econ 121.
Intermediate Microeconomics. Eduardo Faingold
Yale University Lecture 6 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)
Endowment income effect
Intertemporal choice III. Competitive markets
IV. Market failure Slutsky equation
Recall that x1 .p1; p2; m/ designates the demand for good 1 under prices
p1, p2 and income m. Deﬁne the compensated demand for good 1 given prices p1, p2 and a
bundle x as follows:
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 .
0
This means that when the price of good 1 changes from p1 to p1, the
consumer’s income is adjusted by
0
m D .p1 p1/x1 : Slutsky equation
Fix p and m and write x D x .p1; p2; m/. By the revealed preference
argument we saw in the previous lecture,
0
p1 > p1 Thus, H) 0
s
x1 .p1; p2; x /
0
p1 and therefore, 0
s
x1 .p1; p2; x / s
x1 .p1; p2; x / < 0: s
x1 .p1; p2; x /
0
< 0 for all p1 ¤ p1;
p1
s
@x1
.p1; p2; x / < 0:
@p1 That is, the substitution effect is always negative. Slutsky equation
s
Let us calculate @x1 =@p1 using the deﬁnition
s
x1 .p1; p2; x / D x1 .p1; p2; p1x1 C p2x2 /: By the chain rule of calculus,
s
@x1
@x1
@x1
.p1; p2; x / D
.p1; p2; p1x1 C p2x2 / C
.p1; p2; p1x1 C p2x2 / x1 :
@p1
@p1
@m Omitting the arguments and rearranging yields
s
@x1
@x1
D
@p1
@p1
@x1
x;
@m 1 that is,
Total effect D Subst. effect Income effect: So far....
... we have assumed that ppl have some exogenous amount of
money—their income m—to exchange for goods.
In reality, ppl sell things they own (e.g. labor hrs) to acquire goods. Want
to model this idea. Net and gross demands
endowment: .!1; !2/  what you have before you enter the market
gross demands: .x1 ; x2/  what you end up consuming
net demands: .x1
sell (if negative) !1; x2 !2/  what you actually buy (if positive) or Budget Constraint
value of what you consume = value of what you have
p1x1 C p2x2 D p1!1 C p2!2
See picture. Endowment belongs to the budget line.
with 2 goods, always net demander on one good and net supplier of the
other Comparative Statics
Changing the endowment
– normal vs inferior
– consumer always better off when value of endowment increases.
Different from increasing value of consumption bundle. Changing prices
– if price of a good consumer is selling goes down and consumer
remains seller, welfare goes down. See ﬁgure.
– if consumer is a net buyer and price goes down, consumer will remain
a net buyer. See ﬁgure. Slutsky Equation
when prices change, we now have 3 effects
– ordinary substitution effect
– ordinary income effect
– endowment income effect  change in the value of endowment affects
demand
– Slutsky equation
s
@x1
N
@x1
.p1; p2; !/ D
.p1; p2; x/ C .!1
N
@p1
@p1
@x1
x1/
N
.p1; p2; p1!1 C p2!2/
@m – Proof: follows from the regular Slutsky eq. and the deﬁnition
x1.p; !/ D x1 .p; p1!1 C p2!2/:
N Labor supply
consumption C
labor L
money M Budget constraint for labor supply
pC D M C wL
N
pC C w.L N
N
L/ D p C C w L N
leisure = R D L L N
N
pC C wR D p C C w L
just like ordinary budget constraint
supply of labor like demand of leisure
w=p is price of leisure (opportunity cost) Comparative statics
Slutsky:
@R
N
D SE C .R
@w @R
R/
@m Leisure is normal good. Yet, ambiguous sign.
Backward bending supply New topic: intertemporal choice
.m1; m2/ money in each time period is endowment
allow the consumer to borrow and lend at rate r
c2 D m2 C .1 C r/.m1 c1/ note that this works for both borrowing and lending, as long as it is at the
same interest rate if borrowing and lending interest rates are different, then budget line has
a kink. See picture. Budget Constraint
.m1; m2/ money in each time period is endowment
allow the consumer to borrow and lend at rate r
c2 D m2 C .1 C r/.m1 c1/ note that this works for both borrowing and lending, as long as it is at the
same interest rate Various forms of the budget constraint
.1 C r/c1 C c2 D .1 C r/m1 C m2  future value
c1 C 1c2r D m1 C 1m2r  present value
C
C
choice of numeraire
See picture
preferences  monotonocity and convexity are very natural Comparative Statics
If consumer is initially a lender and interest rate increases, he remains a
lender, by revealed preference. See ﬁgure. A borrower is made worse off by an increase in interest rate, by revealed
preference. See ﬁgure. Slutsky allows us to look at the effect of increasing the price of today’s
consumption (increasing the interest rate)
– change in consumption today when interest rate increases equals SE C .m1 c1/ IE – assuming normality, an increase in interest rate lowers current
consumption for a borrower, and has an ambiguous effect for a lender Intuition? Inﬂation
Previous analysis implicitly assumed price of “consumption good”
remains unchanged in period 2. What if there is inﬂation? put in prices p1 D 1 and p2
budget constraint takes the form
p2c2 D m2 C .1 C r/.m1
or c2 D m2 1 C r
C
.m1
p2
p2 if is rate of inﬂation, then p2 D .1 C /p1
1C D
D 1 Cr
1 C 1 Cr
1 C is the real interest rate 1r c1/; c1/ Closer look at present value
Recall intertemporal budget constraint:
c2
m2
c1 C
D m1 C
1Cr
1Cr
Righthand side expresses the present value of endowment
Recall that if the value of the endowment increases, consumer is better
off. Hence, provided the consumer can borrow and lend freely at a constant
interest rate, consumer always prefers a pattern of income with a higher
present value to a pattern with lower present value. Present value works for any number of periods
c2
m2
c3
m3
c1 C
D m1 C
C
C
1 C r .1 C r/2
1 C r .1 C r/2 also works for timevarying interest rates
c1 C c2
c3
m2
m3
C
D m1 C
C
1 C r1 .1 C r1/.1 C r2/
1 C r .1 C r1/.1 C r2/ ...
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This note was uploaded on 03/01/2012 for the course ECON 121 taught by Professor Samuelson during the Spring '09 term at Yale.
 Spring '09
 SAMUELSON
 Microeconomics

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