macroeconomics+ two+period+consumer+model+:+ …jpd48/presentation10_savings_market.pdf ·...
TRANSCRIPT
Macroeconomics+Two+Period+Consumer+Model+:+
Savings+Market+ECON+321+
Extra+Credit+
• Rick+Grimes+has+income+of+y1=$10,000+today+but+is+expecKng+income+of+y2+=$110,000+in+the+future.+The+student+has+no+assets+and+you+can+ignore+money+in+this+problem.+Rick+can+also+borrow+and+lend+at+a+real+interest+rate+of+10%+and+he+has+the+following+uKlity+funcKon:+++ + + + + + +U(c1,c2)=lnc1++lnc2+++ + +s.t.+y1+=+c1++b+++ + + ++y2++(1+r)b+=+c2+
Extra+Credit+Quiz+
• Fill+this+in+with+arrows.+– Sub+Effect+of+an+increase+in+the+interest+rate.+
+r+ +c1_____+c2________ +Savings________+– Income+effect+of+an+increase+in+the+interest+rate.+
• Net+Borrower++r+ +c1_____+c2________ +Savings________+
• Net+Saver++r+ +c1_____+c2________ +Savings________+
– Overall+effect+of+an+increase+in+the+interest+rate.+• Net+Borrower+
+r+ +c1_____+c2________ +Savings________+• Net+Saver+
+r+ +c1_____+c2________ +Savings________+
Extra+Credit+Quiz+
• Fill+this+in+with+arrows.+– Sub+Effect+of+an+increase+in+the+interest+rate.+
+r+ +c1++ +c2++ +Savings++
– Income+effect+of+an+increase+in+the+interest+rate.+• Net+Borrower+
+r+ +c1++ +c2++ +Savings++• Net+Saver+
+r+ +c1++ +c2++ +Savings++
– Overall+effect+of+an+increase+in+the+interest+rate.+• Net+Borrower+
+r+ +c1++ ++c2+?" "Savings++
• Net+Saver++r+ +c1+? + +c2++ +Savings++?"
Household+
!s.t.!
!! !1st!!period:!
!! !2nd!period:!
!! !Life1me:!
€
Maxc1U = ln(c1) + βln(y 2 + (1+ r)(a + y1 − c1))
€
Maxc1,c2,b
U = ln(c1) + βln(c2)
€
a + y1 = c1+ b
€
c2 = y 2 + (1+ r)(a + y1 − c1)
€
y2 + (1+ r)b = c2
OpKmal+Choices+
€
c1* =1
1+ βy2
(1+ r)+ (a + y1)
#
$
% % %
&
'
( ( (
c 2 *(1+ r)
=β
1+ βy2
(1+ r)+ (a + y1)
#
$
% % %
&
'
( ( (
b* =β
1+ β(a + y1) − 1
1+ βy 21+ r*
+ ,
-
. /
Aggregate+Level:++No+Borrowing+&+No+Lending+
• At+the+aggregate+level+there+is+only+one+price+here:+(1+r).+
• All+Markets+Must+Clear:+Supply+=+Demand+1st+period+goods+market,+y1+++a+=+c1+2nd+period+goods+market,+y2+=+c2+3rd++savings+market,+b+=+0.+
+This+is+a+representaKve,+homogeneous+agent+model,+no+borrowing+or+lending.+
Savings+Market+Clearing+Interest+Rate+
+++++++++(1+r)+
S,I
++Borrowing (Investment)
Savings
+++++S*=I*
(1+r)*+
The+market+clearing+interest+rate+is+the+interest+rate+that+results+in+b+=+0.+
What+is+the+Market+Clearing+Rate+
FOC:+
€
Maxc1U = ln(c1) + βln(y 2 + (1+ r)(a + y1 − c1))
€
1c1−β(1+ r)c2
= 0
c2c1
= β(1+ r)€
1c1−
β(1+ r)y 2 + (1+ r)(a + y1 − c1)
= 0
What+is+the+Market+Clearing+Rate+
• Now,+AFTER"TAKING"FOC’S,+impose+the+market+clearing+condiKons,+y1+++a+=+c1,+y2+=+c2,+and+b+=+0.++
• We+don’t+internalize+mrkt.+clearing+condiKons.+
€
(1+ r) =c2βc1
(1+ r*) =y2
β(a + y1)
Savings+Market+Clearing+Interest+Rate+
+++++++++(1+r)+
S,I
++Borrowing (Investment)+
Savings
S*=I*
(1+r)*+
y1,+we+want+to+consume+and+save+more,+so+r*++
(1+r’)*+
Savings+Market+Clearing+Interest+Rate+
+++++++++(1+r)+
