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.+