S,I
++Borrowing (Investment)
Savings
+++S*=I*
(1+r’)*+
y2,+we+want+to+consume+and+borrow+more,+so+r*+
(1+r)*+
Why+did+the+Savings+Rate+Fall?+Lets+look+at+Wealth+(a).+
The+stock+market+booming+and+housing+values+both+increased+dramaKcally+for+a+while,+which+increased+wealth,+(a),+and+reduced+the+desire+to+save.++Then+they+both+crashed.+a: +C1,+C2,+(Y1cc1)+
€
c1* =1
1+ βy2
(1+ r)+ (a + y1)
#
$
% % %
&
'
( ( (
c 2 *(1+ r)
=β
1+ βy2
(1+ r)+ (a + y1)
#
$
% % %
&
'
( ( (
b* =β
1+ β(a + y1) − 1
1+ βy 21+ r*
+ ,
-
. /
Stock+Market+
• Dow+Jones+Charts+• 1900cPresent+• 1960c1980+• 1980c2000+• 2000cPresent+
Savings+=+Investment+
• S+(NaKonal+Savings)+=+YcCcG++++++++++++++++++++++++++++++++++++++++++=+YcCcT+TcG+=+(YcCcT)+(TcG)++Y=C+I+G++I=YcC+G+TcT++I=+S+(NaKonal+Savings)+=+(YcCcT)+(TcG)++where+(YcCcT)+is+private+savings+and+(TcG)+is+public+savings+and+(YcT)+is+disposable+income.++++ + + + + + +TcG+>+0,+is+a+fiscal+surplus.++ + + + + + +TcG+<+0,+is+a+deficit.+
An+Increase+Current+Income+(Y1)+r+
S,I
++Investment Demand
Savings
+++S*=I*
r*+
Savings’
r*’+
S*’=I*’
An+increase+in+current+income+results+in+a+lower+interest+rate.+
Y1: c1,+c2,+(Y1cc1),+r +
An+Increase+Future+Income+(Y2)+r+
S,I
++Investment Demand
Savings’
+++S*=I*
++r’*+
Savings
r*+
S*’=I*’
An+increase+in+current+income+results+in+a+lower+interest+rate.+
Y2: c1,+c2,+(Y1cc1),+r +
Crowding"Out:++++++++++(G)+With+No+Change+in+(T)+
r+
S,I
++ID
S’
+++S*’=I*’
r*’+
S
r*+
S*=I*
G: (TcG),+r+,+I+ +
(T)+With+No+Change+in+(G) r+
S,I
Investment Demand
Savings Supply
+++S*=I*
r*+
No+Change+in+the+Graph.+The+consumer+knows+T+will+have+to+go+up+in+the+future.++They+want+to+save+and+spend+more+now+because+of+the+current+decrease+in+T,+but+because+future+T+will+increase+they+want+to+save+more+and+spend+less.+
Ricardian+Equivalence+ProposiKon+
• Ricardian Equivalence Proposition: Changes in the government budget caused by changes in taxes only, have no effect on the economy. – Hinges on a few things:
1. Assumes Lump sum taxes. 2. Consumers are well informed and forward looking.
Aggregate data shows consumers are pretty well informed.
3. Assumes no change in planned government expenditures.
Ricardian+Equivalence+ProposiKon+
SN=+(YcCc+T+)+(T+cG),+we+see+the+naKonal+savings+does+not+change.+
Government+Budget+Must+Hold+in+the+long+run:+
+ +++
€
G1+G2
1+ r= T1+ T 2
1+ rIf+you+cut+T1,+then+T2+must+go+up+and+we+save+the+money+to+pay+taxes+in+the+future.++This+will+fail+with+distorKonary+taxes,+notcforward+looking+consumers+or+if+there+are+credit+constraints.+
Credit+Constrained:+(y1cc1)>(ycc)+
C2+
C1+
Want+to+be+here,+but+can’t.+
Demand+=+Investment+
€
Y = AKαL1−α
π = PyAKαL1−α − wL − (r +δ)k
FOC : dπdk
= αPyAKα−1L1−α − (r +δ) = 0
++++++++++++MPK+ ++++++++++++MC+
€
k* =(r +δ)αPyAL1−α%
& ' (
) *
11−α
User+Cost+of+Capital+(UCC)+
MPK=UCC+
Two Components of the UCC: 1. r = opportunity cost of lost savings. i.e: Pk=$2000.00 ; r=10%; lose $200.00 in interest.
2. � = The depreciation rate at which the capital loses value. i.e: Pk=$2000.00 but after a year = $1500.00; then � = 25% UCC = $2000.00(.10+.25) = $700 ; Think of it as wages paid to the machine.
P*MPK+and+UCC+!!!Pk*MPK,!UCC!!!!+
!!!k*!!!!+
The+difference+is+the+Profit.+
!!!Pk*MPK+
Savings and Investment r+
S,I
Investment Demand
Savings Supply
+++S*=I*
r*+
The+negaKve+slope+is+due+to+the+UCC.++
Permanent+Versus+Temporary+Tax+Cuts+
€
c1* =1
1+ βy2
(1+ r)+ (a + y1)
#
$
% % %
&
'
( ( (
c 2 *(1+ r)
=β
1+ βy2
(1+ r)+ (a + y1)
#
$
% % %
&
'
( ( (
b* =β
1+ β(a + y1) − 1
1+ βy 21+ r*
+ ,
-
. /
Temporary+Tax+Cut:+++ + + +Y1: $c1,+c2,+(Y1cc1)%Permanent+Tax+Cut:+++ ++++Y1&Y2: c1,+c2,+(Y1cc1)++?"
Temporary"cuts"have"a"bigger"impact"on"savings"while"permanent"tax"cuts"have"a"bigger"impact"on"consumpFon."
Open+Economy+
€
Y = C + I +G + NXSN =Y −C −GI =Y −C −G − NXI = SN − NX
Savings and Investment r+
S,I
I
+S
+++S*=I*
+rA+
+rw+
+rw+
++++NX+>+0:+Trade+Surplus+
++++NX+<+0:+Trade+Deficit+
rA+is+the+Autarky+interest+rate,+or+the+interest+rate+if+the+economy+were+closed.+
Trade+Surplus/Deficit+
• When+S > I, there is a trade surplus and our extra savings are in banks all over the world.
• When+S < I, there is a trade deficit and there is borrowing to fund investment.
• Current Account : is the flow of goods and services. (Exports, Imports, Net Income from abroad, and Unilateral Transfers.)
• Capital Account : is the flow of assets.
Trade+Surplus/Deficit+
• Net Capital Outflows (NCO): is the change in domestic ownership of foreign assets minus the net change in foreign ownership of domestic assets.
NX (close to current account)=NCO This is an accounting identity,
i.e. Debits = Credits
NX=NCO++(assume+$1.00+=+1+euro)+
1. We+sell+$100+in+cheesesteaks+to+Italy+and+are+paid+in+dollars+:+
Nx"="+$100.00" "NCO"="+$100.00""
NCO:"they"reduce"their"ownership"of"our"dollars"(assets)."
2.+We+sell+$100+in+cheesesteaks+to+Italy+and+they+sell+100+euro+worth+of+wine+to+us+:+
Nx"="0 " "NCO"="0"
NX=NCO+
3.+We+sell+$100+in+cheesesteaks+to+Italy+and+are+paid+in+euro+we+put+in+an+Italian+Bank.+
Nx"="+$100.00" "NCO"="+100.00"euro"
NCO:"We"increase"our"ownership"of"euro"(assets)."
4.+We+sell+$100+in+cheesesteaks+and+are+paid+in+Euro+that+we+trade+back+to+the+Italian+Bank+for+$100.00:+
Nx"="+$100.00" "NCO"="+$100.00"
Two+Types+of+Open+Economies+
• Small+Open+Economy+(SOE)+– A+change+in+domesKc+interest+rates+have+no+effect+on+world+interest+rates.+
• Large+Open+Economy+(LOE)+– A+change+in+domesKc+interests+rate+have+an+effect+on+world+interest+rates.+
Large+Open+Economies+(Two+Country+World):+can+effect+world+interest+rate+
• In+U.S.+++
U.S.+ China+ World+
I+
S+
I+ I+
rw*+
S+
S+
Small+Open+Economy:+can’t+effect+world+interest+rate+
• In+U.S.+++
Jersey+ Rest+of+the+World+
World+
I+
S+
I+ I+
rw*+
S+
S+
The+Graph’s+can’t+actually+capture+this.+The+gaps+are+different,+but+to+small+to+noKce.+